Nonlinear waves in pantographic beams induced by transverse impulses

Turco, Emilio; Barchiesi, Emilio; Ciallella, Alessandro; Dell’Isola, Francesco

doi:10.1016/j.wavemoti.2022.103064

Cited by 11 publications

(1 citation statement)

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“…Additionally, it may serve as a preparatory step towards the establishment of a comprehensive thermo-mechanical formulation, a synthetic viewpoint to facilitate the proof of many mathematical theorems, and the theoretical basis for the application of modern numerical techniques like, for instance, the finite element method [30][31][32][33][34][35][36][37][38]. Variational principles are a widely accepted method of organizing information about dynamic systems and developing their evolution equations [7,[39][40][41][42][43][44][45][46]. By utilizing a singular quantity, such as the Lagrangian or Hamiltonian functional, one can deduce all aspects of a system, including its equations of motion, symmetries, and conservation laws.…”

Section: Introductionmentioning

confidence: 99%

A variational formulation for three-dimensional linear thermoelasticity with ‘thermal inertia’

Giorgio,

Placidi

2024

Meccanica

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A variational model has been developed to investigate the coupled thermo-mechanical response of a three-dimensional continuum. The linear Partial Differential Equations (PDEs) of this problem are already well-known in the literature. However, in this paper, we avoid the use of the second principle of thermodynamics, basing the formulation only on a proper definition (i) of kinematic descriptors (the displacement and the entropic displacement), (ii) of the action functional (with kinetic, internal and external energy functions) and (iii) of the Rayleigh dissipation function. Thus, a Hamilton–Rayleigh variational principle is formulated, and the cited PDEs have been derived with a set of proper Boundary Conditions (BCs). Besides, the Lagrangian variational perspective has been expanded to analyze linear irreversible processes by generalizing Biot’s formulation, namely, including thermal inertia in the kinetic energy definition. Specifically, this implies Cattaneo’s law for heat conduction, and the well-known Lord–Shulman model for thermo-elastic anisotropic bodies is then deduced. The developed variational framework is ideal for the perspective of analyzing the thermo-mechanical problems with micromorphic and/or higher-order gradient continuum models, where the deduction of a coherent system of PDEs and BCs is, on the one hand, not straightforward and, on the other hand, natural within the presented variational deduction.

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