Three-dimensional solutions for free vibrations of initially-stressed thermoelectroelastic multilayered plates Original Research Article

Analytic three-dimensional solutions are presented for the free vibration frequencies of initially stressed hybrid multilayered composite plates. The plates consist of a combination of fiber-reinforced cross-ply and piezothermoelastic layers. The initial stresses are generated by either a temperature change and/or an electric field. Sensitivity coefficients are also evaluated and used to study the sensitivity of the vibrational response to variations in the different mechanical, thermal and piezoelectric material properties of the plate. Both the temperature change and the electric field are assumed to be independent of the surface coordinates, but have arbitrary variation through the thickness of the plate. A linear constitutive model is used, and the material properties are assumed to be independent of both the temperature and the electric field. The thermoelectroelastic response of the plate is subjected to time-varying displacements, strains and stresses. A mixed formulation is used with the fundamental unknowns consisting of the three increments of the transverse stress components and the three displacement components. Each of the fundamental unknowns is expressed in terms of a double Fourier series in the Cartesian surface coordinates. A state space approach is used to generate the vibrational response and to evaluate the sensitivity coefficients. Approximate and closed-form expressions are developed relating the vibration frequency for the initially-stressed plate to the corresponding frequency of the unstressed plate. A nonlinear eigen-derivative theory is applied to obtain the sensitivity coefficients of the vibration frequency of the plate. Approximate expressions for the sensitivity coefficients are also derived. Extensive numerical results are presented showing the effects of variation in the plate thickness and the location of the piezothermoelastic layers on the vibration frequencies and their sensitivity coefficients.