Multiphysical model of CMUT array based on modal decomposition and the Rayleigh integral

Abstract

There is a high number of modeling techniques for calculation of characteristics of capacitive micromachined ultrasound transducers. Very few of them are capable of calculation of the acoustic field, especially when the number of cells in the array is huge. Implementation of an approach based on superposition of modes and the Rayleigh integral is suggested. A computer model, utilizing this approach, also includes other methods for calculation of related parameters. A mass-spring-damper model is used to determine the lumped parameters and influence of the softening effect. Solution to a thin plate equation gives eigenfrequencies and eigenmodes used to find the membrane's response to an arbitrary excitation. For accurate evaluation of an acoustic field, the model discretizes normal velocity on a surface of the array. The array supports simple generation with individual phase shifts between the cells. The model is parametrized and adapted for an interface with user. An example object with specified physical and geometrical parameters is given. The key mechanical and acoustical characteristics are presented for the provided example object with a detailed description for their calculation. The model is verified by comparison to FEM within these characteristics. An acoustical study is conducted for an array with 4 example cells for two cases of phase shifts. The effectiveness of the proposed method in comparison with FEA is provided: in terms of time for following studies: lumped parameters, eigenvalues, frequency response (mechanical and acoustical) and radiation pattern; in terms of accuracy for a parametric lumped parameters study.