Linear and non‐linear problems of plate dynamics

Abstract

This paper presents a comparative analysis of linear and non‐linear problems of plate dynamics. By expressing the internal friction coefficient of the material by power polynomial γ= γ₀ + γ₁ϵ₀ + γ₂ϵ₀ ²+…, we assume γ= γ0 = const for a linear problem. When at least two polynomial terms are taken, a non‐linear problem is obtained. The calculations of resonance amplitudes of a rectangular plate yielded 3 per cent error: a linear problem yields a higher resonance amplitude. Using the Ritz method and the theory of complex numbers made the calculations. Similar methods of calculation can be used in solving the dynamic problems of thin‐walled vehicle structures.

First published online: 14 Oct 2010