黒田 雅治

Recently, there is a high expectation for viscometer to measure polymeric solutions, adhesive agents, coating materials, abrasives, and so on. Vibration-type viscometer is known as a sensor to be able to measure time variation of the viscosity with change of the material characteristics. However, conventional vibration-type viscometer uses Quality factor of frequency response curve under external excitation, and requires the observation of the frequency response curve near the resonance peak. In this research, to overcome the drawback, we theoretically proposed a viscometer based on self-excited oscillation under positive linear feedback. The critical feedback gain which produces the self-excited oscillation corresponds to the viscosity. Also, from experimental results, the validity of the proposed method is discussed.

A Micro viscosity sensor manufactured by micro processing technology has been developed. The principle of the viscosity sensor is improvement of vibrating viscometer. The viscosity sensor has a vibrating body which is excited by an actuator and a tracking body which is subjected to a shear stress. The shape of vibrating body and tracking body is double volute. The sensor can measure the flow curve of Non-Newtonian fluid. The manufacturing process of the basic structure using the micro processing technology was verified.

Micro-cantilever probe behaves as a van der Pol oscillator by linear-plus-nonlinear feedback control. The nonlinear dynamics of van der Pol-type self-excited micro-cantilever probe is investigated by considering atomic force between the tip of the probe and a sample surface. By applying the method of multiple scales to the equation of motion, we derive the amplitude equation expressing the slow time variation of the response amplitude. It is noticed from the nonlinear analysis that the response amplitude can be kept small by high-gain nonlinear feedback. The response frequency in the van der Pol-type self-excited micro-cantilever probe cannot be deviated from the effective natural frequency independent of the magnitude of amplitude response.

We proposed application of van der Pol-type self-excited oscillation as the method to excite the probe-cantilever in AFM. The van der Pol-type self-excited oscillation presents the advantage that the oscillation frequency always coincides with the natural frequency of the probe-cantilever. Furthermore, it has another advantage: we can suppress the steady state amplitude of the cantilever to an extremely low level thanks to the nonlinear feedback effect, while maintaining stable self-excited oscillation. The quality of images obtained using vdP-AFM is comparable to that of pictures obtained using contact-mode AFM. Moreover, the non-contact state is maintained during themeasurement experiments. In each case, the distance between the sample and the probe-cantilever is greater than the vibration amplitude of the cantilever. This fact confirms results of the non-contact observation.

Atomic force microscopy (AFM) is indispensable for studies in nano-biotechnology. The AFM principle is that a micro-cantilever with a probe attached to the tip scans an object's surface to measure its shape. Toward observation of nanometer-scale biological samples in a liquid, this paper reports frequency-modulation atomic force microscopy (FM-AFM). It can avoid collisions by the probe-cantilever with the sample surface and stop oscillation by vibrating the probe-cantilever similarly to van der Pol-type self-excited oscillation.

原子間力顕微鏡（AFM)による液中生体資料観察に向けた、マイクロカンチレバープローブの自励発振とその振幅低減化に関する制御法の提案を理論的ならびに実験的に行った。液中におけるQ値の低減は強制加振によるカンチレバーの等価的固有振動数の推定を困難にする。しかしながら、正帰還フィードバックによる自励発振をカンチレバーに発生されることにより、その応答周波数から投下固有振動数を推定することが可能になる。このとき、試料との接触を防ぐためには応答振幅の低減化が必要であるが、本研究ではhopf分岐に対する分岐制御を行うことにより、低減化する手法を提案し、実験によって低減化効果を確認する

Atomic force microscopy (AFM) is recognized as indispensable for micro-electromechanical systems (MEMS), nanotechnology, and nano-biotechnology. Although observing bio-related samples in a liquid environment using AFM is increasingly important, deformable, uneven, and easily damaged surfaces of biological specimens require establishment of non-contact AFM observation. Contact mode and dynamic mode are AFM's two measurement methods. The latter reproduces the surface shape from variation appearing in the vibrating micro-cantilever's resonance, depending on change in the atomic force acting between the probe and the sample surface during measurement. Because soft irregular bumpy surfaces of biogenic samples are easily damaged, contact-mode AFM is unsuitable for samples of biological origin. Instead, non-contact observation using dynamic-mode AFM must be established. Toward observation of nanometer-scale biological samples in a liquid, this paper reports frequency-modulation atomic force microscopy (FM-AFM). It can avoid both collisions by the probe-cantilever with the sample surface and stops of oscillation by vibrating the probe-cantilever similarly to van der Pol-type self-excited oscillation.

