In this paper Fourier transform is used to derive the analytical solution of a Kirchhoff plate on a viscoelastic foundation subjected to harmonic circular loads. The solution is first given as a convolution of the Green’s function of the plate. Poles of the integrand in the integral representation of the solution are identified for different cases of the foundation damping and the load frequency. The theorem of residue is then utilized to evaluate the generalized integral of the frequency response function. A closed-form solution is obtained in terms of the Bessel and Hankel functions corresponding to the frequency response function of the plate under a harmonic circular load. The result is partially verified by comparing the static solution of a point source obtained in this paper to a well-known result. This analytical representation permits one to construct fast algorithms for parameter identification in pavement nondestructive test.
Dynamic Response of Kirchhoff Plate on a Viscoelastic Foundation to Harmonic Circular Loads
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, Jan. 25, 2000; final revision, Sept. 15, 2002. Associate Editor: V. K. Kinra. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Chair, Department of Mechanics and Environmental Engineering, University of California–Santa Barbara, Santa Barbara, CA 93106–5070, and will be accepted until four months after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Sun, L. (August 25, 2003). "Dynamic Response of Kirchhoff Plate on a Viscoelastic Foundation to Harmonic Circular Loads ." ASME. J. Appl. Mech. July 2003; 70(4): 595–600. https://doi.org/10.1115/1.1577598
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