Effect of surface stresses on the dynamic behavior of bi-directional functionally graded nonlocal strain gradient nanobeams via generalized differential quadrature rule

In this article, a first-order shear deformable model is expanded based on the nonlocal strain gradient theory to vibration analysis of smart nanostructures under different boundary conditions. The governing equations of motion of rotating magneto-viscoelastic functionally graded cylindrical nanoshell in the magnetic field and corresponding boundary conditions are obtained using Hamilton’s principle. To discretize the equations of motion, the generalized differential quadrature method is applied. The aim of this work is to investigate the effects of the temperature changes, nonlocal parameter, material length scale, viscoelastic coefficient, various boundary conditions, and the rotational speed of this smart structure on natural frequencies of rotating cylindrical nanoshell made of magneto-viscoelastic functionally graded material.

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Nonlinear semi-analytical nonlocal strain-gradient dynamic response investigation of phase-transition-induced transversely graded hierarchical viscoelastic nano/microplates

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406219846145 ◽

2019 ◽

Vol 233 (15) ◽

pp. 5388-5409 ◽

Cited By ~ 1

Author(s):

M Shariyat ◽

F Farrokhi

Keyword(s):

Strain Gradient ◽

Viscoelastic Model ◽

Functionally Graded ◽

Special Technique ◽

Stress And Strain ◽

Transient Vibration ◽

Size Dependent ◽

Integration Schemes ◽

Series Type ◽

Nonlocal Strain Gradient

A functionally graded Boltzmann hierarchical viscoelastic model with both stress- and strain-gradient nonlocalities is developed and implemented to extract results that are more precise than results of Eringen's nonlocal elasticity model. The available size-dependent vibration analyses of the nano/microplates have focused on the frequency analysis and even not the time-dependent transient vibration analyses. In the present research, the forced and transient responses of the microplates are studied comprehensively, for the first time, using a three-element standard solid viscoelastic model. The studied transversely symmetric graded viscoelastic microplate and the relevant function of the material properties variations contain notable hints as well. Furthermore, the resulting new sixth-order nonlocal strain gradient integrodifferential equations are solved by a special technique that includes an analytical spatial Navier series-type solution and a trapezoidal and Runge–Kutta integration schemes, in time domain. Finally, the influences of the stress- and strain-gradient nonlocality parameters and the viscoelasticity parameters on the dynamic behaviors of the viscoelastic FGM microplates are investigated in details. Results show that the effects of the strain gradient nonlocality on the viscodynamic results may be much remarkable than those of the length scale nonlocality, in microscales.

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