Thermomechanical Coupling and Transient to Steady Global Dynamics of Orthotropic Plates

Abstract

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Nonlinear dynamics of a third-order reduced model of thermomechanically coupled plate under different thermal excitations

“…However, for a thin plate here considered, the two models prove to furnish essentially the same dynamical response, in terms of both local and global dynamics behavior. Thus, this section summarizes the main dynamical features high- lighted in the previous works [28,29,30], to refer to for all details.…”

“…The formulation ends up as three coupled nonlinear, nondimensional ordinary differential equations (ODEs). Thanks to the richness and flexibility of the underlying continuum formulation, the model allows to account for a variety of thermomechanical assumptions, excitations and boundary conditions, thus representing a substantial improvement of the thermomechanical model previously investigated by the authors in the nonlinear dynamics regime [28,29,30], characterized by shear indeformability and linear temperature variation along the thickness (CTC model). As regards the mechanical aspect, in the present investigations we consider a simply supported plate, with movable edges subjected to uniform stretching forces of magnitudes p x = p y = p in x and y direction, and transversal resonant harmonic forcing (Fig.…”

“…2(a), while the coupled system displays an (almost) monostable behavior, with the presence of the sole pre-buckling solution (gray) basin, suggesting the inability of the thermal boundary condition to induce mechanical buckling. As exten-sively discussed in [29,30], this discrepancy is due to the long transient needed by the thermal variables to attain their steady values, which provides a slow contribution to the mechanical stiffness responsible for the buckling occurrence. As a consequence, the mechanical response, which has a much quicker dynamics, settles at its first steps of the temporal evolution to the sole stable solution depicted by the system in the pre-buckling regime, i.e.…”

“…Still in the two-way thermomechanical coupling perspective, a minimal reduced model of shear-indeformable composite plate with von Kármán nonlinearities and assumed linear temperature distribution along the thickness, with one mechanical and two thermal generalized variables, labelled CTC [1], has been used for a systematic investigation of the general features of local and global response, under either passive [28] or active [29,30] thermal conditions. In the latter case, depending on the kind of considered thermal excitation (of either membrane or bending nature), local bifurcation analysis of thermomechanically coupled response has highlighted a quite variable and involved transition from monostable to multistable dynamics, with the latter exhibiting a variety of buckled solutions [31] to be possibly avoided or induced via thermal excitation.…”

Unveiling Transient to Steady Effects in Reduced Order Models of Thermomechanical Plates via Global Dynamics

“…Reduced order modeling and nonlinear dynamics of composite plates under different excitation conditions in a thermomechanical environment have been the subject of recent papers aimed at highlighting the role of multiphysics coupling and the main local and global features of the nonlinear response [1][2][3][4][5].…”