黒田 雅治

Toward the application to the tapping mode AFM (Atomic Force Microscope), we propose a new control method to keep the state of a soft impact between an object surface and the tip of a cantilever whose supporting point is periodically and laterally excited. In the practical usage of AFM, the surface of the object is scanned by the excited cantilever. Depending on the profile of the surface, the distance between the surface and the center of the excitation is varied and then, the state of the contact is changed. To keep the state of contact, the center of the excitation is automatically shifted in AFM. As a result, we can know the profile of the object from the shift of the center while scanning. By the way, it is known that various bifurcations of the responses of the beam occur according to impact conditions and variation of the excitation frequency. In our previous study, we indicated theoretically and experimentally that when the excitation frequency N is set to 2.5 times the first natural frequency ω_1 of the cantilever, i.e., N=2.5aω_1, the contact produces the frequency component of the 1.25 time the first natural frequency in the cantilever response, i.e., 1.25ω_1. In this paper, by using this phenomenon, we propose a control method to shift the center of the excitation according to the profile of the object surface, keeping soft contact. For this purpose, a real-time signal processing method is suggested to determine the magnitude of the targetted frequency component. Also, a servo system is designed to periodically excite and to control the center of the excitation precisely. Finally, validity of the proposed control method is experimentally confirmed by using a macro-beam.

Toward the application to the tapping mode AFM (Atomic Force Microscope), we propose a new control method to keep the state of a soft impact between an object surface and the tip of a cantilever whose supporting point is periodically and laterally excited. In the practical usage of AFM, the surface of the object is scanned by the excited cantilever. Depending on the profile of the surface, the distance between the surface and the center of the excitation is varied and then, the state of the contact is changed. To keep the state of contact, the center of the excitation is automatically shifted in AFM. As a result, we can know the profile of the object from the shift of the center while scanning. By the way, it is known that various bifurcations of the responses of the beam occur according to impact conditions and variation of the excitation frequency. In our previous study, we indicated theoretically and experimentally that when the excitation frequency N is set to 2.5 times the first natural frequency ω₁ of the cantilever, i.e., N=2.5ω₁, the contact produces the frequency component of the 1.25 time the first natural frequency in the cantilever response, i.e., 1.25ω₁. In this paper, by using this phenomenon, we propose a control method to shift the center of the excitation according to the profile of the object surface, keeping soft contact. For this purpose, a real-time signal processing method is suggested to determine the magnitude of the targetted frequency component. Also, a servo system is designed to periodically excite and to control the center of the excitation precisely. Finally, validity of the proposed control method is experimentally confirmed by using a macro-beam.

In recent years, applications of fractional calculus have flourished in various science and engineering fields. Particularly in engineering, control engineering appears to be expanding aggressively in their applications. Exemplary are the CRONE controller and the PIλDμ controller, which is categorizable into applications of fractional calculus in classical control theory. A state equation can be called as the foundation of modern control theory. However, the relationship between fractional derivatives and the state equation has not been examined sufficiently. Consequently, a systematic procedure referred to every researcher on the fractional-calculus side or control-theory side has not yet been established For this study, therefore, involvement of fractional-order derivatives into a state equation is demonstrated here for ready comprehension by researchers. First, the procedures are explained generally; then the technique to incorporate a fractional-order state vector into a conventional state equation is given as an example of the applications. The state-space representation in this study is useful not only to model a controlled system with fractional dynamics but also for design and implementation of a controller to control fractional-order states. After introducing the basic parts, the benefits of modern control theory including robust control theories, such as H∞ and μ-analysis and synthesis in their integrities, can be applied to this fractional-order state equation. Copyright © 2008 by ASME.

Recently, considerable attention of material scientists and mechanical engineers has been devoted to measurement based on atomic force microscopy (AFM). Self-excitation is known to be an effective excitation method for AFM probe to measure the surface of a biological molecule in liquid. For practical use of a probe in liquid, we must realize a self-sensing and self-actuating AFM probe using PZT instead of using a conventional optical lever method. However, frequency characteristics of the PZT are very complex in applications for probe behavior measurement. For detecting sensor characteristics, the dynamics of the cantilever to which the PZT is attached are extracted from the PZT sensor output signal. To this end, we examine the frequency response of the PZT output signal in the case where the cantilever is excited with constant response amplitude using a PZT actuator. Then, we establish a method to process the signal so that the frequency characteristic of the PZT sensor has no high gain for the frequency range other than the first natural frequency. Finally, we conduct experiments to verify that the resultant signal is suitable to generate van der Pol-type self-excited oscillation.