Recently, there is a high expectaion for biological samples to be observed in liquid by the use of Atomic Force Microscopes (AFM). However, viscous damping makes it difficult to observe the samples in liquid using conventional methods. Moreover, it is required that a cantilever oscillates with a small amplitude to prevent the contact between the cantilever and the samples. In this research, we proposed a microcantilever which behaves as van der Pol oscillator. Then, we realized a self-excited oscillation with a small steady state amplitude.

We proposed application of van der Pol-type self-excited oscillation as the method to excite the probe-cantilever in AFM. The van der Pol-type self-excited oscillation presents the advantage that the oscillation frequency always coincides with the natural frequency of the probe-cantilever. Furthermore, it has another advantage: we can suppress the steady state amplitude of the cantilever to an extremely low level thanks to the nonlinear feedback effect, while maintaining stable self-excited oscillation. The quality of images obtained using vdP-AFM is comparable to that of pictures obtained using contact-mode AFM. Moreover, the non-contact state is maintained during the measurement experiments. In each case, the distance between the sample and the probe-cantilever is greater than the vibration amplitude of the cantilever. This fact confirms results of the non-contact observation.

We propose a self-excited cantilever beam by positive velocity feedback and nonlinear feedback. The self-excited oscillation keeps the resonant condition independent of the modulation of system parameters and the resonance characteristic of self-excited oscillation is utilized for auto-resonance machines such as AFM micro-cantilever proble. Because the amplitude of self-excited oscillation grows with time, a special control method is required for the amplitude control. In this study, we use the dynamics of van der Pol oscillator and realize the amplitude control of a cantilever beam by using only integral control without differential control.

原子間力顕微鏡(AFM)のカンチレバープローブの駆動および振幅制御の方式として，積分制御によるファンデルポール型の自励発振法を提案する．試作AFMに提案手法を適用し，大気中および液中環境下で試料接近によるカンチレバーの挙動を観察し，ＡＦＭとしての実用に向けた検討を行う．

近年、分数階微積分の科学技術応用が活発化しているが、特に制御工学においてその傾向は顕著である。しかし、伝達関数モデルに基礎を置く古典制御理論の適用は研究されてきたものの、分数階微分とその状態方程式モデルとの関係は十分考察されてきたとは言えない。そこで、本論文では分数階微分応答を含むダイナミクスの状態方程式モデルへの変換方法について述べる。一旦、状態方程式として定式化できれば、ロバスト制御を含む現代制御理論の優位性を分数階微分で記述される動的システムのモデル化、さらにはその制御則の導出において活用することが可能となる。また、分数階微分応答の検出には従来法では特殊な変換デバイス等を必要としたが、本報告において提案する手法は、分布定数系における多点計測法を用いることによって、特殊なデバイスを用いることなく分数階微分応答を検出することも可能にしている。

Self-excitation thechnique is known as an effective excitation method for a cantilever probe of the atomic force microscope to measure the surface of a biological sample in a liquid environment. In this research, we deal with a van der Pol type cantilever probe, which is previously proposed to realize the non-contact mode, and experimentally examine the relationships between the response frequency and amplitude and the gap of the cantilever probe and the surface of sample. We examine the natural frequency of the cantilever in liquid. From the result, it is confirmed that the cantilever oscillates with a low amplitude that can detect the surface of the sample without giving damage. While it is difficult to estimate natural frequency of the cantilever under external excitation in liquid, it is easy to estimate it under van der Pol type self-excited oscillation.

Usage of self-excitation as an excitation method has been proposed for vibration machines as well as the cantilever-probe in an atomic force microscopy (AFM). The amplitude control is carried out by producing the dynamics of the van der Pol oscillator in the cantilever. The control has been performed by applying nonlinear feedback proportional to the squared angle and the angular velocity. In this study, we propose a new control method which has high performance even in the high-frequency range and realize van der Pol oscillator in the cantilever with laterally exited fixed end by not using differential of the measurement signal, but integral control with respect to the angle at the tip of the cantilever. This control method is demonstrated by our own making analog electrical circuit. Then, the steady state amplitude of self-excited oscillation with amplitude of 4nm is experimentally realized.

