Nobuharu Aoshima

Bifurcation in an inverted pendulum with tilted high-frequency excitation: analytical and experimental investigations on the symmetry-breaking of the bifurcation

In this study, we investigate the dynamics of an inverted pendulum subjected to high-frequency excitation. In particular, we focus on bifurcation phenomena in the dynamics and analyze the effect of the tilt of the excitation direction with respect to gravity direction on the bifurcation. It is analytically clarified that the tilt produces stable equilibrium states different from the directions of the gravity and the excitation. The stability of the stable equilibrium states under the effect of the tilt is discussed non-locally. Also, an analogy of the bifurcation of the inverted pendulum to that of the buckling phenomenon is presented. The theoretically predicted effects of the tilt are qualitatively confirmed by performing some experiments.

Stabilization of 1/3-order subharmonic resonance using an autoparametric vibration absorber

The paper proposes a stabilization method for 1/3-order subharmonic resonance with an autoparametric vibration absorber. A main system with nonlinear spring stiffness and harmonic excitation, i.e., subjected to a sinusoidally changed magnetic force, is introduced as a model which produces 1/3-order subharmonic resonance. A damped pendulum system, whose natural frequency is in the neighborhood of one-half of the main system, is attached to the main system as an absorber, in order to induce 1:2 internal resonance. The 1/3-order subharmonic resonance which occurs in the case of locked pendulum is avoided due to energy transfer between the main system and the absorber, and due to energy dissipation by the absorber. It is also theoretically shown that a stable nontrivial steady state with respect to the 1/3-order subharmonic frequency component is changed into an unstable one due to the absorber. Experimental results show the validity of the autoparametric vibration absorber for the 1/3-order subharmonic resonance.

Swing-up and stabilization of an underactuated manipulator without state feedback of free joint

A technique without state feedback of the free link is theoretically and experimentally proposed for the swing-up and the stabilization at the upright position of the free link in a two-link underactuated manipulator. An appropriate actuation of the bifurcations produced in the free link realizes the control objectives.

Suppression of Parametric Resonance in Cantilever Beam With a Pendulum (Effect of Static Friction at the Supporting Point of the Pendulum)

The dynamic response of a parametrically excited cantilever beam with a pendulum is theoretically and experimentally presented. The equation of motion and the associated boundary conditions are derived considering the static friction of the rotating motion at the supporting point (pivot) of the pendulum. It is theoretically shown that the static friction at the pivot of the pendulum plays a dominant role in the suppression of parametric resonance. The boundary conditions are different between two states in which the motion of the pendulum is either trapped by the static friction or it is not. Because of this variation of the boundary conditions depending on the pendulum motion, the natural frequencies of the system are automatically and passively changed and the bifurcation set for the parametric resonance is also shifted, so that parametric resonance does not occur. Experimental results also verify the effect of the pendulum on the suppression of parametric resonance in the cantilever beam.

Stabilization of the Parametric Resonance of a Cantilever Beam by Bifurcation Control with a Piezoelectric Actuator

In this work, bifurcation control using a piezoelectric actuator isimplemented to stabilize the parametric resonance induced in acantilever beam. The piezoelectric actuator is attached to the surfaceof the beam to produce a bending moment in the beam. The dimensionlessequation of motion for the beam with the piezoelectric actuator on itssurface is derived and the modulation equations for the complexamplitude of an approximate solution are obtained using the method ofmultiple scales. We then acquire the bifurcation set that expresses theboundary of the stable and unstable regions. The bifurcation set ischaracterized by the modulation equations. Next, we determine the orderof feedback gains to modify these modulation equations. By actuating thepiezoelectric actuator under the appropriate feedback, bifurcationcontrol is carried out resulting in the shift of the bifurcation set andthe expansion of the stable region. The main characteristic of thestabilization method introduced above is that the work done by thepiezoelectric actuator is zero in the state where the parametricresonance is stabilized. Thus zero power control is realized in such astate. Experimental results show the validity of the proposedstabilization method for the parametric resonance induced in thecantilever beam.