Usage of self-excitation as an excitation method for a cantilever probe in atomic force microscopy (AFM) has been proposed to improve the low quality factor Q in liquid environments. To realize non-contact mode AFM, it is necessary to reduce the amplitude of the self-excited cantilever probe. For this study, the self-excited oscillation of the cantilever probe is generated by the angular velocity feedback. In addition, the small steady state amplitude is achieved using nonlinear feedback proportional to the squared deflection angle and the angular velocity. Regarding the microcantilever probe as a microcantilever beam, we present the equation of motion, which incorporates the geometrical nonlinear effect. The averaged equation is derived by applying the method of multiple scales and the bifurcation diagram is described theoretically. Results clarify that increasing the nonlinear feedback gain can reduce the cantilever-probe amplitude. Using an AFM that we produced, we demonstrate the nonlinear dynamics of a "van der Pol" type of self-excited cantilever. The steady state amplitude of the self-excited oscillation was 8 nm.

In this effort, a new control method to keep the state of the arbitrary impact between the tip of the excited cantilever and the object surface is proposed. It is known that various bifurcations of the responses of the beam occur according to impact conditions and variation of the excitation frequency. We propose a control method to keep the magnitude of a specific frequency component constant and the state of particular impact independent of changes in the distance between the cantilever and the contact surface. For this purpose, a real-time signal processing method is suggested to determine the magnitude of the frequency component at half the excitation frequency. A servo system is designed to control the center of the excitation precisely for the above purpose. Finally, validity of the proposed control method is confirmed by experiments. Copyright © 2007 by ASME.

In recent years, applications of fractional calculus have flourished in various science and engineering fields. Particularly in engineering, control engineering appears to be expanding aggressively in its applications. Exemplary are the CRONE controller and the PIλDμ controller, which is categorizable into applications of fractional calculus in classical control theory. A state equation can be called the foundation of modern control theory. However, the relationship between fractional derivatives and the state equation has not been examined sufficiently. Consequently, a systematic procedure referred to by every researcher on the fractional-calculus side or control-theory side has not yet been established. For this study, therefore, involvement of fractional-order derivatives into a state equation is demonstrated here for ready comprehension by researchers. First, the procedures are explained generally; then the technique to incorporate the fractional-order state-vector into a conventional state equation is given as an example of the applications. The state-space representation in this study is useful not only for modeling a controlled system with fractional dynamics, but also for design and implementation of a controller to control fractional-order states. After we complete installation of the basic parts, we can apply the benefits of modern control theory, including robust control theories such as H-infinity and μ-analysis and synthesis in their integrities, to this fractional-order state-equation. Copyright © 2007 by ASME.

Recently, considerable attention of material scientists and mechanical engineers has been devoted to measurement based on atomic force microscopy. Self-excitation is known as an effective excitation method for AFM probe to measure the surface of a biological molecule in liquid. For practical use of a probe in liquid, we must realize a self-sensing and self-actuating AFM probe using PZT instead of using a conventional optical lever method. However, frequency characteristics of the PZT are very complex in applications for measurement of probe behavior. For detecting sensor characteristics, the dynamics of the cantilever to which the PZT is attached are extracted from the PZT sensor output signal. To this end, we examine the frequency response of the PZT output signal in the case where the cantilever is excited with constant response amplitude by a PZT actuator. Then, we construct a method to process the signal so that the PZT sensor frequency characteristic has no high gain for the frequency range other than the first natural frequency. Finally, we conduct experiments to verify that the resultant signal is suitable to produce of van der Pol type self-excited oscillation.

