Semi-analytical investigation of nonlinear vibration of circular plates subjected to thermal parametric excitation

چکیده مقاله

An effective semi-analytical approach is presented in this study to investigate the nonlinear vi- bration of circular plates subjected to harmonic thermal load. The two-dimensional (2D) heat conduction equation for the plate is established and solved to obtain the 2D temperature distrib- ution. By employing the First-Order Shear Deformation Theory (FSDT) along with the von Kár- mán nonlinear assumptions, the geometric nonlinearity is incorporated into the strain relations, and the governing partial differential equations (PDEs) are derived using Hamilton's principle. A model reduction procedure is then carried out by using the Galerkin method to reduce these PDEs into a set of ordinary differential equations (ODEs). To compute the nonlinear responses, the Incremental Harmonic Balance (IHB) method is used. This method serves as an effective semi-analytical strategy to obtain the governing equations for the steady-state responses. The re- sulting non-linear algebraic equations are solved to plot the frequency-amplitude curve. The precision of the proposed procedure is confirmed by comparison the natural frequencies with numerical results presented in the literature. Besides, a convergence investigation is completed to determine the number of terms where are essential for the Fourier series expansion. The time history responses and phase portraits of the circular plate are also studied using the Newmark- beta method. The influence of several parameters on the frequency-amplitude curve and dy- namic response is also reported. The results demonstrate that the proposed semi-analytical tech- nique is an operative approach for a parametric study of the dynamic behavior of circular plates. Besides, the results show that key parameters such as boundary conditions, thickness-to-radius ratio, and temperature magnitude significantly influence the frequency-amplitude response. The analysis shows that increasing the excitation temperature significantly shifts the bifurcation points, which leads to the jump phenomenon and widens the resonance region.