Nonlinear vibration of fluid conveying cantilever nanotube resting on visco‐pasternak foundation using non‐local strain gradient theory

Abstract

Frequency analysis and forced vibration response of fluid conveying viscoelastic nanotubes that resting on nonlinear visco-pasternak foundation under magnetic field using size-dependent non-local strain gradient theory are considered in this study. It is supposed that the nanotube is modelled as cantilever type beam and subjected to a harmonic load. The material property of the nanotube is modelled by Kelvin-Voigt viscoelastic constitutive relation and slip boundary conditions of nanotube conveying fluid are taken into account. Extended Galerkin method is used to obtain the nonlinear differential equation of the motion and the multiple timescales method is utilised to investigate the primary vibration resonance of the nanotube. Firstly, the frequency analysis is performed on the linear system and the effects of foundation coefficients on the natural frequency are investigated at several flow velocities. Moreover, the resonance properties of the system are solved in closed form and analysed from the frequency-response curves, and then the effects of the non-local parameter, length scale parameter and magnetic field are fully investigated. In this case, non-local parameter, length scale parameter and foundation coefficients are highly influential on the frequency response of the considered system.

Sound Transmission Loss of a Honeycomb Sandwich Cylindrical Shell with Functionally Graded Porous Layers

“…The resulting vibrations can specifically create a strong noise in the surroundings, and are thus required to be fully investigated under such circumstances [13][14][15][16][17]. In this regard, forced and free vibrations of cylindrical shells and mechanical properties of polymer based nanocomposite have been thoroughly investigated in the past, as in the works of [18][19][20][21][22][23][24].…”

A Review on the Mechanical Behavior of Size-Dependent Beams and Plates using the Nonlocal Strain-Gradient Model

“…employed various size-dependent methods such as the nonlocal elasticity of Eringen, the strain gradient theory, the modified couple stress model, the micromorphic theory, as well as the nonlocal-stress gradient (as a hybrid model) procedure [10][11][12][13][14][15][16][17][18][19][20] to introduce the differences between classical and non-classical models. Many researchers studied the mechanical behavior of micro-/nano-structures based on the non-classical continuum mechanics models induced by different types of loadings including vibration [21][22][23][24][25][26][27][28][29][30][31][32], wave propagation [33][34][35][36][37][38][39][40][41][42][43], and buckling phenomenon [44][45][46][47][48][49][50][51][52][53][54] associated with linear and nonlinear approaches related to the kinematic relations. According to their hypothesis as well as ob...…”

“…Of course, for certain boundary conditions, the results are not accurate and correct. Moreover, some key applications of this theory are wave dispersion analysis of FGM, biological tissues, energy harvesting, M/NEMS cantilever actuators [24,[61][62].…”

“…At a specific speed of nanofluid, the coupled bifurcation variation of the nanofluid-conveying micro/nanotubes was examined. Roodgar Saffari et al [24] worked on the vibration behavior of fluid conveying SWCNT surrounded by a visco-Pasternak substrate with nonlinearity effects using the nonlocal strain-gradient model. They indicated that the size-dependent parameters have considerable effects on the dynamic behavior of the proposed model.…”

A Nonlocal Strain Gradient Approach for Out‐of‐Plane Vibration of Axially Moving Functionally Graded Nanoplates in a Hygrothermal Environment

“…Recently, the nonlocal strain gradient theory has become one of the most widely applied nonclassical continuum approaches [30]. For instance, Saffaria et al [31] studied the dynamics of a cantilever nanotube resting on a nonlinear viscous Pasternak foundation in the context of the nonlocal strain gradient theory, in which the viscoelastic fluid was conveyed, and the magnetic field and harmonic loads were also taken into account. Based on the nonlocal strain gradient theory, Li et al [32] examined the effect of size-dependent parameters on the stiffness of functionally gradient beams using the Timoshenko beam model.…”