Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams

In the present article, wave dispersion behavior of a temperature-dependent functionally graded (FG) nanobeam undergoing rotation subjected to thermal loading is investigated according to nonlocal strain gradient theory, in which the stress enumerates for both nonlocal stress field and the strain gradient stress field. Mori–Tanaka distribution model is considered to express the gradual variation of material properties across the thickness. The governing equations are derived as a function of axial force due to centrifugal stiffening and displacements by applying Hamilton’s principle according to Euler–Bernoulli beam theory. By applying an analytical solution, the dispersion relations of rotating FG nanobeam are obtained by solving an eigenvalue problem. Obviously, numerical results indicate that various parameters such as angular velocity, gradient index, temperature change, wave number, and nonlocality parameter have significant influences on the wave characteristics of rotating FG nanobeams. Hence, the results of this research can provide useful information for the next generation studies and accurate design of nanomachines including nanoscale molecular bearings and nanogears, etc.     

Hygrothermal effects on static stability of embedded single-layer graphene sheets based on nonlocal strain gradient elasticity theory

Abstract

This article develops a nonlocal strain gradient plate model for buckling analysis of graphene sheets under hygrothermal environments. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. Graphene sheet is modeled via a two-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient graphene sheet on elastic substrate are derived via Hamilton’s principle. Galerkin’s method is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as moisture concentration rise, temperature rise, nonlocal parameter, length scale parameter, elastic foundation and geometrical parameters on buckling characteristics a graphene sheets are examined.     

Thermal dynamic buckling of temperature-dependent sandwich nanocomposite quadrilateral microplates using visco-higher order nonlocal strain gradient theory

This research deals with the nonlocal temperature-dependent dynamic buckling analysis of embedded laminated quadrilateral micro plates reinforced by functionally graded carbon nanotubes (FG-CNTs). The material properties of structure are assumed viscoelastic based on Kelvin–Voigt model. The effective material properties of structure are considered based on mixture rule. The elastic medium is simulated by orthotropic visco-Pasternak medium. The motion equations are derived applying Sinusoidal shear deformation theory (SSDT) in which the size effects are considered using higher order nonlocal strain gradient theory. The transformed weighing (TW) and differential quadrature (DQ) method in conjunction with the Bolotin’s method are applied for calculating resonance frequency and dynamic instability region (DIR) of structure. The effects of different parameters such as volume percent of CNTs, distribution type of CNTs, temperature, nonlocal parameter and structural damping on the dynamic instability of visco-system are shown. The results are compared with other published works in the literature. Results indicate that the CNTs have an important role in dynamic stability of structure and FGX distribution type is the better choice.     

Thermoelastic damping in strain gradient microplates according to a generalized theory of thermoelasticity

Abstract

This paper deals with the small-scale effects on the thermoelastic damping (TED) in microplates. The coupled equations of motion and heat conduction are provided utilizing the strain gradient theory (SGT) and the dual-phase-lag (DPL) heat conduction model. Solving these equations and adopting the Galerkin method, the real and imaginary parts of frequency are extracted. The complex frequency approach is then employed to present a size-dependent expression for evaluating TED in thin plates. An analytical expression for TED incorporating small-scale effects is also derived on the basis of the energy dissipation approach. To survey the effect of different continuum theories on TED, the results obtained by SGT are compared with those predicted by the modified couple stress theory (MCST) and the classical continuum theory. Furthermore, through a number of parametric studies, the effects of some variables on the amount of TED, such as microplate thickness, type of material and boundary conditions are discussed.