Moment Impedance of Plates

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Abstract
The moment impedance of an infinitely extended plate is calculated with the use of plate equations that allow for transverse shear deformation and rotatory inertia. It is shown that the effects of transverse shear deformation may be important even for thin plates, a result that is not contained in classical theory. Classical theory is shown to be inadequate when the distance over which the moment is applied is smaller than plate thickness. The moment impedance for geometries of greatest practical interest is found to consist of a resistance connected in series with a stiffness reactance, both roughly inversely proportional to frequency, with the reactance of greater magnitude. Both the resistance and the reactance decrease with decreasing distance over which the moment is applied, because of the increasing importance of transverse shear flexibility. The practical implications of the results are discussed, and some thoughts are given concerning other problems where classical theory for flexural waves in thin plates may not be applicable.

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