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The present paper is devoted to the study of phase velocity and attenuation of longitudinal shear vibrations of hollow poroelastic circular cylinders in the presence of dissipation. The explicit expressions for phase velocity and attenuation of longitudinal shear vibrations are derived. The frequency equation of longitudinal shear vibrations and modes obtained in a previous paper are used to compute the phase velocity and attenuation for different dissipations for thin and thick poroelastic cylindrical shells and poroelastic solid cylinder. The physical parameters of sandstone saturated with kerosene and sandstone saturated with water are used for the purpose of computation. It is found that the phase velocity is linear beyond certain frequency. Phase velocity is smaller for a typical anti-symmetric mode compared to the flexural mode. It is greater for the second mode than that of the first mode. Also the phase velocity is larger for a thin poroelastic cylindrical shell than that of a thick poroelastic cylindrical shell. The same is true for attenuation also. Attenuation is very high for the considered dissipations and it increases with the increase in dissipation.

In this paper, Free vibration analysis of a finite length composite shell panel with an embedded piezoelectric sensor, using three-dimensional elasticity solution, is presented. To this end, two different methods are applied to solve the governing equations of the problem. In the first method, the displacement field is derived using trigonometric function expansion in circumferential and longitudinal directions. Using the method of changing variables, the governing partial differential equations are reduced to ordinary differential equations. Then these equations are solved simultaneously with outer and inner boundary conditions to give the natural frequencies and shape modes of the shell panel. In the second method the highly coupled partial differential equations are reduced to ordinary differential equations by means of trigonometric function expansion in circumferential and axial directions and then the finite difference method is applied to evaluate the obtained differential equations in radial direction. Then, the natural frequencies of the multi-layered panel are calculated using the obtained ordinary differential equations. At last, some numerical examples are presented to compare the results obtained by these two different methods. Three layered laminated shell panel is assumed to be [0/90/P].