About the journal
The Journal of Solid Mechanics (JSM) is a quarterly journal which is dedicated to the publication of original and peer-reviewed papers relating to the mechanics of solids and structures. This influential publication covers a broad area of mechanical engineering activities associated with the classical problems of structural analysis to mechanics of solids, fracture mechanics, heat transfer, thermal effects in solids, optimum design methods, and numerical techniques.
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.
Recent Articles
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Open Access Article
1 - Nonlinear Hybrid Bistable Vibration-Energy-Harvester Modeling Considering Magnetostrictive and Piezoelectric Behaviors
K Niazi M. J Kazem Zadeh Parsi M MohammadiIssue 4 , Vol. 15 , Autumn 2023The present study investigates a novel two degrees of freedom (2DOF) modeling of hybrid-bistable vibration energy harvester (VEH) considering nonlinear magnetic interaction and elastic magnifier to improve the efficiency and expand the action bandwidth. The main part of MoreThe present study investigates a novel two degrees of freedom (2DOF) modeling of hybrid-bistable vibration energy harvester (VEH) considering nonlinear magnetic interaction and elastic magnifier to improve the efficiency and expand the action bandwidth. The main part of harvesting mechanism is a composite cantilever beam consists of three layers of magnetostrictive, piezoelectric and a metallic core with internal damping. Such a novel architecture generates more electrical power and operates at larger bandwidth than common piezoelectric or magnetostrictive energy harvesting systems. In the present work, a coupled 2DOF model is developed to investigate the vibration behavior and energy harvesting rate of the harvester. The harmonic balance method is used to obtain the frequency responses and then the Runge-Kutta method is utilized to calculate the dynamic responses. A parametric study is done to investigate the effects of the key features of the harvester such as magnets distances, base acceleration level and excitation frequency on the rate of electricity generation. Manuscript profile -
Open Access Article
2 - Thermal Buckling Analysis of Temperature Dependent Porous FGM Mindlin Nano Circular Plate on Elastic Foundation
M. M Mohieddin GhomsheiIssue 4 , Vol. 15 , Autumn 2023In the present work, the symmetric thermal buckling behavior of shear deformable heterogonous nano/micro circular porous plates resting on a two parameter foundation is studied. The material behavior of the nano plate is modeled by the modified couple stress theory. The MoreIn the present work, the symmetric thermal buckling behavior of shear deformable heterogonous nano/micro circular porous plates resting on a two parameter foundation is studied. The material behavior of the nano plate is modeled by the modified couple stress theory. The plate material properties assumed to be graded across the thickness direction according to a simple power law, and has a uniform porosity. Using Mindlin’s plate theory and the nonlinear von-Karman strain field and implementing the energy method, the plate stability equations together with the membrane equilibrium equation are derived and expressed in terms of the displacement field components. Then the nondimensionalized forms of the equations are discretized using differential quadrature method (DQM). The resulting eigenvalue problem is solved to evaluate the plate critical buckling temperature difference. Comparative studies are carried out. Also the influences of some important parameters including length scale factor, porosity factor and Winkler& Pasternak stiffness coefficients are investigated.. Manuscript profile -
Open Access Article
3 - Simulation of Residual Stress and Distortion in Welded Carbon Steel Pipe by Considering Solid-State Phase Transformation
M. R Jahanban S FeliIssue 4 , Vol. 15 , Autumn 2023In this paper, a sequentially coupled 3-D thermal-metallurgical-mechanical analysis is developed to predict welding residual stresses and distortion during single-pass tungsten inert gas arc welding (TIG) of low and medium carbon steel pipes (S45C and S15C). The axial a MoreIn this paper, a sequentially coupled 3-D thermal-metallurgical-mechanical analysis is developed to predict welding residual stresses and distortion during single-pass tungsten inert gas arc welding (TIG) of low and medium carbon steel pipes (S45C and S15C). The axial and hoop residual stresses and welding deformation by allowing volumetric change due to solid-state phase transformation are determined. In ABAQUS finite element simulation, the moving heat source is modeled by a user subroutine [DFLUX], and a user subroutine [UEXPAN] is applied for computing the fraction of martensite and volume change during heating and cooling. The simulation results show that for the S15C pipe, solid-state phase transformation has an insignificant effect on welding residual stress and distortion but for the S45C pipe the solid-state phase transformation reduces the axial residual stress in the fusion (FZ) and heat-affected zones (HAZ). Also, the sign of hoop residual stress changes in FZ, and its value of it decreases in HAZ. Manuscript profile -
Open Access Article
4 - On the Aeroelastic Stability of a Two-Directional FG GNP-Enriched Conical Shell
