Size-dependent thermo-mechanical free vibration analysis of functionally graded porous microbeams based on modified strain gradient theory

Abstract

In present study, vibration analysis of functionally graded (FG) porous microbeam under thermal effects is investigated considering modified strain gradient theory (MSGT) of elasticity. As the main novelty of this study, in order to effectively acquire the effects of size of size-dependent porous structures, MSGT is employed (considers three material length scale parameters) rather than modified couple stress theory (MCST) (considers one material length scale parameter). The nonlinear governing equation of microbeam based on MSGT is derived from Hamilton's principle and to determine the natural frequency of the system under simply supports, Navier solution is employed. Numerical results presented for different beam models and theories and are compared with those available in previous studies. The obtained results show that frequencies from MSGT are higher than those from MCST and also classical theory (CT), especially when the microbeam thickness is comparable to the microbeam length scale parameter. Also, increases in the temperature of microbeam working environment, lead to decrease of microbeam natural frequency. Finally, parametric study is performed on natural frequency of FG microbeams to indicate the effects of: temperature changes, length scale parameter, slender ratio, and gradient index and porosity volume fraction.

Isogeometric small-scale-dependent nonlinear oscillations of quasi-3D FG inhomogeneous arbitrary-shaped microplates with variable thickness

“…By considering the similar process, the discretized form of the rotation gradient tensor can be presented as in which (27…”

“…Yuan et al [24][25][26] established smallscale-dependent shell formulations to anticipate nonlinear stability and dynamics of FG inhomogeneous truncated conical microshells. Zanoosi [27] captured the strain gradient size effects in the thermo-mechanical free oscillations of FG porous microbeams. Sahmani et al [28][29][30][31] applied the nonlocal stress, surface stress, and strain gradient size dependencies in primary resonant dynamics of microshells having through thickness FG heterogeneity.…”

Strain gradient theory-based vibration analyses for functionally graded microbeams reinforced by GPL

“…To better account for the size effect, the MSGT [10], and the modified couple stress theory (MCST) [11], were proposed, which introduced the characteristic size parameters related to the microstructure of materials into the constitutive equations. Based on the MSGT, Zanoosi [12], studied the vibration of the FG microbeams. It was found that the fundamental frequencies based on MSGT is higher than that of MCST and classic theory (CT).…”

Reformulated Strain Gradient (Rsg) Elasticity Theory for Free Vibration of Thermal Bi-Directional Fg Microbeam

“…In this regard, many studies have been conducted to explore the thermal and mechanical effects on the dynamic behavior of these structures [27]. Zanoosi [28] studied the effect of the thermal environment on the vibration response of porous (FG) microbeams considering (MSGT). Hamilton's principle was acquired to get the simply supported beam governing equation and Navier's solution was employed to obtain the system's natural frequency.…”