Random vibration analysis of axially compressed cylindrical shells under turbulent boundary layer in a symplectic system

Abstract

A random vibration analysis of an axially compressed cylindrical shell under a turbulent boundary layer (TBL) is presented in the symplectic duality system. By expressing the cross power spectral density (PSD) of the TBL as a Fourier series in the axial and circumferential directions, the problem of structures excited by a random distributed pressure due to the TBL is reduced to solving the harmonic response function, which is the response of structures to a spatial and temporal harmonic pressure of unit magnitude. The governing differential equations of the axially compressed cylindrical shell are derived in the symplectic duality system, and then a symplectic eigenproblem is formed by using the method of separation of variables. Expanding the excitation vector and unknown state vector in symplectic space, decoupled governing equations are derived, and then the analytical solution can be obtained. In contrast to the modal decomposition method (MDM), the present method is formulated in the symplectic duality system and does not need modal truncation, and hence the computations are of high precision and efficiency. In numerical examples, harmonic response functions for the axially compressed cylindrical shell are studied, and a comparison is made with the MDM to verify the present method. Then, the random responses of the shell to the TBL are obtained by the present method, and the convergence problems induced by Fourier series expansion are discussed. Finally, influences of the axial compression on random responses are investigated.