A new perturbed multivariable finite element method with potential for DSAW computation in plates and layered solids

摘要

Based on extended Hamilton functional this paper constructs a new efficient yet accurate modified or perturbed multivariable electromechanical finite element method (FEM) with shift parameter and added potential for piezoelectric surface acoustic waves (PSAW) and disturbed surface acoustic waves (DSAW) with electrodes surface mounted, and investigates the numerical and comparative performances of p-type multi-variable plane strain, plate and generalized plane strain FEM. The shifted element methods are theoretically estimated a priori and numerically evaluated a posteriori. Incompatible modes are included and considered for generalized plate element methods. With the generality and validity discussed one new perturbed multivariable piezoelectric generalized plane strain FEM called PQ9 with potential is numerically found to be accurate and around 40% more efficient than traditional ones in multiplications and divisions, and will open possibilities of large-scale multi-periodic PSAW analysis, and save a huge amount of computer time and storage without losing assurance of accuracies. Although the shifted element matrices can indirectly lead to a small amount of spurious piezo-hardening for free vibrations and bulk acoustic waves, numerical examples about ST-cut crystal plate and plane element results show attractive merit and agreement with available analytical and test approaches for PSAW and DSAW studies.