The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface e...The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface effects is derived. The fractional integro-partial differential governing equation is first converted into a fractional-ordinary differential equation in the time domain using the Galerkin scheme. Thereafter, the set of nonlinear fractional time-dependent equations expressed in a state-space form is solved using the predictorcorrector method. Finally, the effects of initial displacement, fractional derivative order, viscoelasticity coefficient, surface parameters and thickness-to-length ratio on the nonlinear time response of simply-supported and clamped-free silicon viscoelastic nanobeams are investigated.展开更多
In nanoresonators,thermoelastic damping(TED)is a primary energy dissipation mechanism.As a result,when designing nanoresonators,it is critical to limit this type of dissipation.This paper investigates the nonlocal TED...In nanoresonators,thermoelastic damping(TED)is a primary energy dissipation mechanism.As a result,when designing nanoresonators,it is critical to limit this type of dissipation.This paper investigates the nonlocal TED of circular single-layered graphene sheet(SLGS)nanoresonators in axisymmetric out-of-plane vibration utilizing the generalized dual-phase-lag thermoelasticity theory.The nonlocal elasticity and Gurtin-Murdoch surface elasticity theories are employed to capture the small-scale and surface energy effects,respectively.By incorporating these effects into the model,the non-classical equations of the coupled thermoelastic problem are first obtained and then an analytical expression is introduced to predict TED in circular nanoplates.Moreover,the results obtained herein are validated by those of the classical continuum theory which can be found in the open literature.The influences of the aspect ratio,surface elastic modulus,surface residual stress and nonlocal parameter on TED of circular SLGS nanoresonators are investigated using numerical data.The calculated results show the significance of surface and nonlocal effects in nanoplate TED continuum modeling.展开更多
文摘The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface effects is derived. The fractional integro-partial differential governing equation is first converted into a fractional-ordinary differential equation in the time domain using the Galerkin scheme. Thereafter, the set of nonlinear fractional time-dependent equations expressed in a state-space form is solved using the predictorcorrector method. Finally, the effects of initial displacement, fractional derivative order, viscoelasticity coefficient, surface parameters and thickness-to-length ratio on the nonlinear time response of simply-supported and clamped-free silicon viscoelastic nanobeams are investigated.
文摘In nanoresonators,thermoelastic damping(TED)is a primary energy dissipation mechanism.As a result,when designing nanoresonators,it is critical to limit this type of dissipation.This paper investigates the nonlocal TED of circular single-layered graphene sheet(SLGS)nanoresonators in axisymmetric out-of-plane vibration utilizing the generalized dual-phase-lag thermoelasticity theory.The nonlocal elasticity and Gurtin-Murdoch surface elasticity theories are employed to capture the small-scale and surface energy effects,respectively.By incorporating these effects into the model,the non-classical equations of the coupled thermoelastic problem are first obtained and then an analytical expression is introduced to predict TED in circular nanoplates.Moreover,the results obtained herein are validated by those of the classical continuum theory which can be found in the open literature.The influences of the aspect ratio,surface elastic modulus,surface residual stress and nonlocal parameter on TED of circular SLGS nanoresonators are investigated using numerical data.The calculated results show the significance of surface and nonlocal effects in nanoplate TED continuum modeling.
