Development of the Flexible Ring on an Elastic Continuous Foundation Tire Model for Planar Vibration of the Heavy Load Radial Tire

This paper investigates the planar vibration characteristic of heavy load radial tires with a large flat ratio. A proposed tire model with a flexible ring on an elastic continuous foundation is investigated utilizing kinematic modeling and experimental modal analysis. Planar coupling deformation of the radial and tangential direction is considered to enrich the kinematic characteristic of the flexible belt and the continuous sidewall; a flexible ring on an elastic continuous foundation tire model is proposed to investigate the coupling vibration characteristic between the flexible belt and the continuous sidewall. In-extensibility assumption is utilized to simplify the proposed tire model and the planar vibration modal features of the heavy load radial tire are discussed. The variation of the inflation pressure on the radial and tangential stiffness of the sidewall spring model is enriched into the flexible ring on an elastic continuous foundation tire model to extend the modal prediction of the tires with a different inflation pressure. Taking the relative error between the experimental and analytical modal resonance frequency of the tested tire with a different inflation pressure as the object value, structural parameters of the proposed tire model are identified by a backward genetic algorithm. Experimental and theoretical results show that: the planar coupling vibration characteristic of the heavy load radial tire can be predicted precisely with the flexible ring on an elastic continuous foundation tire model; meanwhile, considering the linear variations of the radial and tangential sidewall stiffness due to the inflation pressure, the proposed tire model can be extended to analyze the vibration characteristic of the heavy load radial tire with a different inflation pressure.

A Linear Piezoelectric Linear Motor Driven by the in-Plane Longitudinal and Bending Vibrations of an H-Shaped Vibrator

In order to develop theoretical instructions for design of high performance linear motor, a piezoelectric linear motor based on an H-shaped vibrator is proposed, which employed the vibrator’s 2nd bending vibration mode and 1st longitudinal planar vibration to drive the motor in this paper. Firstly, the driving principle of the motor is presented, and the elliptical motion generated on the driving end of the vertical bars of the vibrator is proved. Then, FEM simulation model is built for the vibrator, which is used to calculate the vibrator’s working modes and to execute harmonic response analysis and sensitivity analysis for the vibrator. Furthermore, the vibration’s optimal size is given and the motor assembly structure is designed. Finally, modal test is done for the vibrator to validate the anticipated work modes vibration and the bending vibration and longitudinal planar vibration could be 1.4μm and1.2μm under normal drive.

Steady-State Transverse Response in Coupled Planar Vibration of Axially Moving Viscoelastic Beams

Steady-state periodical response is investigated for planar vibration of axially moving viscoelastic beams subjected external transverse loads. A model of the coupled planar vibration is established by introducing a coordinate transform. The model can reduce to two nonlinear models of transverse vibration. The finite difference scheme is developed to calculate steady-state response numerically. Numerical results demonstrate there are steady-state periodic responses in transverse vibration, and resonance occurs if the external load frequency approaches the linear natural frequencies. The effect of material parameters and excitation parameters on the amplitude of the steady-state responses are examined. Numerical results also indicate that the model of coupled vibration and two models of transverse vibration predict qualitatively the same tendencies with the changing parameters, and the two models of transverse vibration yield satisfactory results.