FORCED MOTION OF SEMI-INFINITE AND CIRCULAR PLATES OF LINEARLY VARYING THICKNESS

Abstract

Beams, plates, and shells of variable thickness are widely used in several engineering fields to achieve lightness with strength or sometimes to satisfy certain specific design requirements. Predicting the dynamic response of solids and structures to time dependent loads and/or boundary conditions is a task which occurs in many branches of engineering and applied science. Such problems arise from considerations as diverse as gust response of aircraft, earthquake response of tall buildings, vibration of machine part and shock response of electron tube filaments. The eigenfunction superposition or the modal expansion method has extensively been used in the past to solve the forced motion problems of beam, plates and shells, but its application has been restricted to structural elements of constant thickness only, because their exact, closed form free vibration solutions are obtainable. The eigenfunction superposition method has not yet been applied to structural elements of variable thickness. The non-applicability of the method to structural elements of variable thickness could be attributed to the fact that their exact free vibration mode shapes are not available, except for a very few particular cases and numerical methods give approximate mode shapes which do not form an orthogonal set. In this thesis an attempt has been made to apply the eigenfunction superposition method to solve forced motion problems of structural elements of variable thickness. The free vibration analysis is done by the Frobenius (power series) method. This being an exact method, gives mode shapes which remain orthogonal. Moreover, the integral involved in their orthogonality condition is evaluated with considerable ease. The validity of the method is tested by comparing the results obtained, as a particular case, for plates of constant thickness with analytical and previously published results. A very good agreement is found...