Session: P2J

A novel Spectral Element (SE) is formulated to capture surface acoustic wave (SAW) in layered piezoelectric materials when subjected to mechanical loading or piezo-electrical actuation. Conventional modeling of layers by time domain Finite Elements (FEs) for wave propagation analysis requires solving large systems (as the element sizes should be approximately 8 elements per wavelength). This problem can be alleviated in SE method of solving hyperbolic partial differential equation. Here the equations are solved in transformed domain(s) and thereby reducing the number of independent variables to a point where the transformed equations can be solved exactly. For structural acoustics problem, this amounts to a numerical model with exact mass distribution. Consequently, a single element can represent a layer of any length. This results in a very small system sizes for the problem even in the case of structure with multiple layers. In the present work, the developed SE has two degrees of freedom per node corresponding to the displacements in the directions of the two coordinates of the plane considered for analysis. The governing equations for piezoelectric materials are first transformed in frequency domain. Then solutions for the displacements are sought in the form of summation over discrete wavenumbers in the two coordinate directions. The major difficulties of finding wavenumbers and wave amplitudes are solved by reformulating the whole problem in a new matrix structure and employing singular value decomposition of the pertinent matrix. Relations between interface tractions and interface displacements establish dynamic stiffness matrix which need to be solved for each frequency and wavenumber. Once the whole solution is obtained in transformed domain, the quantities of interest are obtained in time domain by employing the fast Fourier transform and Fourier series. The element is suitable for capturing surface waves as wel as interface waves generated by piezoelectric actuation. The element can be used both as sensor and actuator.