Masatsugu Yoshizawa

Nonstationary Vibrations of a String with Time-Varying Length and a Mass-Spring Attached at the Lower End

The purpose of this paper is to study the nonstationary vibration of a string with time-varying length and a mass-spring system attached at the lower end. The string is hung vertically and excited sinusoidally by a horizontal displacement at its upper end. The mass is supported by a guide spring horizontally and has two-degrees-of-freedom, vertical and horizontal. It is shown analytically that axial velocity of the string influences the peak amplitude of the string vibration at the passage through resonances. Moreover, it is shown numerically that the amplitudes of both the string and the mass vibrations depend on the sign of the axial velocity, when the natural frequency of the mass-spring system is close to the frequency of the excitation. The above two theoretical results are confirmed experimentally with a simple experimental setup.

Mechanical stability of a high-T/sub c/ superconducting levitation system

This research deals with dynamics of a permanent magnet freely levitated above an excited high-T/sub c/ superconductor. Vertical restoring forces acting on the magnet were evaluated by analysis based on the critical state and flux flow models. The results show nonlinearity and frequency-dependence of the forces, which were observed in experiments. Vertical vibration properties of the system were also evaluated analytically by considering the above properties of the restoring forces. The results show good agreement with experimental ones, which include effect of the frequency-dependent stiffness on the resonant frequency, the primary resonance characteristics, stability of the steady-state motions and so on.

Parametrically excited horizontal and rolling motion of a levitated body above a high-T/sub c/ superconductor

This research deals with a kind of parametric excitation of a permanent magnet freely levitated above a high-T/sub c/ superconductor excited in the vertical direction. We find the magnet has two vibration modes of linearly coupled horizontal translation and roll motion. These two modes are coupled nonlinearly with the vertical motion by the magnetic force and torque. Through nonlinear analysis and numerical simulation, this research discusses parametric resonance of each mode caused by vertical excitation at the frequency in the neighborhood of twice the natural frequency of that mode. Analytical and numerical results show qualitative agreement with experimental ones.

Asymptotic analysis of the formation of thin liquid film in spin coating

Unsteady thin liquid film flow of non-uniform thickness on a rotating disk is analyzed by asymptotic methods. Short- and long-time-scale solutions for the transient film profile near the rotating axis are independently derived as a function of space and time. Analyses were performed for a case in which the initial film thickness is even in radial distance and the peripheral effects of the liquid film are assumed to be negligible. The result reveals the effects of the gravitational and surface tension forces, coupled with inertial force, on the film planarization and thinning process.

Nonlinear Oscillation of an Elastic Body Supported by High-

This research deals with nonlinear dynamics of an elastic bar supported at both its ends by electromagnetic forces from high-Tc superconducting bulks, under vertical excitation. Experimental results show parametric resonance of an asymmetric mode consisting of pitching motion and deflection in a symmetric system. This resonance has nonlinear characteristics such as soft-spring response and hysteresis. It was also confirmed by numerical analysis. Nonlinearity originated in electromagnetic forces caused this resonance.

T_{c}

This research deals with nonlinear dynamics of a rotating magnet levitated above a high-Tc superconducting bulk. Under no contact support by magnetic force, the magnet levitates stably without control. Such a low-damping system can show complex dynamical behaviors, because of nonlinearity of the magnetic force. In multi-degree-of-freedom nonlinear systems one can find energy transfer between modes through nonlinear coupling, which is called internal resonance. In this research, mechanism of the internal resonance was discussed from the equations of motion. This resonance was confirmed by numerical analyses and experiments.

