3D Solutions for Free Vibration of Initially Stressed Thermoelectroelastic Multilayered Cylinders

Abstract

Analytic three-dimensional solutions are presented for the free vibration problems of initially stressed hybrid multilayered composite circular cylindrical shells. The shells 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 shells. Both the temperature change and the radial component of the electric field are assumed to have uniform distribution in each layer of the shells. 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 shell is subjected to time-varying displacements, strains, and stresses, and the free vibration response is studied. A mixed formulation is used with the fundamental unknowns consisting of the increments of the three transverse stress components and the three displacement components of the shell. Each of the fundamental unknowns is expressed in terms of a double Fourier series in the axial and circumferential surface coordinates. A state space approach is used to generate the vibrational response and to evaluate the sensitivity coefficients. A sublayer method is used for evaluating vibration frequencies and their sensitivity coefficients. Numerical results are presented showing the effects of variation in the shell thickness, and the location of the piezothermoelastic layers on the vibration frequencies and their sensitivity coefficients.