Recently, considerable attention of material scientists and mechanical engineers has been devoted to measurement based on atomic force microscopy. Self-excitation is known as an effective excitation method for AFM probe to measure the surface of a biological molecule in liquid. For practical use of a probe in liquid, we must realize a self-sensing and self-actuating AFM probe using PZT instead of using a conventional optical lever method. However, frequency characteristics of the PZT are very complex in applications for measurement of probe behavior. For detecting sensor characteristics, the dynamics of the cantilever to which the PZT is attached are extracted from the PZT sensor output signal. To this end, we examine the frequency response of the PZT output signal in the case where the cantilever is excited with constant response amplitude by a PZT actuator. Then, we construct a method to process the signal so that the PZT sensor frequency characteristic has no high gain for the frequency range other than the first natural frequency. Finally, we conduct experiments to verify that the resultant signal is suitable to produce of van der Poi type self-excited oscillation.

Usage of self-excitation as an excitation method for cantilever-probe in atomic force microscopy (AFM) has been proposed in order to improve the low quality factor Q in liquid environments. For realization of non-contact mode AFM, it is necessary to reduce the amplitude of the self-excited cantilever-probe. In this study, the self-excited oscillation of the cantilever-probe is generated by the angular velocity feedback. In addition, the small steady state amplitude is achieved by nonlinear feedback proportional to the squared deflection angle and the angular velocity. Regarding the micro cantilever-probe as a micro cantilever beam, we show the equation of motion in which the geometrical nonlinear effect is taken into account. Averaged equation is derived by applying the method of multiple scales and the bifurcation diagram is theoretically described. Then, it is clarified that the amplitude of the cantilever-probe can be reduced by increasing the nonlinear feedback gain. By using our own making AFM, we demonstrate the nonlinear dynamics of a "van der Pol" type self-excited cantilever. Steady state amplitude of self-excited oscillation is reduced to 8 nm.

Usage of self-excitation as an excitation method for cantilever-probe in atomic force microscopy (AFM) has been proposed in order to improve the low quality factor Q in liquid environments. For realization of non-contact mode AFM, it is necessary to reduce the amplitude of the self-excited cantilever-probe. In this study, the self-excited oscillation of the cantilever-probe is generated by the angular velocity feedback. In addition, the small steady state amplitude is achieved by nonlinear feedback proportional to the squared deflection angle and the angular velocity. Regarding the micro cantilever-probe as a micro cantilever beam, we show the equation of motion in which the geometrical nonlinear effect is taken into account. Averaged equation is derived by applying the method of multiple scales and the bifurcation diagram is theoretically described. Then, it is clarified that the amplitude of the cantilever-probe can be reduced by increasing the nonlinear feedback gain. By using our own making AFM, we demonstrate the nonlinear dynamics of a “van der Pol” type self-excited cantilever. Steady state amplitude of self-excited oscillation is reduced to 8 nm.

Transition from local complexity to global spatio-temporal dynamics in a two-dimensional array of fluid-elastic oscillators is examined experimentally with an apparatus comprising 90-1000 cantilevered rods in a wind tunnel as the Reynolds number (based on rod diameter) is increased from 200 to 900. A cluster-pattern entropy measure is introduced as a quantitative measure of local complexity. As the intensity of interaction among neighboring elements (in this case, frequency of collisions among rods) increases, a set of the elements (in this case, a rod-array) achieves globally better-organized behavior. On the basis of accelerometer data, the rod impact rate versus flow velocity shows a power-law scaling relation. Video images reveal that, initially, each rod moves individually; then clusters consisting of several rods emerge. Finally, global wave-like motion occurs at higher flow velocities. Each wave-like motion has its specific frequency and spatial wavelength, which vary according to wind velocity. © 2007 Wiley Periodicals, Inc.

Recently, active wave control theory has attracted great interest as a novel method for vibration control of large space structure (LSS). The method can be applied to suppress vibration in large flexible structures that have high modal density, even for relatively low frequencies. In this report, we formulate a feedback-type active wave control law, described as a transfer function including a Laplace transform with an s1/2 or s 3/2 term. As an example, we present the fractional-order derivatives and integrals of structural responses in the vibration suppression of a thin, light cantilevered beam. © 2007 Springer.

