Subharmonic resonance for in-plane motion of orthotropic plates under linear loads

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (15) : 163-171.

HU Yuda1,2, ZHANG Xiaoyu1,2,HAO Ying1,2

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Abstract

Here, subharmonic resonance problems for in-plane motion of orthotropic plates under linear loads were studied.The kinetic and potential energy expressions for in-plane motion of an orthogonal plate were derived and nonlinear vibration equations of an orthotropic strip-shaped plate with geometric nonlinearity were deduced.Under simply supported boundary conditions, considering the first three order modes and using Galerkin integral method, a non-dimensional Duffing nonlinear vibration differential equation system with respect to time variables was deduced.The subharmonic resonance problem of this nonlinear system was solved using the multi-scale method to acquire resonant amplitude equations for different order modes of steady-state response solution.Lyapunov stability theory was applied to analyze solution stability, and obtain the steady-state solution’s stability discriminant.The amplitude characteristics variation curves were obtained with numerical examples.Effects of parameters, such as, velocity, linear load and material properties on the system’s resonance characteristics were analyzed.The results showed that the system reveals more obvious nonlinear resonance characteristics.

Key words

Orthotropic plates / subharmonic resonance / In-plane exercise / linear load / multiple scales method

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HU Yuda1,2, ZHANG Xiaoyu1,2,HAO Ying1,2. Subharmonic resonance for in-plane motion of orthotropic plates under linear loads[J]. Journal of Vibration and Shock, 2019, 38(15): 163-171

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