Dynamic instability region analysis of sandwich piezoelectric nano-beam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal strain gradient theory

Mohammad Arefi,Mahmoud Pourjamshidian,Ali Ghorbanpour Arani 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.32 No.2

In this research, the dynamic instability region (DIR) of the sandwich nano-beams are investigated based on nonlocal strain gradient elasticity theory (NSGET) and various higher order shear deformation beam theories (HSDBTs). The sandwich piezoelectric nano-beam is including a homogenous core and face-sheets reinforced with functionally graded (FG) carbon nanotubes (CNTs). In present study, three patterns of CNTs are employed in order to reinforce the top and bottom face-sheets of the beam. In addition, different higher-order shear deformation beam theories such as trigonometric shear deformation beam theory (TSDBT), exponential shear deformation beam theory (ESDBT), hyperbolic shear deformation beam theory (HSDBT), and Aydogdu shear deformation beam theory (ASDBT) are considered to extract the governing equations for different boundary conditions. The beam is subjected to thermal and electrical loads while is resting on Visco-Pasternak foundation. Hamilton principle is used to derive the governing equations of motion based on various shear deformation theories. In order to analysis of the dynamic instability behaviors, the linear governing equations of motion are solved using differential quadrature method (DQM). After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various shear deformation theories, nonlocal parameter, strain gradient parameter, the volume fraction of the CNTs, various distributions of the CNTs, different boundary conditions, dimensionless geometric parameters, Visco-Pasternak foundation parameters, applied voltage and temperature change on the dynamic instability characteristics of sandwich piezoelectric nano-beam.

Non-linear free and forced vibration analysis of sandwich nano-beam with FG-CNTRC face-sheets based on nonlocal strain gradient theory

Ali Ghorbanpour Arani,Mahmoud Pourjamshidian,Mohammad Arefi 국제구조공학회 2018 Smart Structures and Systems, An International Jou Vol.22 No.1

In this paper, the nonlinear free and forced vibration responses of sandwich nano-beams with three various functionally graded (FG) patterns of reinforced carbon nanotubes (CNTs) face-sheets are investigated. The sandwich nano-beam is resting on nonlinear Visco-elastic foundation and is subjected to thermal and electrical loads. The nonlinear governing equations of motion are derived for an Euler-Bernoulli beam based on Hamilton principle and von Karman nonlinear relation. To analyze nonlinear vibration, Galerkin’s decomposition technique is employed to convert the governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE). Furthermore, the Multiple Times Scale (MTS) method is employed to find approximate solution for the nonlinear time, frequency and forced responses of the sandwich nano-beam. Comparison between results of this paper and previous published paper shows that our numerical results are in good agreement with literature. In addition, the nonlinear frequency, force response and nonlinear damping time response is carefully studied. The influences of important parameters such as nonlocal parameter, volume fraction of the CNTs, different patterns of CNTs, length scale parameter, Visco-Pasternak foundation parameter, applied voltage, longitudinal magnetic field and temperature change are investigated on the various responses. One can conclude that frequency of FG-AV pattern is greater than other used patterns.

Non-linear free and forced vibration analysis of sandwich nano-beam with FG-CNTRC face-sheets based on nonlocal strain gradient theory

Arani, Ali Ghorbanpour,Pourjamshidian, Mahmoud,Arefi, Mohammad Techno-Press 2018 Smart Structures and Systems, An International Jou Vol.22 No.1

In this paper, the nonlinear free and forced vibration responses of sandwich nano-beams with three various functionally graded (FG) patterns of reinforced carbon nanotubes (CNTs) face-sheets are investigated. The sandwich nano-beam is resting on nonlinear Visco-elastic foundation and is subjected to thermal and electrical loads. The nonlinear governing equations of motion are derived for an Euler-Bernoulli beam based on Hamilton principle and von Karman nonlinear relation. To analyze nonlinear vibration, Galerkin's decomposition technique is employed to convert the governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE). Furthermore, the Multiple Times Scale (MTS) method is employed to find approximate solution for the nonlinear time, frequency and forced responses of the sandwich nano-beam. Comparison between results of this paper and previous published paper shows that our numerical results are in good agreement with literature. In addition, the nonlinear frequency, force response and nonlinear damping time response is carefully studied. The influences of important parameters such as nonlocal parameter, volume fraction of the CNTs, different patterns of CNTs, length scale parameter, Visco-Pasternak foundation parameter, applied voltage, longitudinal magnetic field and temperature change are investigated on the various responses. One can conclude that frequency of FG-AV pattern is greater than other used patterns.

