On Forced Vibration in the Linear Theory of Micropolar Elasticity.
WATERVLIET ARSENAL N Y
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The present work is concerned with the problem of determining the dynamic response of a finite micropolar elastic body subject to time-dependent surface loads, body forces, and body moments. The general free vibration problem is formulated in terms of the displacements Mu sub i and the rotations Phi sub i. Assuming the existence of an infinite set of natural frequencies and eigenfunctions, the general orthogonality condition is derived. The solution of the general forced motion problem consists of a superposition of the quasi static and dynamic portions of the displacements, rotations, force stresses, and couple stresses. A convenient, simple expression for the generalized forces is developed on the basis of certain symmetry properties of the general theory of micropolar elasticity. As a specific example of this theory, the forced thickness-shear vibrations of an infinite plate are studied, and plots of frequencies, displacements, and stresses are given. Author