近年,原子間力顕微鏡(AFM)による液中での生体観察が期待されている.本研究では液中でも高感度でかつ試料を傷つけないためのAFMカンチレバの低振幅な定常振動をファンデルポール型自励発振法を用いて実現する.また圧電膜によりマイクロカンチレバの加振とたわみの検知の両方を行なう手法について検討する.この手法はレーザによるカンチレバの変位の計測を必要とせず,液中観察に有利といえる.さらに光点をカンチレバ先端に合わせる作業を必要としないことから操作も簡略化でき,また従来のものより装置の小型化が期待される.

In this study, we investigate the dynamics of a self-excited cantilever beam by a positive feedback proportional to the velocity. In particular, we focus on the response amplitude in the self-excited oscillation and analyze the effect of the nonlinear component of the restoring force in the cantilever. It is theoretically and experimentally clarified that the response amplitude grows with time under the positive feedback proportional to the velocity (positive feedback). Furthermore, van der Pol type self-excited cantilever beam is designed by applying the nonlinear feedback proportional to the squared deflection and the velocity, and the steady state response is realized in the cantilever beam. The theoretically predicted effects of the nonlinear feedback are qualitatively confirmed by performing some experiments. Copyright © 2005 by ASME.

一様直交流中に片持ち倒立の弾性ロッドを格子上に配列する実験において,観測された複雑な現象とその背後に隠された動的構造について実験ビデオを交えて紹介する.特に,(1)風速の閾値データ,(2)スケーリング関係,(3)大域的パターンの創発,(4)1000本ロッド配列の辺上に沿って測定された波動について議論する.総じて,風洞内に弾性ロッド群からなる格子配列を設置するという,機械系としては極めてシンプルな実験であったが,多種多様で複雑な現象を観測することができた.また,その一見複雑な現象の裏に隠された美しい動的構造をつまびらかにすることもできた.

A new gas-liquid two-phase flow simulation method has been developed based on the extended two-fluid model, which has capabilities of both the two-fluid and the interface-tracking models. The VOF (Volume of Fluid) technique has been introduced for suitable interface calculations. Interfaces of free surface and large bubbles are calculated directly by solving transport of a steep void fraction gradient corresponding to interface, while averaged behavior of microscopic dispersed bubbles and droplets are calculated in the two-fluid model scheme. It is expected that the present method can treat effects of significant kinetic interaction between the phases directly without empirical correlations. The calculated propagation of wet front in a dam break problem is close to experimental data. The predicted flow patterns of complex gas-liquid two-phase flow in a flat tube are quite similar to observations with a video camera. The present simulation will be a useful tool for predictions of integral behavior of thermal-hydraulic phenomena in large-scale nuclear power plants. © 2003 Taylor & Francis Group, LLC.

Transition from local complexity to global spatio-temporal dynamics in a two dimensional array of fluid-elastic oscillators is examined experimentally with an apparatus comprising 90-1000 cantilevered rods in a wind tunnel. Wave-like behavior is observed which may be related to soliton solutions in nonlinear arrays of nonlinear oscillators. The 90 to 1000 steel and polycarbonate rods have gap ratios ranging from 1.0 to 2.5. As the Reynolds number (based on rod diameter) increases from 200 to 900, a pattern with characteristics of spatio-temporal chaos emerges in global behavior of the elastic-rod array. There are local and global patterns. Local patterns comprise transient rest, linear motion, and elliptical motion. In 90-rod experiments, a cluster-pattern entropy measure based on these three patterns is introduced as a quantitative measure of local complexity. No significant dynamics appear below a threshold wind velocity. Video images reveal that, at first, each rod moves individually; then clusters consisting of several rods emerge. Finally, global wave-like motion occurs at higher flow velocities. Spatial patterns in rod-density distribution appear as more rods impact with their nearest neighbors. Furthermore, these collective nonlinear motions of rods are observed and categorized into several global modes. Using accelerometer data, the rod impact rate versus flow velocity shows a power-law scaling relation. This phenomenon may have application to plant-wind dynamics and damage as well as heat exchangers in energy systems. This experiment may also be a two dimensional analog of impact dynamics of granular materials in a flow. Copyright © 2002 by ASME.

