Modeling and analysis of shear-induced flexural vibrations of annular piezoceramic actuators

Piezoceramic materials are widely used in solid-state actuators and sensors. Since the shear piezoelectric coupling coefficient {d}₁₅ is much higher than the other piezoelectric coefficients {d}₃₁ or {d}₃₃ , the application of shear actuators is of particular interest. Shear-induced vibrations in piezoceramics are more complex to describe mathematically than longitudinal or transverse vibrations. Furthermore, as the complexity of the model increases, the coupling of electrical and mechanical terms precludes the analytical solution of the field equations for all but the simplest case. For a moderately complex piezoceramic model, the implementation of an analytical method to obtain the closed-form solution is very challenging. The use of approximate energy methods, such as the Rayleigh–Ritz method, is explored in this work to obtain the eigenvectors and eigenfrequencies for annular piezoceramic actuators. Series comprising orthogonal polynomial functions, generated using the Gram–Schmidt method, is used in the Rayleigh–Ritz method to formulate the linear eigenvalue problem. The advantage of the presented methodology lies in its adaptability for software implementation, which reduces the efforts to obtain fairly accurate results for more complex piezoceramic structures in future. The efficacy of the presented approximate method is assessed by comparing the results with the experiments.