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Finite element for dynamic analysis of a C-shape piezoelectric actuator

A.N.Mtawa, W.Mwita

A Finite element model based on the Euler-Bernoulli theory was developed and used to investigate the dynamic behaviour of a C-shape piezoelectric actuator subjected to sinusoidal voltage. The main goal of this study was to develop and validate numerical analysis tools for semicircular shape piezoelectric devices. Once validated for a simple configuration the results can ultimately be extended for more complicated geometries and be helpful in the optimization of the design of curved shape piezoelectric actuators. The dynamic solutions for a free and forced undamped piezoelectric actuator were obtained using a modal analysis method. For the verification of finite element formulation, a MATLAB code was developed to aid in the computation of the fundamental frequency and the corresponding normal mode of a four elements model. The results have been validated by comparing them with published data. The general purpose Finite Element software MSC Marc was also used to simulate the first 3 natural frequencies and their respective mode shapes as well as locating the resonance points for three actuators from three different substrate materials and for three different substrate/Piezoceramic thickness ratios. Results show that an increase of both substrate to piezoceramic thickness ratio and the elastic modulus of the substrate contributed to raise the fundamental frequency of the actuator. It was also found that an actuator with mild steel substrate operated at higher frequencies compared with the aluminium and brass substrates of the same thickness.