Nonlocal strain gradient-based vibration analysis of embedded curved porous piezoelectric nano-beams in thermal environment

Farzad Ebrahimi,Mohsen Daman and Ali Jafar 국제구조공학회 2017 Smart Structures and Systems, An International Jou Vol.20 No.6

This disquisition proposes a nonlocal strain gradient beam theory for thermo-mechanical dynamic characteristics of embedded smart shear deformable curved piezoelectric nanobeams made of porous electro-elastic functionally graded materials by using an analytical method. Electro-elastic properties of embedded curved porous FG nanobeam are assumed to be temperature-dependent and vary through the thickness direction of beam according to the power-law which is modified to approximate material properties for even distributions of porosities. It is perceived that during manufacturing of functionally graded materials (FGMs) porosities and micro-voids can be occurred inside the material. Since variation of pores along the thickness direction influences the mechanical and physical properties, so in this study thermo-mechanical vibration analysis of curve FG piezoelectric nanobeam by considering the effect of these imperfections is performed. Nonlocal strain gradient elasticity theory is utilized to consider the size effects in which the stress for not only the nonlocal stress field but also the strain gradients stress field. The governing equations and related boundary condition of embedded smart curved porous FG nanobeam subjected to thermal and electric field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is utilized to achieve the natural frequencies of porous FG curved piezoelectric nanobeam resting on Winkler and Pasternak foundation. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality parameter, electric voltage, coefficient of porosity, elastic foundation parameters, thermal effect, gradient index, strain gradient, elastic opening angle and slenderness ratio on the natural frequency of embedded curved FG porous piezoelectric nanobeam are successfully discussed. It is concluded that these parameters play important roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.

Buckling of porosity-dependent bi-directional FG nanotube using numerical method

Wang, Haiquan,Zandi, Yousef,Gholizadeh, Morteza,Issakhov, Alibek Techno-Press 2021 Advances in nano research Vol.10 No.5

This article focused on studying the buckling behavior of two-dimensional functionally graded (2D-FG) nanosize tubes, including porosity based on first shear deformation and higher-order theory of tube. The nano-scale tube is simulated based on the nonlocal gradient strain theory, and the general equations and boundary conditions are derived using Hamilton's principle for the Zhang-Fu's tube model (as higher-order theory) and Timoshenko beam theory. Finally, the derived equations are solved using a numerical method for both simply-supported and clamped boundary conditions. The parametric study is performed to study the effects of different parameters such as axial and radial FG power indexes, porosity parameter, nonlocal gradient strain parameters on the buckling behavior of di-dimensional functionally graded porous tube.

Nonlocal strain gradient theory for bending analysis of 2D functionally graded nanobeams

Aicha Bessaim,Mohammed Sid Ahmed Houari,Smain Bezzina,Ali Merdji,Ahmed Amine Daikh,Mohamed-Ouejdi Belarbi,Abdelouahed Tounsi 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.86 No.6

This article presents an analytical approach to explore the bending behaviour of of two-dimensional (2D) functionally graded (FG) nanobeams based on a two-variable higher-order shear deformation theory and nonlocal strain gradient theory. The kinematic relations are proposed according to novel trigonometric functions. The material gradation and material properties are varied along the longitudinal and the transversal directions. The equilibrium equations are obtained by using the virtual work principle and solved by applying Navier’s technique. A comparative evaluation of results against predictions from literature demonstrates the accuracy of the proposed analytical model. Moreover, a detailed parametric analysis checks for the sensitivity of the bending and stresses response of (2D) FG nanobeams to nonlocal length scale, strain gradient microstructure scale, material distribution and geometry.

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.

Nonlinear thermal buckling of bi-directional functionally graded nanobeams

Yang Gao,Wan-Shen Xiao,Haiping Zhu 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.71 No.6

We in this article study nonlinear thermal buckling of bi-directional functionally graded beams in the theoretical frameworks of nonlocal strain graded theory. To begin with, it is assumed that the effective material properties of beams vary continuously in both the thickness and width directions. Then, we utilize a higher-order shear deformation theory that includes a physical neutral surface to derive the size-dependent governing equations combining with the Hamilton’s principle and the von Kármán geometric nonlinearity. It should be pointed out that the established model, containing a nonlocal parameter and a strain gradient length scale parameter, can availably account for both the influence of nonlocal elastic stress field and the influence of strain gradient stress field. Subsequently, via using a easier group of initial asymptotic solutions, the corresponding analytical solution of thermal buckling of beams is obtained with the help of perturbation method. Finally, a parametric study is carried out in detail after validating the present analysis, especially for the effects of a nonlocal parameter, a strain gradient length scale parameter and the ratio of the two on the critical thermal buckling temperature of beams.

Flexure mechanics of nonlocal modified gradient nano-beams

Faghidian S Ali 한국CDE학회 2021 Journal of computational design and engineering Vol.8 No.3

Two frameworks of the nonlocal integral elasticity and the modified strain gradient theory are consistently merged to conceive the nonlocal modified gradient theory. The established augmented continuum theory is applied to a Timoshenko–Ehrenfest beam model. Nanoscopic effects of the dilatation, the deviatoric stretch, and the symmetric rotation gradients together with the nonlocality are suitably accommodated. The integral convolutions of the constitutive law are restored with the equivalent differential model subject to the nonclassical boundary conditions. Both the elastostatic and elastodynamic flexural responses of the nano-sized beam are rigorously investigated and the well posedness of the nonlocal modified gradient problems on bounded structural domains is confirmed. The analytical solution of the phase velocity of flexural waves and the deflection and the rotation fields of the nano-beam is detected and numerically illustrated. The transverse wave propagation in carbon nanotubes is furthermore reconstructed and validated by the molecular dynamics simulation data. Being accomplished in revealing both the stiffening and softening structural responses at nano-scale, the proposed nonlocal modified gradient theory can be beneficially implemented for nanoscopic examination of the static and dynamic behaviors of stubby nano-sized elastic beams.