Effect of Lateral Linear Stiffness on Nonlinear Characteristics of Hunting Motion of a Railway Wheelset

Railway wheelset experiences the problem of hunting above a critical speed, which is a kind of self-excited oscillation. At the critical speed, it is known that the system undergoes a subcritical Hopf bifurcation. Therefore, for clarifying the nonlinear characteristics of hunting it is very important to detect, for example, the nonlinear forces in the wheelset due to the creep forces acting between the wheels and rails, and the nonlinear component of the resorting forces by the suspensions. However, it is impossible to determine each force quantitatively. In the present paper, it is first shown, by using the center manifold theory and the method of normal form, that the nonlinear characteristics of the bifurcation in a wheelset model with two degrees of freedom are governed by a single parameter, hence each nonlinear force need not be detected when examining the nonlinear characteristics. Also, a method of determining the governing parameter from experimentally observed radiuses of the unstable limit cycle is proposed. Next, we experimentally investigate the variation of the parameter due to the presence of linear spring suspensions in the lateral direction and discuss the variation of the nonlinear characteristics of the hunting motion, which depends on the lateral stiffness. As a result, the improvement of the stability of the wheelset against the disturbance by the linear spring suspensions is clarified.

Analog Gabor transform filter with complex first order system

We propose an analog Gabor transform filter. Gabor function is widely used for digital time-frequency analysis as nonorthogonal wavelet. However, it has never been reported in analog filtering. The proposed filter is realized as cascade connection of CFOS (complex first order system). The impulse response of the filter will be considered as the product of a window function and a sinusoidal wave. Because the window function is approximated to Gaussian function, we regard the whole system as Gabor transformer. We have actually constructed the proposed filter, and measured the characteristics. Its mathematical foundation and experimental results are presented.

Study on Estimation of the Finite-Length Unknown Input Waveform from a Given Input Waveform Response

The information obtained by measuring a system can be regarded as a response given by the Black Box when there is an input. In this study, estimation of the finite-length unknown input waveform from a given input waveform response in a second order damped oscillation system is conducted. The theory is shown and verified with the simulation on MATLAB. While the effectiveness of this theory in the real system is shown by carrying out an experiment. The unknown input waveform form is estimated as followed. The impulse response is estimated from the response waveform of the system. Then, Fourier transformation for the response waveform and the estimation waveform of the impulse response was conducted, and the spectrum of the response wave was decided by the spectrum of the estimated impulse response. Lastly, inverse Fourier transform was conducted to this result. This end result obtained is the estimated waveform of the unknown input waveform. In this experiment, the output waveform of the system was measured with an laser displacement sensor. The result was influenced by the noise, however the input waveform was able to be estimated

Effect of Coulomb Damping on Buckling of a Two-Rod System

This paper describes a significant influence of a slight Coulomb damping on buckling, using a simple two rods system. Coulomb damping produces equilibrium regions around the well-known stable and unstable steady states under the pitchfork bifurcation which occurs in the case without Coulomb damping. Also, the stability of the states in the equilibrium regions is examined by using the phase portrait. As a consequence, due to the slight Coulomb damping, it is theoretically clarified that the states in the equilibrium regions are locally stable, even in the neighborhood of the unstable steady states under the pitchfork bifurcation in the case without Coulomb damping, i.e., even in the neighborhood of the unstable trivial steady states in the postbuckling and the unstable nontrivial steady states under the subcritical pitchfork bifurcation. Furthermore, the experimental results are in qualitative agreement with the theoretically predicted phenomena.

Ultrasonic Measurement System for Detecting Penetration of Boulders by Autocorrelation Analysis

An elastic impact wave method is used as a typical nondestructive test method to investigate the depth of boulder penetration. However, in the elastic impact wave method using, for example, a hammer, the discrimination of the reflection wave produced by minute cracks is difficult. Theoretically, if it becomes possible to input the vibration of an ultrasonic domain into artificial structures, such as a concrete and a boulder, with a strong amplitude, deeper investigation depth compared to the conventional way with a high precision will be attained. In this study, a concrete block, with a known size, which was, unlike boulders, not buried under ground, was used as a test piece in a basic experiment. As analysis methods, a wavelet analysis for checking the reflection wave and an autocorrelation analysis for identifying the time lag of the reflection wave were used. As a result, the reflection wave was detected in a down chirp signal from 50 kHz to 40 kHz.