Zhupanenko I. Analysis of thick plates and shells under dynamic effects

The numerical and analytical calculation procedure of determination of natural frequencies and modes and the dynamic unstable response of thick homogeneous isotropic linearly elastic variable-thickness plates and shells under dynamic effects is developed. The dynamic unstable response of the system is defined by the decomposition on free vibration modes technique for new discrete-continuum computation model. The procedure of determination of natural frequencies and modes is based on reduction of three-dimensional problem of elasticity theory to sequence of one-dimensional eigenvalue problems. The reduction of dimensionality of the problem has been realized with method of finite integral transforms and Fourier method. The reduced one-dimensional problems are solved numerically with step-by-step method. Efficiency and reliability of the procedure has been checked by solving of test problems. The calculation procedure has been applied to solve oscillations problems for the turbine disk, the tube of artillery weapon, the reactive stripe of free fall sideshow.