Application of nonlocal elasticity theory on the wave propagation of flexoelectric functionally graded (FG) timoshenko nano-beams considering surface effects and residual surface stress

Ali Ghorbanpour Arani,Mahmoud Pourjamshidian,Mohammad Arefi,M.R. Ghorbanpour Arani 국제구조공학회 2019 Smart Structures and Systems, An International Jou Vol.23 No.2

This research deals with wave propagation of the functionally graded (FG) nano-beams based on the nonlocal elasticity theory considering surface and flexoelectric effects. The FG nano-beam is resting in Winkler-Pasternak foundation. It is assumed that the material properties of the nano-beam changes continuously along the thickness direction according to simple power-law form. In order to include coupling of strain gradients and electrical polarizations in governing equations of motion, the nonlocal non-classical nano-beam model containg flexoelectric effect is used. Also, the effects of surface elasticity, di-electricity and piezoelectricity as well as bulk flexoelectricity are all taken into consideration. The governing equations of motion are derived using Hamilton principle based on first shear deformation beam theory (FSDBT) and also considering residual surface stresses. The analytical method is used to calculate phase velocity of wave propagation in FG nano-beam as well as cut-off frequency. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as flexoelectric coefficients of the surface, bulk and residual surface stresses, Winkler and shear coefficients of foundation, power gradient index of FG material, and geometric dimensions on the wave propagation characteristics of FG nano-beam. The numerical results indicate that considering surface effects/flexoelectric property caused phase velocity increases/decreases in low wave number range, respectively. The influences of aforementioned parameters on the occurrence cut-off frequency point are very small.

Thermal, electrical and mechanical buckling loads of sandwich nano-beams made of FG-CNTRC resting on Pasternak’s foundation based on higher order shear deformation theory

Ali Ghorbanpour Arani,Mahmoud Pourjamshidian,Mohammad Arefi,M.R. Ghorbanpour Arani 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.69 No.4

This research deals with thermo-electro-mechanical buckling analysis of the sandwich nano-beams with face-sheets made of functionally graded carbon nano-tubes reinforcement composite (FG-CNTRC) based on the nonlocal strain gradient elasticity theory (NSGET) considering various higher-order shear deformation beam theories (HSDBT). The sandwich nano-beam with FG-CNTRC face-sheets is subjected to thermal and electrical loads while is resting on Pasternak's foundation. It is assumed that the material properties of the face-sheets change continuously along the thickness direction according to different patterns for CNTs distribution. In order to include coupling of strain and electrical field in equation of motion, the nonlocal non-classical nano-beam model contains piezoelectric effect. The governing equations of motion are derived using Hamilton principle based on HSDBTs and NSGET. The differential quadrature method (DQM) is used to calculate the mechanical buckling loads of sandwich nano-beam as well as critical voltage and temperature rising. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various HSDBTs, length scale parameter (strain gradient parameter), the nonlocal parameter, the CNTs volume fraction, Pasternak's foundation coefficients, various boundary conditions, the CNTs efficiency parameter and geometric dimensions on the buckling behaviors of FG sandwich nano-beam. The numerical results indicate that, the amounts of the mechanical critical load calculated by PSDBT and TSDBT approximately have same values as well as ESDBT and ASDBT. Also, it is worthy noted that buckling load calculated by aforementioned theories is nearly smaller than buckling load estimated by FSDBT. Also, similar aforementioned structure is used to building the nano/micro oscillators.

Influence of electro-magneto-thermal environment on the wave propagation analysis of sandwich nano-beam based on nonlocal strain gradient theory and shear deformation theories

Ali Ghorbanpour Arani,Mahmoud Pourjamshidian,Mohammad Arefi 국제구조공학회 2017 Smart Structures and Systems, An International Jou Vol.20 No.3

In this paper, the dispersion characteristics of elastic waves propagation in sandwich nano-beams with functionally graded (FG) face-sheets reinforced with carbon nanotubes (CNTs) is investigated based on various high order shear deformation beam theories (HOSDBTs) as well as nonlocal strain gradient theory (NSGT). In order to align CNTs as symmetric and asymmetric in top and bottom face-sheets with respect to neutral geometric axis of the sandwich nano-beam, various patterns are employed in this analysis. The sandwich nano-beam resting on Pasternak foundation is subjected to thermal, magnetic and electrical fields. In order to involve small scale parameter in governing equations, the NSGT is employed for this analysis. The governing equations of motion are derived using Hamilton's principle based on various HSDBTs. Then the governing equations are solved using analytical method. A detailed parametric study is conducted to study the effects of length scale parameter, different HSDBTs, the nonlocal parameter, various aligning of CNTs in thickness direction of face-sheets, different volume fraction of CNTs, foundation stiffness, applied voltage, magnetic intensity field and temperature change on the wave propagation characteristics of sandwich nano-beam. Also cut-off frequency and phase velocity are investigated in detail. According to results obtained, UU and VA patterns have the same cut-off frequency value but AV pattern has the lower value with respect to them.