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Planar harmonic Green function for periodic elastic strips

Danicki E.

Journal of Technical Physics

2007

Vol. 48, no 2

95-109

A system of periodic elastic strips (each one considered as a fragment of a plate) is characterized by a matrix relation between the Bloch series of displacements and stress at the bottom side of the system, which will remain in contact with the substrate supporting a propagating Rayleigh wave. The theory exploits the mechanical field representation in a spectral domain. It was found advantageous in formulation of the scattering problem for an elastic plate with stress-free cross-section, allowing us to apply ordinary boundary conditions instead of the variational ones. The result satisfies the energy conservation law with great accuracy, provided that sufficient number of complex modes are included in the solution. An algorithm is presented for modes evaluation; asymptotic properties of modes can be applied as well for higher modes. Perfect agreement of the proposed model with the experimentally verified perturbation model of thin strips is demonstrated.