Transition from local complexity to global spatio-temporal dynamics in a two dimensional array of fluid-elastic oscillators is examined experimentally with an apparatus comprising 901000 cantilevered rods in a wind tunnel. Wave-like behavior is observed which may be related to soliton solutions in nonlinear arrays of nonlinear oscillators. The 90 to 1000 steel and polycarbonate rods have gap ratios ranging from 1.0 to 2.5. As the Reynolds number (based on rod diameter) increases from 200 to 900, a pattern with characteristics of spatio-temporal chaos emerges in global behavior of the elastic-rod array. There are local and global patterns. Local patterns comprise transient rest, linear motion, and elliptical motion. In 90-rod experiments, a cluster-pattern entropy measure based on these three patterns is introduced as a quantitative measure of local complexity. No significant dynamics appear below a threshold wind velocity. Video images reveal that, at first, each rod moves individually; then clusters consisting of several rods emerge. Finally, global wave-like motion occurs at higher flow velocities. Spatial patterns in rod-density distribution appear as more rods impact with their nearest neighbors. Furthermore, these collective nonlinear motions of rods are observed and categorized into several global modes. Using accelerometer data, the rod impact rate versus flow velocity shows a power-law scaling relation. This phenomenon may have application to plant-wind dynamics and damage as well as heat exchangers in energy systems. This experiment may also be a two dimensional analog of impact dynamics of granular materials in a flow.

New experiments on the dynamics of 300 elastic oscillators in a steady cross flow are described. Impact constraints between the rods mimic Toda-type exponential potentials. Unlike single row dynamics, which lead to limit cycle behavior, multi-row arrays seem to exhibit chaotic though not necessarily, low-dimensional dynamics, at a critical flow value. With increasing flow velocity, organized wave-like structures appear to develop as the impact rate between rods increases. Experimental models of this type may serve to help understand complex dynamics in large array heat exchange systems. It may also be a model to understand wind crop dynamics and damage. © 2001 Elsevier Science B.V. All rights reserved.

This paper deals with the modal control of a planar structure using distributed-parameter sensors designed with a view to extracting a particular vibration mode. First, this paper overviews the modal control based upon distributed-parameter sensors and actuators. It is found that the utilization of either distributed-parameter sensors or distributed-parameter actuators leads to the elimination of spillover destabilization of a feedback control system. In addition, the distributed-parameter sensors have the advantage of achieving the modal control of a targeted mode of the structure; however, a mere usage of the distributed-parameter actuators results in uncontrollability of the targeted mode. Finally, with one-dimensional PVDF film sensors attached to the planar structure, an experiment is conducted, demonstrating the capability of the distributed-parameter sensors for suppressing the mode of interest without causing any effect on the remaining modes of the structure.

This paper considers the modal filtering of a planar structure using point sensors designed for extracting a particular modal amplitude of the structure. It is purpose of this paper to establish the design procedure of a modal filtering based upon point sensors. Much as a distributed modal sensor outstrips a point sensor in the sensing potential, the handling and maintenance are odious. To cope with this problem, this paper presents a design methodology of modal filtering using point sensors easy to handle and maintain it. It is found that modal filtering design of point sensors can be achieved by simply following the design procedure of distributed modal sensors already presented by the authors. It is also found that point sensors perfectly replace the distributed sensors for modal filtering in the frequency range of interest. Experiment is conducted, demonstrating the validity of the point sensor-based modal filtering.

This paper considers the active power flow control of a distributed- parameter planar structure, with particular emphasis on a vortex power flow which has the potential to confine the vibrational power into a restricted area of the structure. Without letting the vibrational power, a cause of exciting structural modes, disperse into the structure, control of the structural response can be achieved. This paper begins by deriving the necessary condition for producing a vortex power flow in the vicinity of a disturbance point force at an arbitrary exciting frequency. Then, with a wave visualization system newly developed, it becomes possible to observe the wave propagation (the vortex power flow) taking place in the structure. In order to investigate the contribution of structural modes to the vortex power flow configuration, an energy stream function as well as a vorticity function is derived in a general form. By using these functions, the generation mechanism of a vortex power flow actively induced around a disturbance force location is quantitatively studied.