A.R Shahidi A DarakhshIssue 4 , Vol. 15 , Autumn 2023In this article, the supersonic flutter analysis of a truncated conical shell made of polymer enriched with graphene nanoplatelets (GNPs) exposed to supersonic fluid flow is discussed. It is assumed that the mass fraction of the GNPs is functionally graded (FG) along th MoreIn this article, the supersonic flutter analysis of a truncated conical shell made of polymer enriched with graphene nanoplatelets (GNPs) exposed to supersonic fluid flow is discussed. It is assumed that the mass fraction of the GNPs is functionally graded (FG) along thickness and length directions according to different dispersion patterns. Modeling of the shell is done using the first-order shear deformation theory (FSDT), the mechanical properties are computed according to the Halpin-Tsai model alongside the rule of the mixture, and the aerodynamic pressure is computed utilizing the piston theory. Utilizing Hamilton’s principle, the boundary conditions and the governing equations are achieved. Harmonic trigonometric functions are used to provide an analytical solution in the circumferential direction and an approximate solution is presented in the meridional direction using the differential quadrature method (DQM). The efficacy of various parameters on the aeroelastic stability are discussed such as the percentage and dispersion pattern of the GNPs and gradient indices. It is observed that to achieve higher aeroelastic stability in the GNP-enriched truncated conical shells, it is better to dispense the GNPs near the small radius and the inner surface of the shell. Manuscript profile -
Open Access Article
5 - Fractional Cattaneo Heat Equation in a Multilayer Elliptic Ring Membrane and its Thermal Stresses
G Dhameja L Khalsa V VargheseIssue 4 , Vol. 15 , Autumn 2023A fractional Cattaneo model from the generalized Cattaneo model with two fractional derivatives of different orders is considered for studying the thermoelastic response for a multilayer elliptic ring membrane with source function. The solution is obtained by applying a MoreA fractional Cattaneo model from the generalized Cattaneo model with two fractional derivatives of different orders is considered for studying the thermoelastic response for a multilayer elliptic ring membrane with source function. The solution is obtained by applying an integral transform technique analogous to Vodicka's approach considering series expansion functions in terms of an eigenfunction to the generalized fractional Cattaneo-type heat conduction equation within an elliptic coordinates system. The analytical expressions of displacement and stress components employing Airy's stress function approach are investigated. The results are obtained as a series solution in terms of Mathieu functions and hold convergence test. The effects of fractional parameters on the temperature fields and their thermal stresses are also discussed. The findings are depicted graphically for different kinds of surface temperature gradients, and it is distinguished that the higher the fractional-order parameter, the higher the thermal response. Lastly, the generalized theory of thermoelasticity predicts an instantaneous response, but the fractional theory, which is currently under consideration, predicts a delayed response to physical stimuli, which is something that can be seen occurring in nature. This delayed response can be explained by the fact that fractional theories are currently being considered. This gives credibility to the motivation behind this topic of study in the research. Manuscript profile -
Open Access Article
6 - Three-Dimensional Simulation of a Steel Plate Deformation as a Result of Underwater Shock Wave using Fluid-Solid Interaction
A Jafari Valdani A AdamianIssue 4 , Vol. 15 , Autumn 2023Present study considered deformation of a solid plate as result of external pressure wave. So, a detailed investigation of underwater explosions (UNDEX) and their effects on solid structures is the main objective of this paper. To accomplish this, numerical methods have MorePresent study considered deformation of a solid plate as result of external pressure wave. So, a detailed investigation of underwater explosions (UNDEX) and their effects on solid structures is the main objective of this paper. To accomplish this, numerical methods have been used to analyze the UNDEX structure qualitatively and quantitatively. Afterward, perpendicular blades are used to reinforce a marine structure. Governing equations in solid and fluid media were discretized using finite element and finite volume schemes, respectively. As for fluid-structure interaction (FSI), two-way coupling methods were used to map the results of fluid and solid media. The numerical method's validity can be confirmed by comparing numerical results with the analytical solution. Pressure-time diagrams follow the analytical solution reasonably well, indicating that the numerical method is valid. Additionally, results indicate that a pressure wave with amplitude of 20 MPa is generated by the detonation of explosive charge under water. Furthermore, reinforcement blades appear to reduce deformation in structures by increasing their resistance to explosive charges. These blades increase the strength of the plate where it could tolerate the Von-Mises stress up to 750 MPa. Manuscript profile -
Open Access Article
7 - An Analytical Study on Surface Energy Effect on Free Longitudinal Vibration of Cracked Nanorods
