Anelastic Waves in Thin Plates
In investigating small displacements and the resulting state of stress in thin plates or shells obeying a linear stress-strain law, the three-dimensional problem is reduced to a two-dimensional one by means of a hypothesis concerning the distribution of the relevant geometric and mechanical quantities along the thickness of the shell or plate. The simplest hypothesis in bending is the Kirchhoff hypothesis, while for the motion “in the xy plane” it is usually assumed that a plane state of stress prevails. However, in the case of high frequencies and short wave lengths, particularly in the case of anelastic materials the equations of which contain higher time derivatives, the above assumptions are incorrect and it is necessary to establish a system of equations taking into account additional phenomena, such as rotary inertia, shear displacement, etc. This is done by changing the hypothesis or employing a method of successive approximations.
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