Random Response Analysis Of Semispherical Shell With Calmped Edge

Semispherical shell is widely adopted in modern engineering structure, and those kinds of structures are always subjected stochastic excitations. So, the stochastic response problem of those shell structures is one of the key problems in modern structural engineering. This paper focused on random response problems of the semispherical shell with clamped edges, which is subjected several kinds of stochastic excitation. The researchs presented in this paper are limited in axisymmetric case, and the main contents of this paper are listed as below:First, based on the classical bending shell theory, the relationships of strain-stress, strain-displacement, and internal forces-strain of the elastic shell are presented in this paper. Then the equations governing the motion of the shell are derived by means of the Hamilton principle. And the partial deviation equations (PDE) governing the axisymmetric free vibration of the semispherical shell are obtained. Then the natural frequencies and the corresponding natural mode functions of the shell with its boundary conditions are gained by numerical computation.Secondly, the semispherical shell response problem is reduced into its equivalent discrete one by mode theory. The decoupled equations of the general coordinates are derived and its general solutions are gained. The Impulse Response Function (IRF) of the system under distributed normal load is obtained by modal analysis method. And the shell responses under several deterministic excitations are calculated through the Duhamel integral.At last, the IRF and the Frequency Response Functions of the shell under several kinds of distributed loads are presented. The stationary Mean Square Response (MSR) of the shell to a uniform normal white noise load, and the transient Mean Square Response of the shell while the load mentioned above was suddenly applied are all presented in this paper. At last, the MSR of the shell under a single-point white noise excitation, which is applied on the pole point of the shell, is calculated.