In this paper, we describe the behavioral characteristics of a nonlinear oscillator derived from gear-meshing vibration, which exhibits various successive bifurcations ending in chaos. There are two types of sudden change from a chaotic to a periodic attractor, one of which is called "hysteresis". In a period-doubling bifurcation, a heteroclinic connection between the outset of an inversely unstable fixed point of period 2n and the inset of an inversely unstable fixed point of period n is necessary to generate an n-band chaotic attractor. If a directly unstable fixed point exists in the vicinity of any band attractor and the attractor collides with the inset of the directly unstable fixed point, the attractor expands due to an "interior catastrophe", and transforms into a one-band attractor. In the bifurcation diagram, periodic subharmonic oscillations appear discontinuously as "windows" belonging to the same "family". These "families" are divided into two types: type- I, in which fold bifurcation occurs repeatedly, and type- II, in which fold bifurcation occurs only at both ends of the solution curve. Depending upon whether or not both of the chaotic attractors exist in the same area of the phase plane, either before or after the bifurcation, the discontinuous bifurcation of the chaotic attractor is referred to as an "interior catastrophe" or "hysteresis", respectively.

This study deals with the problem of sensing structural vibration to provide an error signal to an adaptive feedforward control system, which aims to globally attenuate both structural and acoustic disturbance. This paper demonstrates the validity of a newly proposed "smart sensor" as a distributed parameter sensor made of PVDF film which is designed to measure an acoustic power mode of the total acoustic power radiated from a vibrating plate. Firstly, with a PVDF distributed parameter sensor attached on the entire surface of the plate, the formulas for sensing the ;'-th acoustic power mode are derived. Then, by considering the practicability of implementing the smart sensors, alternative formulas for sensing the acoustic power mode are derived for a strip-type smart sensor. The characteristics of the smart sensors optimally shaped for measuring the acoustic power modes are also shown. Moreover, based upon an adaptive feedforward control with the filtered-x LMS algorithm, an experiment was conducted to demonstrate the minimization of the acoustic power radiated from a vibrating plate.

This paper considers the design of distributed parameter modal sensors called "smart sensors", with a particular emphasis on filtering the combination of appropriately weighted vibration modes providing a specific performance index in control strategy. First, by considering a practicability of the distributed parameter smart sensors using PVDF film sensors, one-dimensional smart sensor is presented. It is found that the approach done by the one-dimensional sensors holds only the necessary condition for sensing the transformed mode. This problem is overcome by introducing multiple one-dimensional smart sensors. Moreover, the design procedure for the multiple one-dimensional smart sensors for measuring the transformed mode is established. Then, an experiment is conducted, demonstrating the validity of the smart sensors. Finally, using the smart sensors, the minimization of the total acoustic power radiated from a vibrating plate is carried out.

This paper deals with the acoustic power minimization problem from the viewpoint of an active noise and vibration control. This paper places a particular emphasis on the phenomenon in which the acoustic power output of the control source under optimal conditions always becomes zero. It is found that the acoustic radiation impedance at and around the control point source becomes reactive under the optimal condition, and hence power output of the control source results in null. It is also shown that the reactive acoustic intensity dominates even in the vicinity of the primary source in order to impede the sound radiation from its source. In active vibration control, the power flow in terms of a control force, applied directly to a vibrating structure in an effort to attenuate the radiated sound is found to be zero. Under the optimal condition for minimizing the total acoustic radiation power, the effect of the reactive sound field outweighs that of the active sound field significantly over the vibrating plate.

This paper deals with distributed parameter sensors designed with a view to extracting a vibration mode. Compared to conventional point-type sensors such as acceleration pickups, displacement sensors etc., the distributed parameter sensors have many benefits provided that they are properly designed. First, this paper overviews a conventional modal filter designed by use of point sensors, and enumerates the problems it involves. To overcome the drawbacks of the point sensor based modal filtering, a novel modal filtering technique based upon a PVDF film sensor, a distributed parameter sensor, is proposed. Two dimensional modal filters are discussed, and then, by taking into consideration a practicability of the sensors, a design procedure of one-dimensional modal filters is presented ; the number, location and shaping of the one dimensional sensors are clarified. Finally, an experiment is conducted, showing the capability of the distributed parameter modal filtering.

