Nonlinear dynamic buckling and vibration of thermally post-buckled temperature-dependent FG porous nanobeams based on the nonlocal theory

Abstract

In this paper, nonlinear dynamic snap-through buckling and vibration behavior of the thermally post-buckled functionally graded (FG) porous nanobeams subjected to static and sudden mechanical loads are investigated utilizing the nonlocal elasticity theory. The physical properties of the nanobeam are considered to be functions of temperature based on the Touloukian model. In addition, to describe the FG porous materials, two different patterns of porosity distribution are adopted using trigonometric functions through the thickness of the nanobeam. The equations of motion in conjunction with the von-K ́arm ́an nonlinear assumption are established in the framework of Hamilton’s principle. By employing the Chebyshev-Ritz procedure, the nonlinear equations are discretized for three types of edge supports. Following that, the cylindrical arc-length technique is employed to assess the vibrational responses of the post-buckled nanobeam during static snap-through buckling. To evaluate the nonlinear dynamic buckling of the graded nanobeam under a sudden dynamic load, the Newmark time integration scheme together with the Newton-Raphson iterative method are utilized. Next, by means of the Budiansky-Roth criterion and the phase-plane approach, the dynamic snap-through loads are identified. After validating the developed mathematical model, a comprehensive investigation is carried out to determine the role of various physical and geometrical parameters on the dynamic snap-through buckling and vibration characteristics of the post-buckled FG nanobeams.

Influence of surface effect on post-buckling behavior of piezoelectric nanobeams

“…With the increase of nonlocal parameters, stiffness and critical temperature of functionally graded piezoelectric nanobeams and plates decrease, and the critical buckling temperature decreases with the increase of aspect ratio. At the same time, they also discussed the instability of functionally graded nanobeams and plates with pores [10][11][12]. The conclusions obtained are the same as those of homogeneous nanobeams and plates.…”

Investigation of the effect of viscosity and fluid flow on buckling behaviour of non‐local nanoplate with surface energy

“…The non‐linear buckling of some thermally post‐buckled nanobeams made of FGMs under static and sudden mechanical loads was analysed by Salari et al. [46] on the basis of the non‐local elasticity theory. Civalek et al.…”

“…In addition, some stiffeners with rectangular sections were used in the system, and it was shown that the buckling load grows with the stiffener height to a certain value, after which it ceases to rise. The non-linear buckling of some thermally post-buckled nanobeams made of FGMs under static and sudden mechanical loads was analysed by Salari et al [46] on the basis of the non-local elasticity theory. Civalek et al [47] presented a size-dependent stability study of a restrained FGM nano Euler-Bernoulli beam.…”

Exploring the mechanical response of functionally graded hollow disks: insights from rotation, gravity and variable heat generation

“…Hamilton’s principle was employed to study buckling vibration analysis of functionally graded structures such as circular plate (Ashoori et al. , 2017; Salari and Sadough Vanini, 2023), nano beams and plates (Ebrahimi and Salari, 2017; Salari et al. , 2022; Salari and Sadough Vanini, 2023).…”

“…Finite element method was employed to investigate transient thermal stresses in a thick hollow cylinder for different schemes such as rule of mixture and Mori-Tanaka (Najibi, 2017;Najibi et al, 2021;Najibi and Talebitooti, 2017). Hamilton's principle was employed to study buckling vibration analysis of functionally graded structures such as circular plate (Ashoori et al, 2017;Salari and Sadough Vanini, 2023), nano beams and plates (Ebrahimi and Salari, 2017;Salari et al, 2022;Salari and Sadough Vanini, 2023).…”