Stress analysis of a viscoelastic solid of arbitrary cylindrical shape having a circular cavity and subject to internal vibration pressures

This paper is concerned with a method for solving stress problems of a viscoelastic solid of arbitrary shape with a circular cavity subjected to a vibration pressure along the cavity. In the analysis the exact solutions which satisfy the boundary conditions along the cavity have been derived from the equations of motion of elastic solids based on the two-dimensional theory of elasticity. The boundary conditions along the outer surface of arbitrary shape have been satisfied by means of the Fourier expansion collocation method. The analysis takes account of the viscoelasticity and the structural damping theory is used. As examples, stresses in the solids of circular, hexagonal, square, elliptical and truncated elliptical shapes have been calculated, and curves for the forced vibration response are presented.