LINEAR AND NON-LINEAR PROBLEMS OF PLATE DYNAMICS

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 gamma = gamma(0) + gamma(1) epsilon(0) + gamma(2) epsilon(2)(0) +... ,we assume gamma = gamma(0) = 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.