H Shokrollahi R NazemnezhadIssue 4 , Vol. 15 , Autumn 2023The present work analytically studies the free longitudinal vibration of nanorods in the presence of cracks based on the surface elasticity theory. To this end, governing equations of motion and corresponding boundary conditions are obtained using Hamilton’s princ MoreThe present work analytically studies the free longitudinal vibration of nanorods in the presence of cracks based on the surface elasticity theory. To this end, governing equations of motion and corresponding boundary conditions are obtained using Hamilton’s principle. Due to considering the surface stress effect, as well as the surface density and the surface Lamé constants, the obtained governing equations of motion become non-homogeneous. The non-homogeneous governing equations are solved using appropriate analytical methods, and the natural frequencies are extracted. To have a comprehensive research, the effects of various parameters such as the length and radius of the nanorod, the crack severity, the crack position, the type of boundary condition, and the values of surface and bulk material properties on axial frequencies of the nanorod are investigated. Since this work considers the effects of all surface energy parameters, it can be claimed that it is a comprehensive study in this regard. Manuscript profile -
Open Access Article
8 - Analytical and Numerical Investigation of Energy Absorption in Graded Aluminum Open Cell Foam under Low Velocity Impact Loading
S Davari S. A Galehdari A AtrianIssue 4 , Vol. 15 , Autumn 2023Given the significance of energy absorption in various industries, light shock absorbers such as structures made of metal foam have been considered. In this study, analytical equation of plateau stress is presented for an open cell foam based on the Gibson-Ashby model, MoreGiven the significance of energy absorption in various industries, light shock absorbers such as structures made of metal foam have been considered. In this study, analytical equation of plateau stress is presented for an open cell foam based on the Gibson-Ashby model, which follows elastic perfectly plastic behavior. For comparison of acquired analytical equations, the problem for a cell and then for three cells that make up an aluminum open cell foam is simulated in ABAQUS/CAE. Using the stress strain diagram, plateau stress and densification strain equations, the specific energy absorbed of the open cell metal foam is extracted. The capacity of absorb energy for an aluminum open cell foam with three cell is obtained once using analytical equations and again by using numerical simulation in ABAQUS/CAE. Numerical results retain an acceptable accordance with analytical equations with less than 3% occurred error for absorbed energy. To ensure the accuracy of numerical simulation, the results of simulating are compared with the results of the simulation of the same foam in a reference whose accuracy is verified by the experiment. Based on the results, the effective cross-sectional area of the foam with Gibson-Ashby cell does not follow the cross-sectional that is used for the calculation of plateau stress in adsorbent structures. Then tow equations are extracted to calculate the effective cross-sectional area and the transfer force. Applying sequential quadratic programming method (SQP) and genetic algorithm (GA), to design a graded metal foam with high specific Energy absorption. Manuscript profile
Most Viewed Articles
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Open Access Article
1 - Studying the Mechanical and Thermal Properties of Polymer Nanocomposites Reinforced with Montmorillonite Nanoparticles Using Micromechanics Method
M.H Yas H Shahrani Korani F Zare JouneghaniIssue 1 , Vol. 12 , Winter 2020In this study, the mechanical and thermal behavior of the nano-reinforced polymer composite reinforced by Montmorillonite (MMT) nanoparticles is investigated. Due to low cost of computations, the 3D representative volume elements (RVE) method is utilized using ABAQUS fi MoreIn this study, the mechanical and thermal behavior of the nano-reinforced polymer composite reinforced by Montmorillonite (MMT) nanoparticles is investigated. Due to low cost of computations, the 3D representative volume elements (RVE) method is utilized using ABAQUS finite element commercial software. Low density poly ethylene (LDPE) and MMT are used as matrix and nanoparticle material, respectively. By using various geometric shapes and weight fractions of nanoparticle, the mechanical and thermal properties such as Young’s modulus, shear modulus, heat expansion coefficient and heat transfer coefficient are studied. Due to addressing the properties of interfacial zone between the matrix and nanoparticle, finite element modeling is conducted in two ways, namely, perfect bonding and cohesive zone. The results are validated by comparing with experimental results reported in literature and a reasonable agreement was observed. The prediction function for Young’s modulus is presented by employing Genetic Algorithm (GA) method. Also, Kerner and Paul approaches as theoretical models are used to calculate the Young’s modulus. It was finally concluded that the magnitude of the Young’s and shear modules increase by adding MMT nanoparticles. Furthermore, increment of MMT nanoparticles to polymer matrix nanocomposite decrease the heat expansion and heat transfer coefficients. Manuscript profile -
Open Access Article
2 - Analysis of Reflection Phenomena in a Fiber Reinforced Piezo-Thermoelastic Half Space with Diffusion and Two-Temperature