Longitudinal vibration of a nanorod embedded in viscoelastic medium considering nonlocal strain gradient theory

Balci, Mehmet N. Techno-Press 2022 Advances in nano research Vol.13 No.2

This article investigates the longitudinal vibration of a nanorod embedded in viscoelastic medium according to the nonlocal strain gradient theory. Viscoelastic medium is considered based on Kelvin-Voigt model. Governing partial differential equation is derived based on longitudinal equilibrium and analytical solution is obtained by adopting harmonic motion solution for the nanorod. Modal frequencies and corresponding damping ratios are presented to demonstrate the influences of nonlocal parameter, material length scale, elastic and damping parameters of the viscoelastic medium. It is observed that material length scale parameter is very influential on modal frequencies especially at lower values of nonlocal parameter whereas increase in length scale parameter has less effect at higher values of nonlocal parameter when the medium is purely elastic. Elastic stiffness and damping coefficient of the medium have considerable impacts on modal frequencies and damping ratios, and the highest impact of these parameters on frequency and damping ratio is seen in the first mode. Results calculated based on strain gradient theory are quite different from those calculated based on classical elasticity theory. Hence, nonlocal strain gradient theory including length scale parameter can be used to get more accurate estimations of frequency response of nanorods embedded in viscoelastic medium.

Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter

Mohammed Sid Ahmed Houari,Aicha Bessaim,Fabrice Bernard,Abdelouahed Tounsi,S. R. Mahmoud 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.28 No.1

A size-dependent novel hyperbolic shear deformation theory of simply supported functionally graded beams is presented in the frame work of the non-local strain gradient theory, in which the stress accounts for only the nonlocal strain gradients stress field. The thickness stretching effect (<i>ε_z</i> ≠ 0) is also considered here. Elastic coefficients and length scale parameter are assumed to vary in the thickness direction of functionally graded beams according to power-law form. The governing equations are derived using the Hamilton principle. The closed-form solutions for exact critical buckling loads of nonlocal strain gradient functionally graded beams are obtained using Navier's method. The derived results are compared with those of strain gradient theory.

Wave propagation analysis of carbon nanotubes reinforced composite plates

Mohammad Hosseini,Parisa Chahargonbadizade,Mohammadreza Mofidi 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.88 No.4

In this study, analysis of wave propagation characteristics for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates is performed using first-order shear deformation theory (FSDT) and nonlocal strain gradient theory. Uniform distribution (UD) and three types of functionally graded distributions of carbon nanotubes (CNTs) are assumed. The effective mechanical properties of the FG-CNTRC nanoplate are assumed to vary continuously in the thickness direction and are approximated based on the rule of mixture. Also, the governing equations of motion are derived via the extended Hamilton’s principle. In numerical examples, the effects of nonlocal parameter, wavenumber, angle of wave propagation, volume fractions, and carbon nanotube distributions on the wave propagation characteristics of the FG-CNTRC nanoplate are studied. As represented in the results, it is clear that the internal length-scale parameter has a remarkable effect on the wave propagation characteristics resulting in significant changes in phase velocity and natural frequency. Furthermore, it is observed that the strain gradient theory yields a higher phase velocity and frequency compared to those obtained by the nonlocal strain gradient theory and classic theory.

Vibration analysis of porous nanocomposite viscoelastic plate reinforced by FG-SWCNTs based on a nonlocal strain gradient theory

Pegah Khazaei,Mehdi Mohammadimehr 사단법인 한국계산역학회 2020 Computers and Concrete, An International Journal Vol.26 No.1

This paper investigates the size dependent effect on the vibration analysis of a porous nanocomposite viscoelastic plate reinforced by functionally graded-single walled carbon nanotubes (FG-SWCNTs) by considering nonlocal strain gradient theory. Therefore, using energy method and Hamilton’s principle, the equations of motion are derived. In this article, the effects of nonlocal parameter, aspect ratio, strain gradient parameter, volume fraction of carbon nanotubes (CNTs), damping coefficient, porosity coefficient, and temperature change on the natural frequency are perused. The innovation of this paper is to compare the effectiveness of each mentioned parameters individually on the free vibrations of this plate and to represent the appropriate value for each parameter to achieve an ideal nanocomposite plate that minimizes vibration. The results are verified with those referenced in the paper. The results illustrate that the effect of damping coefficient on the increase of natural frequency is significantly higher than the other parameters effect, and the effects of the strain gradient parameter and nonlocal parameter on the natural frequency increase are less than damping coefficient effect, respectively. Furthermore, the results indicate that the natural frequency decreases with a rise in the nonlocal parameter, aspect ratio and temperature change. Also, the natural frequency increases with a rise in the strain gradient parameter and CNTs volume fraction. This study can be used for optimizing the industrial and medical designs, such as automotive industry, aerospace engineering and water purification system, by considering ideal properties for the nanocomposite plate.