Thermal Buckling And Thermal Vibration Of Beams And Plates With Stick-Slip-Stop Boundaries

Aerospace structures are often subject to aerodynamic and/or solar radiation heating, which will induce thermal stresses in structures because of boundary constraints and/or temperature gradients. Once the thermal stresses are large enough, thermal buckling will occur and may result in the reduction of the load-carrying capacity or even the failure of structure. Moreover, the high temperature also degrades material properties. As a result, the combination of thermal stresses and the degradation of material properties will change the structural stiffness and have significant influences on the natural vibration characteristics of the structures. In order to improve the performance of thermal stability of structures, the boundaries of structures are often designed to be able to move so as to release some stresses. A simple mechanical assembly for this purpose is to preserve clearances between adjacent components. Obviously, the excessive thermal expansion is still confined by adjacent components. Besides, there are normal forces exerted on the edges for assembly purposes. Hence, the sliding edges are subject to a pair of normal force and frictional force that they may go through a stick state, a slip state and a stop state as the temperature increases, i.e., the thermal structure has stick-slip-stop boundaries.The normal forces and clearances have influences on the states of the sliding edges, and the slipping of the sliding edges due to temperature rise will change the thermal stresses and influence the dynamics charateristics. Therefore, it is necessary to investigate the influences of normal forces and clearances on the thermal buckling and dynamics characteristics of structures.As beams and plates are basic elements in aerospace structures, this dissertation focuses on thermal buckling and dynamics problems concerning both slender beams and rectangular thin plates with stick-slip-stop boundaries.The main themes and contributions of the dissertation can be summarized as follows.(1) The physical models of slender beams and rectangular thin plates considering normal forces and clearances are presented. The Hamilton’s principle and principle of virtutal displacement are utilized to obtain the governing equations and constraint equations for beams and plates with sliding edges, respectively.(2) A detailed study is carried out on the thermal buckling, postbuckling and natural vibration in the pre/post buckling regime for the slender beam with an axial stick-slip-stop boundary. Both temperature-dependent material properties and sliding frictional coefficient are taken into consideration. For each case, the explicit equations are derived for the critical buckling temperature rise, deflections of postbuckling, and the natural frequencies in pre/post buckling regime. Then, some numerical results are presented to show the influences of system parameters on the critical buckling temperature rise, deflections of postbuckling and the natural vibration characteristics of the beam.(3) The thermal buckling behavior and natural vibration characteristics of a rectangular thin plate with in-plane stick-slip-stop boundaries are investigated. Both temperature-dependent material properties and friction coefficients are considered and the buckling temperature rise and natural frequencies are presented for each situation. The derived analytical results are verified by finite element software Nastran. Moreover, some parametric studies are made to reveal the influences of both normal forces and clearances of thermal expansion on the critical buckling temperature rise and the natural frequencies of the rectangular thin plate.(4) A study is presented for the primary resonance of lateral vibration of the slender beam with an axial stick-slip-stop boundary and under both uniformly distributed heating and harmonic loads. Firstly, Galerkin’s approach is employed to simplify the partial differential equations to a set of ordinary differential equations. Then, the average approach is used to derive the steady-state primary resonance for each case. Finally, the analytical solutions are well verified through the direct numerical integration and the influences of system parameters, such as the temperature rise and normal force, on the steady-state primary resonance of lateral vibration of the beam.(5) Furthermore, the analysis is given for the nonlinear dynamics of a rectangular thin plate in the presence of 1:1 internal resonance due to in-plane stick-slip-stop boundaries. The conditions are first derived for 1:1 internal resonance between the first two modes of the plate. Subsequently, Galerkin’s approach is implemented to obtain the governing equations for the first two modes of the plate, which can be numerically solved via the Runge-Kutta method. Then, the bifurcation diagram, Poincaré maps and phase portraits are used to demonstrate the nonlinear dynamics behavior of the rectangular thin plate.(6) Finally, random vibration responses of the rectangular thin plate with in-plane stick-slip-stop boundaries are investiaged under a uniformly distributed excitation of stationary white-Gaussian. Galerkin’s approach is utilized to derive multi-mode governing equations, which are solved via the direct numerical integration. Moreover, parametric studies are made to investigate the influences of system parameters on the random responses of the plate.