Dynamic behavior of thermoelastic solid continua using mathematical model derived based on non-classical continuum mechanics with internal rotations. (English) Zbl 1526.74030
Summary: This paper considers dynamic behavior of non-classical thermoelastic solid continua. The mathematical model consists of the conservation and balance laws of non-classical continuum mechanics that incorporates additional physics of internal rotations arising due to deformation gradient tensor. We consider plane stress behavior with small deformation, small strain physics only. Galerkin Method with Weak Form (GM/WF) in space is considered to construct a space-time decoupled finite element formulation giving rise to ordinary differential equations (ODEs) in time containing mass matrix, stiffness matrix due to classical as well as non-classical physics and acceleration and displacement associated with nodal degrees of freedom. This formulation is utilized to: (1) study natural undamped modes of vibration (2) study transient dynamic response by time integrating the ODEs in time (3) study the transient dynamic response by transforming the ODEs in time to modal basis using eigenvectors of the undamped natural modes. The ODEs in modal basis are used to construct transient dynamic response by time integrating them as well as by considering their analytical solutions. The solutions of the model problem obtained using the mathematical model based on non-classical continuum mechanics with internal rotations are presented and are compared with those obtained using the mathematical model based on classical continuum mechanics to demonstrate the influence of new physics due to internal rotations on the dynamic response of solid continua.
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74F05 | Thermal effects in solid mechanics |
| 74A35 | Polar materials |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
Lagrangian description; balance of moment of moments; natural vibration mode; normal mode synthesis; Galerkin finite element methodReferences:
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