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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]

An improved finite element modeling method is developed for isotropic curvilinearly stiffened plates under a thermal environment. The existing modeling method for curvilinearly stiffened plates avoids the difficulty of node overlap, which is suitable for plates with different thicknesses. By introducing the influence of temperature on material parameters and thermal stress on additional stiffness, the existing method is improved and extended to the study of thermodynamics. The proposed method is verified by modal test at normal temperature and commercial finite element software at the thermal environment. The variation of dynamic characteristics with temperature under different boundary conditions was studied. Results show that when the boundary conditions are asymmetric, the influence of temperature on the thermal mode shape is more significant than the case of symmetrical. [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]

In the modal test of lightweight structures, the measured data is easily polluted by mass loading effects of transducers. A method is proposed to eliminate the influence of sensors for accurately estimating the frequency response functions (FRFs) of structures. Considering the situation that the multiple accelerometers lead to changes in the dynamic stiffness matrix, the corrected FRFs are derived from the original measured signals based on the Sherman-Morrison-Woodbury formula. The salient feature of the proposed strategy is that the adverse effects of sensors can be eliminated in only one step. Numerical simulations are conducted by employing a six-degrees of freedom spring-mass system, modal frequencies and mode shapes with high accuracy are obtained by measured signals. Experimental investigation is undertaken by using a laboratory solar panel. Results show that the effects of multi-transducers mass can be removed efficiently and the corrected FRFs are in good agreement with the targeted values. The excitation and measurement points are regarded as active coordinates, and the computational efficiency can be significantly improved when the presented method is applied on active coordinates. [ABSTRACT FROM AUTHOR]