Direct Multiscale Analysis of Transverse Vibrations for an Axially Accelerating Orthotropic Plate


The stability is investigated for transverse vibration of an axially moving orthotropic plate under in-plane loading. the axially moving velocity is assumed as small periodic variation about a constant value. the governing equation of the system is obtained by Hamilton's principle and then the method of multiple scales is applied directly to the governing partial differential equation without truncation. Based on the solvability condition derived from eliminating secular terms, the stability boundaries are obtained for the change of frequency and amplitude of speed variation in the cases of subharmonic resonance and combination resonance. Numerical examples are presented to show the contributions of axially moving speed and excitation magnitude to the stability boundaries. Furthermore, the critical axially moving speed where instability range becomes minimum is found for both the subharmonic and combination resonance.


Mechanical and Aerospace Engineering

Keywords and Phrases

Combination Resonance; Method of Multiple Scales; Orthotropic Plate; Subharmonic Resonance

Document Type

Article - Journal

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© 2010 Jixie Gongyebu, Zhengzhou Jixie Yanjiusuo, All rights reserved.

Publication Date

01 Jan 2010

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