Self-excitation thechnique is known as an effective excitation method for a cantilever probe of the atomic force microscope to measure the surface of a biological sample in a liquid environment. In this research, we deal with a van der Pol type cantilever probe, which is previously proposed to realize the non-contact mode, and experimentally examine the relationships between the response frequency and amplitude and the gap of the cantilever probe and the surface of sample. We examine the natural frequency of the cantilever in liquid. From the result, it is confirmed that the cantilever oscillates with a low amplitude that can detect the surface of the sample without giving damage. While it is difficult to estimate natural frequency of the cantilever under external excitation in liquid, it is easy to estimate it under van der Pol type self-excited oscillation.

Self-excitation thechnique is known as an effective excitation method for a cantilever probe of the atomic force microscope to measure the surface of a biological sample in a liquid environment. In this research, we deal with a van der Pol type cantilever probe, which is previously proposed to realize the non-contact mode, and experimentally examine the relationships between the response frequency and amplitude and the gap of the cantilever probe and the surface. From the result, the performance of the self-excited cantilever probe from viewpoint of the contact between the cantilever and the surface.

原子間力顕微鏡(AFM)のカンチレバープローブの駆動および振幅制御の方式として，積分制御によるファンデルポール型の自励発振法を提案する．試作AFMに提案手法を適用し，大気中および液中環境下で試料接近によるカンチレバーの挙動を観察し，ＡＦＭとしての実用に向けた検討を行う．

積分制御によって、van der Pol型発振する片持ち梁を実現する方法を理論的に提案し、実験によってその有効性を確認した。梁の支配方程式を曲率の非線形性を考慮して導出し、多重尺度法によって振幅方程式を求め、積分制御によってvan der Pol 型の片持ち梁が実現できることを示した。

Flow induced vibrations of tube array occur in general heat exchangers and nuclear reactors. They cause the tube failures through fretting wear or fatigue. The experiments were conducted in cylinder bundles, 15 cylinders ( 3 rows and 5 columns) and 231 cylinders (21 rows and 11 columns) at various flow velocities. The two types of cylinders were made of piano wire and plastic optical fiber (POF ). In the case of 15 piano wire cylinders, the amplitude increases as flow velocity increases and cylinders move largely in transverse direction. For 15 POF cylinders, most cylinders vibrate greatly owing to their small flexibility with frequent collisions of cylinders. In a cylinder array of 231 cylinders, spatial behaviors of cylinders exhibit a pattern like a wave-like motion as flow velocity increases.

Self-excitating technique is known as an effective excitation method for AFM probe to measure the surface of a biological sample in a liquid environment. In this research, the self-excited oscillation in a cantilever probe is generated by linear feedback. In addition, the steady state amplitude is reduced by nonlinear feedback. Then, the cantilever probe has the same dynamics as van der Pol oscillator. We implement the excitation method to a practical cantilever probe of AFM, using the optical lever method and tube PZT scanner. For using our own making AFM, we experimentally confirm that the small steady state amplitude of the cantilever probe is realized.

We propose a new control method of the micro cantilever probe in atomic force microscopy (AFM) for biologic imaging. The observation is concerned with operation in water or aqueous bufferin where the Q value of the cantilever is reduced. In this situation, it is very difficult to obtain the natural frequency of the micro cantilever probe. The utilization of self-excited oscillation is known as a method to overcome the difficulty. Furthermore, for the detection of the characteristics of soft biological material, the non-contact mode, that the probe does not contact to the material, is required for avoidance of local deformation and destruction of the material. In this study, for realizing the no contact mode of the self-excited micro cantilever probe, van der Pol type self-excited micro cantilever beam is designed by bifurcation control due to linear-plus-nonlinear feedback control.

