Abstract
A formal approach is used to obtain two-dimensional differential equations (of infinite order) for dynamical problems in plates. It is assumed that the displacements may be expanded in power series in z, the thickness coordinate. These power series are substituted into the three-dimensional dynamical equations of linear elasticity. The coefficients of powers of z are equated to zero leading to an infinite sequence of differential equations which by formal manipulation are reduced to three differential equations of infinite order in which the midplane displacements are the dependent variables and x, y, t are the independent variables. It is shown how various special theories including the classical theories may be obtained from the general equations by making certain assumptions on the frequency and wavelength of the expected solutions. A short discussion of the solution of an initial value problem by means of the superposition of solutions of the various special theories is also given.
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