Far-field approximation for a point-excited anisotropic plate

An analytic approximation is derived for the far-field response of a generally anisotropic plate to a time-harmonic point force acting normal to the plate. This approximation quantifies the directivity of the flexural wave field that propagates away from the force, which is expected to be useful in the design and testing of anisotropic plates. Derivation of the approximation begins with a two-dimensional Fourier transform of the flexural equation of motion. Inversion to the spatial domain is accomplished by contour integration over the radial component of wave number followed by an application of the method of stationary phase to integration over the circumferential component of wave number. The resulting approximation resembles that of an isotropic plate but involves wave numbers, wave amplitudes, and phases that depend on propagation angle. Numerical results for a plate comprised of bonded layers of a graphite-epoxy material illustrate the accuracy of the method compared to a numerical simulation based on discrete Fourier analysis. Three configurations are analyzed in which the relative angles of the layers are varied. In all cases, the agreement is quite good when the distance between force and observation point is greater than a few wavelengths.