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

Valeria Settimi,Giuseppe Rega,Eduardo Saetta

doi:10.1007/s11012-019-01117-w

Valeria Settimi, Giuseppe Rega + Show 1 more

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https://doi.org/10.1007/s11012-019-01117-w

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Journal: Meccanica	Publication Date: Feb 10, 2020
Citations: 7	License type: cc-by

Affiliation: Sapienza University of Rome

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Thermoelastic analysis of a shear deformable reduced model of laminated plates with von Karman nonlinearities and cubic temperature along the thickness is presented. Parametric investigation of the response is accomplished by means of bifurcation diagrams, phase portraits and planar cross sections of the four-dimensional basins of attraction, in order to describe the local and global dynamical behavior of the model. Different scenarios induced by the boundary conditions are highlighted, along with the effect of a different modeling of temperature distribution (constant/dome-shape) on the system response.The effects of diverse (boundary/body) thermal sources are also comparatively explored. In all examined cases, proper consideration of system global dynamics is shown to be essential for reliably unveiling transient to steady effects due to thermomechanical coupling.

Highlights

Investigation of the effects of thermomechanical coupling on the response of materials and structures in a nonlinear dynamic environment is a research topic of major interest, in connection with the increased importance of multiphysics phenomena occurring in a variety of technological contexts, which range from aerospace engineering, to civil engineering, up to micro-electro-mechanics
The behavior of a reduced model of third order shear deformable single-layer orthotropic plate with thermomechanical coupling is investigated in terms of local and global dynamics
From the shear indeformable model with linear temperature distribution along the thickness analyzed in [28, 29], the temperature evolution described with the cubic function allows the present model to account for a variety of different thermal boundary conditions, as well as to critically discuss the effect of the assumed temperature functions on the overall response of the model

Summary

Introduction

Investigation of the effects of thermomechanical coupling on the response of materials and structures in a nonlinear dynamic environment is a research topic of major interest, in connection with the increased importance of multiphysics phenomena occurring in a variety of technological contexts, which range from aerospace engineering, to civil engineering, up to micro-electro-mechanics. Still in the two-way thermomechanical coupling perspective, a minimal reduced model of shearindeformable composite plate with von Karman 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.

Thermomechanical models

Free heat exchange between plate and environment

Constant prescribed temperature on the external surfaces of the plate

Effect of a different temperature function on the outer surfaces

Effect of an equivalent internal thermal source

Conclusions