Vibrations of a cylindrical shell with longitudinal ribs not reaching its edges

Abstract

We will examine the harmonic vibrations of a circular cylindrical shell with hinged support at the edges. The shell is reinforced in the lengthwise direction by an irregular set of stiffening ribs which undergo flexural, torsional, and longitudinal deformation. The surveys [3, 4, 7] dealt with studies of the vibrations of cylindrical shells having rods of the same length as the shell. Below, we examine the case where the rods do not reach the edges of the shell. The contact problem is solved in order to calculate vibrations. The relationship between the displacements and forces on the contact lines is established by means of the Green's matrix of vibrations of the shell and Green's function of the vibrations of the rod. The kinematic displacement compatibility conditions for the shell and ribs are used to obtain a system of integral equations' for the contact forces and moments. This system has a kernel with a logarithmic singularity. To solve the system, the unknown functions are represented in the form of series in first-order Chebyshev polynomials with allowance for the singularities at the edges of the rods. The coefficients of the polynomials are determined by the collocation method.