6533b82efe1ef96bd129323a

RESEARCH PRODUCT

A bending theory of thermoelastic diffusion plates based on Green-Naghdi theory

Vincenzo TibulloMoncef AouadiFrancesca Passarella

subject

Bending thermoelastic diffusion platesFOS: Physical sciencesGeneral Physics and Astronomy02 engineering and technologyAsymptotic behavior; Bending thermoelastic diffusion plates; Green-Naghdi theory; Impossibility of the localization in time; Spatial decay; Well-posednessMathematics - Analysis of PDEsThermoelastic damping0203 mechanical engineeringFOS: MathematicsGeneral Materials ScienceUniquenessMathematical PhysicsMathematicsThermodynamic processGreen-Naghdi theorySemigroupSpatial decayMechanical EngineeringMathematical analysisMathematical Physics (math-ph)Dissipation021001 nanoscience & nanotechnologyAsymptotic behaviorExponential function020303 mechanical engineering & transportsClassical mechanicsShear (geology)Well-posednessMechanics of MaterialsPlate theory0210 nano-technologyImpossibility of the localization in timeAnalysis of PDEs (math.AP)

description

Abstract This article is concerned with bending plate theory for thermoelastic diffusion materials under Green-Naghdi theory. First, we present the basic equations which characterize the bending of thin thermoelastic diffusion plates for type II and III models. The theory allows for the effect of transverse shear deformation without any shear correction factor, and permits the propagation of waves at a finite speed without energy dissipation for type II model and with energy dissipation for type III model. By the semigroup theory of linear operators, we prove the well-posedness of the both models and the asymptotic behavior of the solutions of type III model. For unbounded plate of type III model, we prove that a measure associated with the thermodynamic process decays faster than an exponential of a polynomial of second degree. Finally, we investigate the impossibility of the localization in time of solutions. The main idea to prove this result is to show the uniqueness of solutions for the backward in-time problem.

yearjournalcountryeditionlanguage
2017-09-01
10.1016/j.euromechsol.2017.03.001http://hdl.handle.net/11386/4688908