NONAXISYMMETRIC VIBRATIONS OF CYLINDRICAL SHELLS PARTIALLY FILLED WITH LIQUID
An algorithm is given for calculating frequencies and natural vibration modes of shells described in the title, taking into account the wave motion of the free surface. Boundary conditions corresponding to the elastic fastening of the cylinder's end rims are assumed. The solution is based on general integral equations of vibrations for a shell without liquid and on the method for solving Fredholm's equations of second kind with degenerate kernel. Numerical results are given for shells freely supported or rigidly clamped at both ends, and shells with one end being free and the other being clamped. Predictions are compared with experimental data.
We study the initial boundary value problem for the nonlinear viscoelastic wave equation with strong damping term and dispersive term. By introducing a family of potential wells we not only obtain the invariant sets, but also prove the existence and nonexistence of global weak solution under some conditions with low initial energy. Furthermore, we establish a blow-up result for certain solutions with arbitrary positive initial energy (high energy case)