Nonlinear Propagation of Coupled First- and Second-Sound Waves in Thermoelastic Solids

  • A. Sellitto
  • V. A. CimmelliEmail author
  • D. Jou


We study coupled nonlinear first- and second-sound propagation along equilibrium and nonequilibrium states of a thermoelastic system undergoing small perturbations. We apply a nonlinear constitutive equation for the Cauchy stress and a nonlinear heat-transport equation ruling the evolution of the heat flux. Both of them account for relaxational and nonlinear effects, as well as for the coupling between strain tensor and heat flux. The speeds of thermomechanical waves are obtained, and we show that they depend on whether the waves are travelling along, or against, a superimposed constant heat flux.


First- and second-sound propagation Nonlinear effects Thermoelasticity Heat waves 

Mathematics Subject Classification

74D10 74A15 74B05 74J05 



Work performed under the auspices of the Italian National Group of Mathematical Physics (GNFM-INdAM) which supported the present research by means of “Progetto Giovani 2018/Heat-pulse propagation in FGMs”

A. Sellitto acknowledges the University of Salerno for the financial supports under grant no. 300395FRB18SELLI and grant “Fondo per il finanziamento iniziale dell’attività di ricerca”.

V.A. Cimmelli acknowledges the financial support of the University of Basilicata under grants Ricerca Autonoma 2012, RIL 2013 and RIL 2015.

D. Jou acknowledges the financial support of Ministerio de Economía y Competitividad of the Spanish Government under grant TEC2015-67462-C2-2-R.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Industrial EngineeringUniversity of SalernoFiscianoItaly
  2. 2.Department of Mathematics, Computer Science and EconomicsUniversity of BasilicataPotenzaItaly
  3. 3.Departament de FísicaUniversitat Autònoma de BarcelonaBellaterraSpain
  4. 4.Institut d’Estudis CatalansBarcelonaSpain

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