Direct CAD based meshless analysis of piezoelectric resonators.

摘要

Finite element analysis is used extensively for analysis of piezoelectric resonators. Though effective and accurate, this method does have shortcomings when used to analyze piezoelectric resonators. Piezoelectric resonators typically have complex geometries and the mesh size (governed by the number of elements and degree of each element) required for analysis is usually very large. As a result, running out of memory for whilst trying to analyze some resonator structures is not unusual.; The electrodes of a piezoelectric resonator have very small thicknesses as compared to the dimensions of the resonator itself which complicates the analysis by creating elements with poor aspect ratios and also increases the number of elements. Hence using approximations for modeling of electrodes is often desirable when using finite element analysis. Three such electrode approximations, viz. merging, guyan reduction and lumping are studied in detail.; Typically finite element analysis is carried out in the following three steps: (i) Creation of a CAD model; (ii) Creation of a finite element mesh (meshing) from the CAD model; (iii) Numerical analysis.; The second step, meshing is not always convenient or possible. However, when the CAD model itself is analyzed, there is no requirement for a finite element mesh. With CAD software being commonplace, using this sort of analysis would further simplify analysis of piezoelectric resonators. Since this method lacks a mesh, it is a meshless problem; thus the interpolation functions have a greater degree of continuity throughout the problem domain, thereby further reducing the overall minimum memory requirement for successful analysis.; Using these concepts, Direct CAD based meshless analysis is implemented and used for analysis of various CAD models of piezoelectric resonators. The results obtained from CAD based analysis are compared with experimental results and results from conventional finite element analysis. Comparison is also made between the memory requirements of CAD based analysis and finite element analysis. It is seen that CAD based analysis provides very good results and requires less memory than conventional Finite Elements.