Avoiding/inducing dynamic buckling in a thermomechanically coupled plate: a local and global analysis of slow/fast response

Abstract

The nonlinear response of a reduced model of an orthotropic single-layered plate with thermomechanical coupling is investigated in the presence of thermal excitations, in addition to mechanical ones. Different issues are addressed via accurate and extended local and global analyses. (i) Assessing the possible occurrence, disappearance or modification of mechanical buckling as a result of thermal aspects; (ii) exploiting global dynamics to unveil the effects of coupling; (iii) highlighting the crucial role played by the slow thermal transient evolution in modifying the fast steady mechanical response; (iv) framing the influence of coupling and underlining the need to use a thermomechanical model to grasp the actual plate dynamics; and (v) getting hints of technical interest as to the outcome robustness with respect to variations in the external/internal thermal parameters.

Thermomechanical Coupling and Transient to Steady Global Dynamics of Orthotropic Plates

“…in terms of the nondimensional reduced variables W (deflection of the center of the plate), T R0 (membrane temperature) and T R1 (bending temperature). Coefficients a i j are defined in Settimi et al (2017) and Settimi et al (2018), while the thermal excitations are represented by the constant thermal difference between plate and environment T ∞ , and by the membrane and bending excitations e 0 and e 1 derived from body source thermal energies, whose distribution along the plate thickness is reported in Fig. 1.…”

“…To deeper investigate this aspect, and in order to detect the simplest model to be used to grasp the main thermomechanical features of the system response, it is of interest to develop a critical analysis of the various models derivable from the general system (1). To this aim, reference is made to an epoxy/carbon fiber composite plate of dimensions a = b = 1 m and h = 0.01 m. The relevant mechanical and thermal properties are reported in Settimi et al (2018), and furnish the following values of the equations coefficients: obtained in primary resonance conditions, which represents the most critical situation for an externally forced system, as a function of the precompression p and of the harmonic forcing amplitude f . With respect to the latter, preliminary analyses in presence of the sole mechanical excitations (Settimi et al, 2017) show the possibility to catch the main dynamical aspects of the system response also for low values of the amplitude f , which is therefore fixed to f = 1, and the ability of the precompression in inducing post-buckling behaviors for values higher than p = 2.52.…”

“…to more quickly provide its contribution into the mechanical equation thanks to the coupling termsā 15 orā 16 . Observing the linear thermal stiffnessesā 23 andā 32 , it results that the membrane temperature evolution is much slower than the bending one (ā 23 /ā 32 ∼ = 0.12), thus slowing down the influence of the membrane excitations (T ∞ and e 0 ) on the mechanical dynamics (Settimi et al, 2018). For these reasons, the model comparison is developed by considering the presence of a bending excitation e 1 with a linear variation along the thickness which reproduces a cooling of an external surface and an equivalent warming of the other.…”

“…However, more extended analyses conducted in the regime of full thermomechanical coupling have originated a meaningful set of outcomes where the much slower time scale over which thermal phenomena develop with respect to mechanical ones entails non-trivial steady effects on the structure overall response (Settimi et al, 2018). This influence has been highlighted by means of a systematic numerical investigation of the structure global dynamics, pursued through properly selected two-dimensional (2D) cross-sections of the actual 4D basins of attraction.…”

“…For the considered thermomechanically coupled plate, even in passive thermal regime global analysis has allowed to detect and understand a substantially different scenario of dynamic response occurring in specific mechanical conditions (i.e., vanishing mechanical stiffness) between coupled and uncoupled models, due to the meaningful role played in the former just by the slow transient evolution of the system thermal dynamics (Settimi et al, 2017). When considering also thermal excitations in addition to mechanical ones, these slow transient effects on the steady structural response are seen to be more pervasive and systematic, as highlighted by the comprehensive investigation in Settimi et al (2018).…”