Equivalent forces and wavenumber spectra of shaped piezoelectric actuators

ISSN： 0022-460X

Source： Journal of Sound and Vibration, Vol.187, Iss.1, 1995-10, pp. : 111-131

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Abstract

Uniformly polarized flat piezo-actuators of elementary shapes (e.g., rectangular, triangular, circular, elliptic, etc.) are analyzed in terms of their equivalent forces and wavenumber spectra to develop a basic understanding of the influence of actuator shape on the modal response characteristics of a flat plate. A general expression for the equivalent forces is derived and transformed into different co-ordinate systems depending on the actuator shape. Several general trends are noted. Piezoelectric actuators generate line moments along the boundaries of the actuator regardless of shape. The line moments are generally constant, with the exception of elliptic actuators. Transverse point forces exist at the corners of the actuators when the corner is not a right angle and the aspect ratio of the actuator is not unity. In addition to line moments, actuators with curved boundaries generate a transverse line force along the boundary. If the curvature of the boundary varies with angle (as for example in an elliptic actuator), the line moments and line forces will vary with angle. The wavenumber spectra of these shaped piezoelectric actuators surface-bonded to rectangular plates also show several general trends. Uniformly polarized piezo-actuators generally have a higher order mode coupling tendency irrespective of shape. This is primarily due to the line moment exerted along the boundaries and is more pronounced for smaller actuators. The wavenumber spectra of shaped piezo-actuators are generally dominated by line moments, except at low wavenumbers where the effect of the point and line forces become comparatively more pronounced.