TRANSVERSE VIBRATION OF A DAMAGED CIRCULAR ANNULAR PLATE WITH A FREE EDGE

Abstract The in-plane stick-slip vibration of two slider systems which are driven together around the surfaces of either side of a flexible vibrating disc, and the induced transverse vibration of the disc, are investigated. The disc is taken to be an elastic annular plate and each slider has flexibility in the circumferential (in-plane) and transverse directions. The static friction coefficient is assumed to be higher than the kinetic friction coefficient. Because of the friction force acting between the disc and the slider systems, the sliders will oscillate in the stick-slip mode in the plane of the disc. The transverse vibration induced by the oscillating sliders will change the normal forces of the slider systems acting on the disc, which in turn will change the in-plane oscillation of the sliders. Therefore, the in-plane oscillation of the sliders and the transverse vibration of the disc are coupled. For different values of system parameters, the coupled in-plane oscillation of the sliders and transverse vibration of the disc will exhibit quasi-periodic as well as chaotic behaviour. Typical patterns of chaotic vibration of the slider systems and of the disc are presented in graphs to illustrate the special behaviour of this non-smooth, nonlinear dynamical system. The physical model represents a car disc brakes.

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Transverse vibration analysis of composite thin annular plate by wave approach

Journal of Vibration and Control ◽

10.1177/1077546317732205 ◽

2017 ◽

Vol 24 (20) ◽

pp. 4661-4675 ◽

Cited By ~ 3

Author(s):

Wei Liu ◽

Donghua Wang ◽

Tongyang Li

Keyword(s):

Transverse Vibration ◽

Vibration Analysis ◽

Natural Frequencies ◽

Annular Plate ◽

Vibration Suppression ◽

Density Ratio ◽

Transmission Properties ◽

Wave Approach ◽

Reflection Matrix ◽

Propagation Matrix

In this paper, free vibration and transmission properties of single and composite thin annular plate (TAP) structures are presented by wave approach. The propagation matrix, continuity matrix and reflection matrix are introduced to carry out the analysis. Using the wave approach, natural frequencies of single and composite TAP are calculated theoretically. The results obtained by this method agree well with those calculated by the classical Bessel and Hankel methods. Additionally, transfer matrix is introduced and combined with the boundary conditions to obtain the transmission behaviors of composite multilayer TAP. To thoroughly understand the composite TAP, the influences of thickness, density ratio and radius ratio on natural frequencies are investigated. This study provides very useful information for transverse vibration suppression of TAP structure.

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Propagation of Transverse Wave for the Piezoelectric Radial Phononic Crystal Annular Plate in a Fibonacci Order

Shock and Vibration ◽

10.1155/2021/3905426 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Wei Liu ◽

Guangbin Yu

Keyword(s):

Transverse Wave ◽

Transverse Vibration ◽

Annular Plate ◽

Structural Parameters ◽

Phononic Crystal ◽

Stop Band ◽

Simulation Method ◽

Element Simulation ◽

Resonance Frequencies ◽

Theoretical Results

Based on the previous conventional phononic crystal (PC) structures infinitely periodic in Cartesian coordinates, this paper addresses a new radial phononic crystal annular plate (RPCAP) modeled in a Fibonacci order along the radial direction. In this study, piezoelectric material PZT4 is simultaneously inserted into this RPCAP model to investigate the stop band behaviors. In order to clearly show the transmission characteristics of transverse wave, in cylindrical coordinates, the transfer matrix is deduced through combining the general solutions, piezoelectric governing equations, and continuity conditions. Compared with conventional PC structures, transmission response of transverse vibration for the Fibonacci RPCAP model is calculated theoretically to analyze the stop band phenomenon. Finite element simulation method (FEM) is conducted here to verify the theoretical results. The results show that the Fibonacci RPCAP model presents two newly emerging resonance frequencies while the radial periodic order is disorganized. To thoroughly understand the RPCAP, the effects of structural parameters, material parameters, and piezoelectric parameters on the stop band are discussed in detail. The proposed Fibonacci RPCAP can be employed in many engineering applications, such as in rotating parts which are often coupled with transverse vibration (like gear driving systems).

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