On the non-linear response of piezoelectric slabs under weak electric fields: Experimental and analytical modelling

Abstract

Piezoceramic materials exhibit different types of non-linearities depending on the magnitude of the mechanical and electric field strength in the piezoelectric continuum. Some of the non-linearities observed under weak electric fields are the presence of superharmonics in the response spectra, jump phenomena, and so on, especially if the system is excited near resonance. In this article, an analytical solution (in the two-dimensional plane stress domain) for the non-linear response of a rectangular piezoceramic slab has been obtained by the use of Rayleigh—Ritz method and perturbation technique. The eigenfunction obtained from the solution of differential equations of the linear problem has been used as the shape function in the Rayleigh—Ritz method. Forced vibration experiments have been conducted on rectangular piezoceramic slabs of two different materials (e.g. PIC 181 and PIC 255) by applying varying electric field strengths across the thickness, and the displacement and current responses have been measured. Experiments have also been conducted for the first two free in-plane modes in the case of the piezoceramic PIC 181. Analytical solutions have been obtained by using the current formulations and they are found to compare well with those of the experiment. These solutions should serve as a method to validate the finite-element formulations as well as to help in the determination of non-linear material property coefficients for these materials.