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The geometric nonlinearity due to static and thermal load can significantly alter the vibration response of structures. This study presents a semi-analytical approach to illustrate the nonlinear vibration of clamped-clamped beams under static and thermal loads. The von Karman strain and Hamilton's principle are employed to derive the nonlinear static equilibrium equation and nonlinear governing equation. The vibration equation's coefficient is variable. The transfer-matrix method and local homogenization are used to solve the equation. The proposed method's accuracy is validated by commercial software and literature. The numerical results indicate that uniform stress caused by thermal load only reduces the structural mode frequencies. The geometric nonlinearity of the structural static deformation affects both the mode frequencies and mode shapes. And the mode shapes cannot be approximated by harmonic functions. When the static deformation is significant, the structure's local RMS response is substantially affected. The combined loads have a more significant impact on the acceleration response than the superposition of individual load effects. [ABSTRACT FROM AUTHOR]

The effect of geometrical nonlinearities due to pressure load on the thermal buckling and dynamic characteristics of composite plates are investigated in this paper, which is the main contribution of this research work. The mechanical behavior of the plate is described with the first-order shear deformation theory. The geometrical nonlinearity due to both thermal effect and pressure load is introduced in the finite element model of the plate via additional stiffness matrices. Thermal buckling and modal analysis of a four-sided simply supported rectangular composite plate under different pressure fields are conducted. Numerical results show that both the mode frequencies and critical buckling temperature of the plate rise with the increase of the pressure. The vibrational mode shapes change with the gradient pressure load field. The maximum buckled deflection point moves from the center to the place where is easier to reach compressive stress state under uniform thermal load. The pressure distribution has a significant effect on the buckling mode shapes of the plate. [ABSTRACT FROM AUTHOR]

The effective numerical model of stitched sandwich composite plays crucial role in dynamics analysis and structural design. A sensitivity-based multistage model updating method is proposed for modeling of the stitched sandwich panel using the experimental modal frequencies. Based on applying the periodic boundary condition, the initial equivalent finite element model of a stitched sandwich composite is constructed; the measured frequencies are obtained from the modal test. According to relative sensitivity analysis of modal frequencies with respect to updating parameters, the different well-conditioned groups of parameters are selected to be updated. This method is applied to a stitched sandwich panel with established configuration of the stitches. Results show that the proposed method with the smallest condition number of relative sensitivity matrix has a better performance than the multistage method using type-based parameter group selection and the traditional model updating approach. [ABSTRACT FROM AUTHOR]

An algorithm that integrates Karhunen-Loeve expansion (KLE) and the finite element method (FEM) is proposed to perform non-stationary random vibration analysis of structures under excitations, represented by multiple random processes that are correlated in both time and spatial domains. In KLE, the auto-covariance functions of random excitations are discretized using orthogonal basis functions. The KLE for multiple correlated random excitations relies on expansions in terms of correlated sets of random variables reflecting the cross-covariance of the random processes. During the response calculations, the eigenfunctions of KLE used to represent excitations are applied as forcing functions to the structure. The proposed algorithm is applied to a 2DOF system, a 2D cantilever beam and a 3D aircraft wing under both stationary and non-stationary correlated random excitations. Two methods are adopted to obtain the structural responses: a) the modal method and b) the direct method. Both the methods provide the statistics of the dynamic response with sufficient accuracy. The structural responses under the same type of correlated random excitations are bounded by the response obtained by perfectly correlated and uncorrelated random excitations. The structural response increases with a decrease in the correlation length and with an increase in the correlation magnitude. The proposed methodology can be applied for the analysis of any complex structure under any type of random excitation. [ABSTRACT FROM AUTHOR]