Hygro thermal vibration characteristics of an axisymmetric piezo electric functionally graded rod

The hygro thermo electro effects on the dispersion of functionally graded piezo electric rod are studied via three-dimensional elasticity equation in linear form. The stiffness and thermal conductivity of the material is considered to transport via radial coordinate. The motion equation is taken from the plain stress and strain form. The resulting partial differential equation is being solved to reach the coupled solution in Laplace domain. Developed power serious Matrix Frobonious method is employed to derive the analytical solutions. Dispersion relation is arrived via stress free initial and boundary conditions. The numerical results are presented to study the influence of hygro, thermal and piezo effects in the physical variables via grading values and moisture constants. The results are given as graphs. Table values are presented for validation.