BENCHMARK SOLUTIONS OF RANDOM VIBRATION RESPONSES FOR MODERATELY THICK CYLINDRICAL SHELLS UNDER STATIONARY/NONSTATIONARY EXCITATIONS

Cylindrical shell structures are frequently adopted in aerospace, ship, automobile and other engineering fields. Due to the complexity of service environments, cylindrical shells are unavoidably subjected to various random excitations, resulting in stochastic dynamic responses. Considering the moderately thick cylindrical shells with transverse shear deformation and moment of inertia effect, the pseudo excitation method is extended to the continuum structure, and the exact benchmark solutions of root mean squares of responses under various random excitations are efficiently obtained. Firstly, the exactly analytical natural frequencies and modal functions of moderately thick cylindrical shells with shear diaphragm boundary conditions are given. Then, according to the random excitation form, by using pseudo excitation method and mode superposition technique, the analytical and exact frequencies and modal functions and the constructed pseudo excitation are introduced into random vibration analysis. The power spectral density functions of stochastic responses of moderately thick cylindrical shells under stationary and nonstationary excitations are derived analytically, and the corresponding root mean squares are achieved via integration. The integral computation involves integration operations in the spatial, frequency and time domains. Analytical integration can obtain the closed-form exact solutions, while the difficulty and efficiency increase with increasing number of participated modes. To take full advantage of the merit of matrix operation of PEM, the discrete analytical method (DAM), with analytical spatial integral as well as numerical integral in the frequency and time domains, is proposed to obtain the exact stochastic responses of moderately thick cylindrical shells in closed and open forms. This procedure can ensure the accuracy of spatial integral, and efficiently obtain the exact distribution of random response, which provides the benchmark solutions for other numerical methods. Comparing the results with those of ABAQUS software and Monte Carlo simulation with as well as related literature illustrates the high accuracy and efficiency of the proposed DAM. Finally, the significant effects of ratio of thickness to radius, load distribution form, and time-modulated function on stochastic dynamic responses of cylindrical shell are revealed.