Superconducting Magnetic Bearings

A great deal of study has been done on the dynamics of straight pipes conveying fluid. Relatively less effort has been directed towards the examination of the dynamics of curved pipes. In this paper, out-of-plane vibrations of a curved pipe due to the pulsating fluid flow are examined. The pipe is hanging horizontally and is supported at both ends. The main purpose of this paper is to investigate the nonlinear interaction between the in-plane and the out-of-plane vibrations analytically and experimentally. First, from the physical discussion of the equation for the spatial motion, the parametric excitation of the out-of-plane vibration and the forced excitation of the in-plane vibration most likely occur by the presence of pulsating fluid flow. Second, the complex amplitude equation of the out-of-plane pipe vibration in the case of the principal parametric resonance, is derived. The out-of-plane vibration is excited by the pulsating fluid flow and the nonlinear interaction between in-plane and out-of-plane vibrations. From the nonlinear analysis, it was clarified that the nonlinear interaction between in-plane and out-of-plane vibrations greatly affects the out-of-plane vibration. Third, the experiments were conducted with a silicon rubber pipe. The deflections of the pipe were measured with increasing the frequency of the pulsating flow gradually. In order to observe the principal parametric resonance, the frequency of the pulsating flow was determined as near twice the natural frequency of the out-of-plane vibration for the first mode. We confirm that the in-plane vibration affects the out-of-plane vibration, qualitatively.Copyright

Internal Resonance of a Rotating Magnet Supported by a High-

This research investigates transient behaviors of a rotor passing through resonance in a high-Tc superconducting bearing system. Such a low-damping multi-degree-of-freedom system, subjected to nonlinear force, can show complex dynamical behaviors, in which energy transfer occurs between modes through nonlinear coupling. Our numerical and experimental results show that, in a system of a high-Tc superconducting bearing, internal resonance can occur even in transient cases where the rotor passes through resonance. Effects of the internal resonance and also effects of the spin-up rate on the transient dynamics of the rotor have been examined and clarified by changing the period of increasing voltage applied to a D.C. motor for rotating the rotor.

T_{c}

This paper deals with transient nonlinear vibration of a rigid body suspended on a foundation by elastic springs and constrained in a plane. In such a three degree-of-freedom vibration isolation system, we assume that ‘2-1-1’ internal resonance exists between the vertical and horizontal vibrations of the rigid body and the rotational vibration about its center of gravity. Next, the vibration of the rigid body is captured into or passes through resonance when the rotation speed of an unbalanced rotor equipped with the rigid body is increased. We theoretically examined the transient behavior of passage through resonance under the condition that a DC motor directly drives the unbalanced rotor with a limited electric current. Moreover, the experiment was conducted with a physical model of such a system, and transient oscillations through resonance were observed and compared with theoretical results in a few cases of limited currents.Copyright

Superconducting Bearing

The development of enhanced sensors and experimental techniques (e.g., high-resolution laser video captures, 3D laser scanner vibrometry, image digital processing) has enabled significant advances to be made in the measurement of complicated phenomena in nonlinear mechanical systems. These developments and the wider availability of general experimental devices have sparked a rich proliferation of experimental studies. Research efforts both in academia and in industry are targeted towards different objectives such as nonlinear dynamical system approaches to data analysis and interpretation; comparisons with analytical/reducedorder model predictions; and novel nonlinear vibration control methods in a variety of fields, such as mechanics, structural engineering, fluid-structure interaction, biomechanics, acoustics, embedded and hybrid multiphysics systems. The research in the field of experimental approaches to nonlinear dynamics and control is inherently multidisciplinary and requires an integrated approach to tackle the open problems. In particular, the following areas are worth highlighting: (i) novel experimental techniques to assess and enhance understanding of dynamical phenomena; (ii) experimental observations of new and complex dynamical phenomena in the broad area of nonlinear mechanical systems and structures; (iii) extraction/identification of reduced-order models of nonlinear systems (including hysteresis, impacts, and delays) via experimental data; (iv) experimental verification and validation of motion stabilization and control by using nonlinear effects; (v) experimental investigation of energy harvesting techniques that exploit nonlinear dynamical phenomena. This has led us to co-organize a Special Issue for the Journal of Vibration and Control in the broad field of experimental dynamics and control. The contributions span the rich diversity of the mentioned research areas and document state-of-the-art approaches and phenomena including studies that focus on nonlinear phenomenology to enhance the system performance and control strategies.