This paper deals with the active power flow control of a simply supported thin plate. Particular emphasis is placed on the vortex power flow pattern that has the potential of confining external energy, a cause of exciting vibration modes, into a restricted area and of diverting the power flow out of a specific region where vibration is to be prohibited. With a view to observing the power flow occurring in a plate, a wave visualization system has been developed. Based upon the visualization system, it is verified experimentally that the vortex power flow can be produced at an arbitrary position of a plate. An energy stream function as well as a vorticity function is derived in a general form. Furthermore, both the energy stream and vorticity functions are calculated as a function of vibration modes which are selected in the order of magnitude of their contribution to the total kinetic energy of the plate. As a result, as many as 100 vibration modes are found to be necessary to form a vortex power flow pattern.

This paper describes a novel vibration-mode filtering method for one-dimensional structures such as a cantilevered beam using a two-mode optical fiber as a distributed-effect sensor. One of the most important problems regarding the optical measurement is how to alter the sensor sensitivity spatially along the longitudinal direction of the beam when the sensor is mounted on the beam surface. In this study spatial variation of the sensor orientation with respect to the longitudinal direction is included in the sensor model. The sensor sensitivity can be experimentally measured and used for design, incorporating the orthogonality of the mode shapes of the structure. Moreover, in the light of practical considerations, a design procedure of optimal fiber placement utilizing bipolar weighting functions is presented. Finally, theoretical predictions are confirmed by experimental results and efficient vibration-mode filtering is demonstrated.

In this paper, a nonlinear oscillator derived from the gear meshing vibration is investigated, which exhibits successive different bifurcations ending in chaos above the first resonance. These bifurcations are examined in detail using bifurcation diagrams, Lyapunov exponents, winding numbers, invariant curves, and Poincare maps. In the bifurcation diagram, periodic subharmonic oscillations appearing nonsuccessively as a "window" belong to the same "families", which are divided into two kinds : type- I , in which fold bifurcation occurs iteratively (multifolding) in the family, and type- II , in which fold bifurcation occurs only at both ends of the family. Depending on whether both of the chaotic attractors before/after the bifurcation exist in the same area on the phase plane or not, the chaotic attractor bifurcates discontinuously according to "hysteresis" or "interior catastrophe". In the case that a 2^n-band attractor transforms into a 2^<n-1>-band attractor without fold bifurcated directly unstable fixed points, and a periodic directly unstable fixed point exists very close to an inset of a 2^<n-1>-periodic inversely unstable fixed point, the unstable 2^<n-1>-band attractor is suddenly transformed into a one-band attractor upon touching an inset of the periodic directly unstable fixed point.

This paper describes a nonlinear oscillator derived from the gear meshing vibration, which exhibits successive different bifurcations ending in chaos below the first resonance. These bifurcations are examined in detail using bifurcation diagrams, Lyapunov exponents, winding numbers, invariant curves, and Poincare maps. There are two types of sudden changes from a chaotic to a periodic attractor. One is the case, named "hysteresis", in which a chaotic attractor is transformed into a periodic one far from the chaotic one, and the other is the case in which a chaotic attractor transforms into a periodic one which lies inside the chaotic one. When an n-periodic attractor transforms into a chaotic one through period-doubling, a heteroclinic connection between the outset of a 2n-periodic inversely unstable fixed point and the inset of an n-periodic inversely unstable fixed point is necessary to generate an n-band chaotic attractor. If a directly unstable fixed point exists in the vicinity of any band attractors and the attractor touches the inset of the directly unstable fixed point on the above-mentioned sequence, the attractor expands due to "interior catastrophe", and immediately transforms into a one-band attractor.

In this paper, a nonlinear oscillator derived from the gear meshing vibration is investigated, which exhibits successive different bifurcations ending in chaos above the first resonance. These bifurcations are examined in detail using bifurcation diagrams, Lyapunov exponents, winding numbers, invariant curves, and Poincare maps. In the bifurcation diagram, periodic subharmonic oscillations appearing nonsuccessively as a "window" belong to the same "families", which are divided into two kinds : type- I, in which fold bifurcation occurs iteratively (multifolding) in the family, and type- II, in which fold bifurcation occurs only at both ends of the family. Depending on whether both of the chaotic attractors before/after the bifurcation exist in the same area on the phase plane or not, the chaotic attractor bifurcates discontinuously according to "hysteresis" or "interior catastrophe". In the case that a 2ⁿ-band attractor transforms into a 2^n-1-band attractor without fold bifurcated directly unstable fixed points, and a periodic directly unstable fixed point exists very close to an inset of a 2^n-1-periodic inversely unstable fixed point, the unstable 2^n-1-band attractor is suddenly transformed into a one-band attractor upon touching an inset of the periodic directly unstable fixed point.

