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Research Papers

Evaluation of Planar Harmonic Impedance for Periodic Elastic Strips of Rectangular Cross Section by Plate Mode Expansion

[+] Author and Article Information
Eugene J. Danicki

 Polish Academy of Science, 21 Świȩtokrzyska Street, Warsaw 00-049, Polandedanicki@ippt.gov.pl

J. Appl. Mech 75(4), 041011 (May 14, 2008) (6 pages) doi:10.1115/1.2912931 History: Received February 22, 2007; Revised February 25, 2008; Published May 14, 2008

A system of periodic elastic strips (each one considered as a piece of a plate) is characterized by a matrix relation between the Bloch series of displacement and traction at the bottom side of the system. Both these mechanical fields are involved in the boundary conditions at the contact plane between the strips and the substrate supporting a Rayleigh wave. The analysis exploits the mechanical field expansion over the plate modes, including complex modes; numerical results satisfy the energy conservation law satisfactorily. The derived planar harmonic Green’s function provides an alternative tool for investigation of surface waves propagation under periodic elastic strips, with respect to pure numerical methods mostly applied in the surface acoustic wave devices literature. Perfect agreement of the presented theory with the experimentally verified perturbation model of thin strips is demonstrated.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

An interdigital transducer comprising a number of periodic strips on a substrate. A piece of plate modeling the strip is shown at the right.

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Figure 2

(a Distribution of the modal wave numbers on the complex p-plane and their asymptotic approximation (circles). (b) Zero lines of real and imaginary parts of det{D} on the p-plane (thick and thin lines, respectively); pm reside at their intersections.

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Figure 4

Dependence of the diagonal elements of the lowest Bloch cells of H on strip thickness d (there is a resonance at d≈0.19λt). Inset: The dependence of H on r nicely compares to the perturbation theory prediction.

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Figure 3

A contour map of the matrix ∣T∣—its characteristic V-like shape (shown upside down) indicates a localized spectrum dependence on the modal number; the spectra of 183rd and 91st modes are drawn in thick lines. Thin frame shows the truncated spectrum.

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