Generalized thermoelasticity model for thermoelastic damping in asymmetric vibrations of nonlocal tubular shells

Abstract

The present article intends to provide a size-dependent generalized thermoelasticity model and closed-form solution for thermoelastic damping (TED) in cylindrical nanoshells. With the aim of incorporating size effect within constitutive relations and heat conduction equation, nonlocal elasticity theory and Guyer–Krumhansl (GK) heat conduction model are exploited. Donnell–Mushtari–Vlasov (DMV) equations are also employed to model the cylindrical nanoshell. By adopting asymmetric simple harmonic form for oscillations of nanoshell and merging the motion, compatibility and heat conduction equations, the nonclassical frequency equation is extracted. By solving this eigenvalue problem and separating the real and imaginary parts of complex frequency analytically, an explicit expression is given to estimate the magnitude of TED in cylindrical nanoshells with arbitrary boundary conditions. Good agreement between the results of this study in special cases and those available in the literature affirms the validity of present formulation. In the following, for some vibration modes, a detailed parametric study is conducted to illuminate the determining role of structural and thermal nonlocal parameters in the amount of TED in simply-supported cylindrical nanoshells. The augmentation of difference between classical and nonclassical results by reduction in dimensions of nanoshell confirms the small-scale effect on TED value at nanoscales.