バイオテクノロジーの発展にナノテクノロジーが融合して"ナノバイオテクノロジー"の時代に入った今日、原子間力顕微鏡(AFM)の高性能化の要求は尽きることはない。特に、今後、 DNAやタンパク質をはじめとする生体高分子などのその場(in-situ)観察において、 AFMによる液中観察の機会は急激に増大することが予想される。しかし、柔軟で表面に凹凸の多い生体関連試料をダイナミックモードAFMにてその場(in-situ)観察するには、カンチレバーによって試料表面が損傷しないために50pN以下の接触力を実現せねばならないとされ、理想的には完全なる非接触モードの実現が望まれている。前記課題の達成方法として、著者らは、カンチレバーの振動速度の正帰還による単なる自励発振だけではなく、非線形フィードバック項を付加することによってファンデルポール型自励振動系を用いる手法を提案してきた。(図A1参照)一方、AFMによる生体高分子の高精度液中観察におけるプローブカンチレバーとして、Si製マイクロカンチレバー上にPZT層を成膜し、電極をセンサ部分とアクチュエータ部分に分割した自己駆動・自己検知型が注目されている。と言うのは、従来AFMの光てこ法と異なり、レーザー光の光点合わせが不要、検出部分をコンパクトにまとめられる、アラインメントや加振も直接行えるなどの利点を十全に享受できるためである(図A2参照)。現在までに、自己駆動・自己検知型マイクロカンチレバーを試作、自励発振系の実装、そして発振の実験に成功したので報告する。

There have been researches on a self-excited cantilever beam for atomic force microscopy (AFM), in order to increase the low quality factor Q of the cantilever in liquid enviroments. For the realization of the non-contact AFM, it is necessary to control the stable steady state amplitude of the self-excited cantilever to be small. We proposed that we can realize the stable steady state amplitude of of the self-excited cantilever by applying nonlinear feedback proportional to the squared deflection and the velocity. In this study, we develop the AFM using a "van der Pol" type self-excited cantilever beam. Then, we confirm the availability and the advantage of the "van der Pol" type self-excited cantilever beam.

In this study, a proto theoretical-model is established to explain observed experimental results. Spatio-temporal patterns, such as wave-like motion emerging in experiments, can be considered as cascading reactions of dynamic bifurcations in a two-dimensional set of closely coupled nonlinear oscillators. Each oscillator exhibits a Hopf-bifurcation between a small amplitude oscillation around the equilibrium and a large amplitude limit-cycle oscillation below the critical wind speed. Collisions among neighboring rods occur as amplitudes of rod vibrations increase with increasing wind velocity. It is possible to overcome the barrier of unstable limit-cycle in subcritical Hopf-bifurcation depending on the rate and magnitude of these collisions. Consequently, a transition from a small amplitude oscillation to a large amplitude limit-cycle, or one from a limit-cycle to a small oscillation, is generated. Thereupon, it is propagated on the two-dimensional lattice. In this manner, the two-dimensional structure of the propagated subcritical Hopf-bifurcations is proven to determine a kind of spatio-temporal pattern. Results from experiments and theoretical analyses agree well qualitatively.

The frequency of self-excited systems depends on the amplitude and under the large amplitude, the excited frequency deviates from the natural frequency. Therefore, to keep the excited frequency near the natural frequency, the response is required to have a small stable steady amplitude. In this paper, a self-excited cantilever beam of Van der Pol type is realized by using nonlinear feedback and the dependence of the response amplitude and frequency on the nonlinear feedback gain is theoretically examined.

流力弾性振動子群の時空ダイナミクスにおける自己組織化について研究している。今回は、直交一様流中の弾性ロッドの大規模配列が示す複雑挙動に関する実験結果について報告する。風洞実験において、風速の上昇と共に、個々のロッド、ロッドのクラスタ、そしてクラスタ鎖の波動へと動的な秩序形成の主役は移り変わり、そして近傍要素間の相互作用の強度（この場合はロッド同士の衝突の頻度）が強くなるほど、要素集団（この場合はロッド配列）は大域的に秩序だった振る舞いを見せること、などが明らかになっている。

This paper describes the instanteneous cross section void fraction measurement in a double cylinder natural circulation test facility using a wire-mesh sensor built in the vessel cross sections. The inner and outer cylinders with their inner diameters of 0.49m and 0.39m, respectively, were placed co-centrically to simulate basic natural circulation flow to be developed around a chimney of a natual circulation nuclear reactor for next generation. Air was uniformly introduced from the bottom plate of the inner cylinder to drive upward flow in the chimney and downward flow in the downcomer. The natural circulation velocity of water remained almost unchanged while air flow rate was increased. This is mainly due to increased amount of bubbles trapped in the downward flow in the downcomer region.

