<p>The motive of the current study is to derive the variational principle of convolutional type and a reciprocity theorem in the context of temperature rate dependent two temperature (TRDTT) piezothermoelasticity theory. This study offers a systematic and mathematically rigorous approach to understand the behavior of complex systems governed by multiple interacting fields. In this work, we consider a homogeneous, regular and anisotropic piezoelectric material. An alternative formulation has been done to recast the initial boundary value problem of the temperature rate dependent two temperature piezothermoelasticity to incorporate the initial conditions explicitly into the field equations. Utilising this alternative formulation, the derivation of variational principle of the convolution type is done. Later, a reciprocity theorem has been stated and derived by using the convolution type relations obtained.</p>

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On some reciprocity and variational theorems in the temperature rate dependent two temperature piezothermoelasticity theory

  • Anjali Srivastava,
  • Santwana Mukhopadhyay

摘要

The motive of the current study is to derive the variational principle of convolutional type and a reciprocity theorem in the context of temperature rate dependent two temperature (TRDTT) piezothermoelasticity theory. This study offers a systematic and mathematically rigorous approach to understand the behavior of complex systems governed by multiple interacting fields. In this work, we consider a homogeneous, regular and anisotropic piezoelectric material. An alternative formulation has been done to recast the initial boundary value problem of the temperature rate dependent two temperature piezothermoelasticity to incorporate the initial conditions explicitly into the field equations. Utilising this alternative formulation, the derivation of variational principle of the convolution type is done. Later, a reciprocity theorem has been stated and derived by using the convolution type relations obtained.