This paper considers the design of distributed parameter modal sensors called "smart sensors", with a particular emphasis on filtering the combination of appropriately weighted vibration modes providing a specific performance index in control strategy. First, with a two-dimensional distributed parameter sensor using a PVDF film, the necessary and sufficient condition for sensing the transformed modes of a structure is derived. Then, by considering the practicability of the two-dimensional sensors, an alternative approach based upon one-dimensional smart sensors is presented. It is found that the latter approach holds the necessary condition for sensing the transformed mode. This problem is overcome by introducing multiple one-dimensional smart sensors. Moreover, the design procedure for multiple one-dimensional smart sensors used for measuring the transformed mode is established. Finally, an experiment is conducted, demonstrating the validity of the smart sensors.

This article examines the characteristics of real vibrational power flow in a simply supported rectangular panel under the action of feedforward vibration control, induced by a control source input which is slightly suboptimal such that the primary source is producing a slight amount of real vibrational power, and the control source is absorbing the same amount. It is found that the path of the power flow is a combination of translations and rotations, the rotations induced by the interference of two modes which produces a “vortex generating block.” A qualitative formula for predicting the number of power flow vortices, as well as the discussion of the vortex period, is put forward. A novel method to induce a vortex at an arbitrary location of the plate is also shown, which may have practical applications in controlling the path of vibrational power flow in systems of large extent. Moreover, the influence of the induced vortex power flow on the plate onto the acoustic intensity distribution is investigated, showing that the rotational direction of the vortex on the plate is not always the same with that of the acoustic intensity in the near field. © 1994, Acoustical Society of America. All rights reserved.

This paper deals with the active control of power flow of a vibrating plate. It is the purpose of this paper to present a wave control method for suppressing vibration of a distributed parameter system such as a beam or a plate. Unlike a conventional modal-based control method, this method has the potential to suppress all vibration modes of a structure. First, from an analytical point of view, this paper presents three kinds of flow patterns appearing in controlled vibration intensity: (1) straight flow patterns from the excitation point to control point, (2) S-shaped flow patterns and (3) vortex flow patterns around the excitation point and control point. Then, the existence of these patterns is verified experimentally. Next, relationships between vibrational and acoustical intensities are discussed, and the acoustic power and acoustic pressure in terms of these patterns are also investigated. Furthermore, the characteristics of the rotational patterns are clarified and a means to generate the vortex of vibration intensity at an arbitrary position on a plate is presented. © 1994, The Japan Society of Mechanical Engineers. All rights reserved.

This paper considers an acoustic power minimization problem from the viewpoint of active noise and vibration control. It is the purpose of this paper to elucidate a common link between : actively attenuating noise in a variety of acoustic environments, using vibration or acoustic control sources. It is shown that if acoustic reciprocity holds between each point on the primary source and each point on the control source, then the acoustic power output of the control source under optimal conditions will always be zero, with the converse also being true. This concept is demonstrated for systems operating in free space, using both acoustic and vibration control sources. The physical meaning of this concept for the employment of vibration control sources, applied directly to a vibrating structure in an effort to attenuate the radiated sound field, is shown.

This paper deals with the problem of sensing structural vibration to provide an error signal to adaptive feedforward control systems implemented to globally attenuate both structural and acoustic disturbances. This paper demonstrates the validity of a newly proposed smart sensor made of PVDF distributed parameter sensors designed to measure power modes of the total acoustic power radiating from a vibrating plate. Firstly, with a PVDF distributed parameter sensor attached over the whole plate, the formulas for sensing the j-th power mode are derived. Then, by considering the practicability of the smart sensors, alternate formulas for sensing the power mode are derived for a strip-type smart sensor. The characteristics of the smart sensors optimally shaped for measuring the power modes are also shown. Moreover, based upon an adaptive feedforward filtered-&chi;LMS algorithm, an experiment was conducted demonstrating the minimization of the acoustic power radiated from a vibrating plate.