Natural circulation type boiling water reactors are expected as promising next generation nuclear reactors, because recirculation system is reduced and loss of coolant event is mitigated. Three-dimensional gas-liquid two-phase flow in the chimney above the core is important for developing natural circulation flow rate through void fraction profile and carry under bubbles into the downcomer. The experiments were carried out using the test section with double cylinders imitating the pressure vessel and the chimney of a natural circulation reactor. Numerical analysis of the experiments have been performed using the extended two-fluid model, which can treat large scale interface directly and small scale interface with the averaged parameters as conventional two-fluid model. Transient gas-liquid two-phase flow after air injection in the bottom cross-section of the inner cylinder are calculated. Predicted natural circulation velocity in the downcomer is overestimated by 10% compared with experimental data.

The formation of air bubbles from a injection nozzle submerged in a water/glycerol solution inside a cylindrical tube is investigated by the methodology of the nonlinear time series analysis. It was found from the bifurcation diagram of bubble interval that the period doubling bifurcation occurred by the increase in gas flow rate. Correlation dimensions were estimated from the nozzle pressure fluctuation, and the results indicate that the bifurcation from periodic orbit to chaos occurred in high air flow rate region. It was shown that the correlation dimension could detect the transition of the pressure fluctuation dynamics that could not be detected by mean values and standard deviations.

Experiments on spatio-temporal dynamics in large arrays of cantilevered elastic-rods in uniform and stationary wind-tunnel cross-flow have been carried out. From 90 to 1000 steel and polycarbonate rods with gap ratios ranging from 1.0 to 2.5 are used. As the Reynolds number (based on the rod diameter) increases, a pattern with the characteristics of spatio-temporal chaos emerges in the global behavior of the array of elastic rods. There are local and global patterns. The local patterns are composed of transient rest, linear motions and elliptical motions. In the 90 rod experiments, a cluster-pattern entropy measure is introduced based on these three patterns as a quantitative measure of the local complexity. Below a threshold wind velocity, no significant dynamics appears. Video images reveal that at first each rod moves individually, then clusters consisting of several rods emerge and finally global wave-like motion takes place with higher flow velocities. Spatial patterns in the rod-density distribution appear as more rods suffer impacts with 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 fluid-structure heat exchange systems. This experiment may also be a two dimensional analog of the impact dynamics of granular materials in a flow.

This study deals with the complex behavior observed in large array of elastic rods in the stationary air cross-flow. The top of each rod shows chaotic spatio-temporal patterns composed of temporally stop, linear motion and elliptical orbit. In this report, the 1000-rod arrays of 25 rows×40 columns and 20 rows×50 columns are used in experiments. As the wind velocity is increased, self-organizing phenomena recognized as spatio-temporal pattern formation in the entire array of rods are demonstarted.

In this paper we discuss the flow-induced vibrations of a periodic array of cantilevered elastic rods in a steady, wind tunnel flow, transverse to the rods (Fig. A1). New experiments on the dynamics of 90 and 300 elastic oscillators in a steady cross flow are described. Our goal is to observe complex patterns in a large spatial array of oscillators as excited by fluid-elastic instabilities and impact between the vibrating rods. Unlike the 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. For Reynolds numbers exceeding 300 (based on the rod diameter.), the array of elastic rods undergoes increase, chaotic patterns of vibration consisting of momentary equilibria, motion along a linear path and elliptical path motions (Fig. A2). We introduced a symbolic measure of this pattern based on these three types of motion and use a pattern entropy measure to characterize the complexity (fig. A3). With increasing flow velocity however, organized wave-like structures appear to develop (Figs. A4 and A5). The corresponding array patterns are analogous to cellular automatic dynamics. Experimental models of this type may serve to help understand complex dynamics in large array heat exchange system. It may also be a model to understand wind crop dynamics and damage.