K Jain S Kumar S DeswalIssue 4 , Vol. 12 , Autumn 2020Present work is concerned with the analysis of transient wave phenomena in a piezo-thermoelastic medium with diffusion, fiber reinforcement and two-temperature, when an elastic wave is made incident obliquely at the traction free plane boundary of the considered medium. MorePresent work is concerned with the analysis of transient wave phenomena in a piezo-thermoelastic medium with diffusion, fiber reinforcement and two-temperature, when an elastic wave is made incident obliquely at the traction free plane boundary of the considered medium. The formulation is applied under the purview of generalized theory of thermoelasticity with one relaxation time. The problem is solved analytically and it is found that there exists four coupled quasi waves: qp (quasi-p ), qMD (quasi mass diffusion), qT (quasi thermal) and qSV (quasi-SV ) waves propagating with different speeds in a two-dimensional model of the solid. The amplitude ratios, phase velocities and energy ratios for the reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programming. Effect of presence of diffusion is analyzed theoretically, numerically and graphically. The number of reflected waves reduce to three in the absence of diffusion as qMD wave will disappear in that case which is physically admissible. Influence of piezoelectric effect, two temperature and anisotropy is discussed on different characteristics of reflected waves such as phase velocity and reflection coefficients. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Thus, the energy conservation law holds at the surface. Finally, all the reflection coefficients are represented graphically through 3D plots to estimate and highlight the effects of frequency and angle of incidence. Manuscript profile -
Open Access Article
3 - The Frequency Response of Intelligent Composite Sandwich Plate Under Biaxial In-Plane Forces
A. A Ghorbanpour-Arani Z Khoddami Maraghi A Ghorbanpour AraniIssue 1 , Vol. 15 , Winter 2023This paper investigates the frequency response of a smart sandwich plate made of magnetic face sheets and reinforced core with nano-fibers. The effective elastic properties of composite core reinforced with carbon nanotube are estimated by the extended rule of Mixture. MoreThis paper investigates the frequency response of a smart sandwich plate made of magnetic face sheets and reinforced core with nano-fibers. The effective elastic properties of composite core reinforced with carbon nanotube are estimated by the extended rule of Mixture. The orthotropic visco-Pasternak foundation is examined to study orthotropic angle, damping coefficient, normal, and shear modulus. The top and bottom face sheets of the sandwich are magnetic and their vibrations are controlled by a feedback control system and magneto-mechanical couplings. Also, the sandwich plate is subjected to the compression and extension in-plane forces in both x and y directions. Five coupled equations of motion are derived using Hamilton’s principle. These equations are solved by the differential quadrature method. The analysis performed by the third-order shear deformation theory (Reddy’s theory) shows useful details of the effective parameters such in-plane forces, modulus of elastic foundation, core-to-face sheet thickness ratio and controller effect of velocity feedback gain on the dimensionless frequency of the sandwich plate. The analysis of such structures can be discussed in the military, aerospace and civil industries. Manuscript profile -
Open Access Article
4 - A Study on Stiffness of a Defective Rippled Graphene Using Molecular Dynamics Simulation
A Hamzei E Jomehzadeh M Rezaeizadeh M MahmoodiIssue 2 , Vol. 15 , Spring 2023Graphene without defects exhibits extraordinary mechanical properties, while defects such as vacancies and Stone-Wales usually impose a suffering effect on graphene's properties. On the other hand, strictly two-dimensional crystals are expected to be unstable due to the MoreGraphene without defects exhibits extraordinary mechanical properties, while defects such as vacancies and Stone-Wales usually impose a suffering effect on graphene's properties. On the other hand, strictly two-dimensional crystals are expected to be unstable due to the thermodynamic requirement for the existence of out-of-plane bending with interatomic interaction generating a mathematical paradox. This paper researches the fracture strength and the stretching stiffness of a rippled defective graphene that is placed under the loading pressure of uniaxial tensile. With the purpose of replicating a model for carbon atoms’ covalence bonding, a molecular dynamics simulation is carried out. This is sorted according to the adaptive intermolecular reactive bond order potential function. The degree of the temperature of the system throughout the experiment is contained through the Nose-Hoover thermostat. The software package large-scale atomic/molecular massively parallel simulator is utilized for the aim of simulation the desired bond formation in the graphene layer structure. The present study offers a physical insight into the mechanisms of topological mechanical defects of graphene, and we propose static ripples as one of the key elements to accurately understand the thermo-mechanics of graphene. The results revealed that the fracture strength of a rippled graphene is significantly reduced when it contains defects, and fracture stress and strain with different vacancy defects are presented and compared. Manuscript profile -
Open Access Article
5 - Investigation of Vacancy Defects on the Young’s Modulus of Carbon Nanotube Reinforced Composites in Axial Direction via a Multiscale Modeling Approach
M.R Davoudabadi S.D FarahaniIssue 3 , Vol. 2 , Summer 2010In this article, the influence of various vacancy defects on the Young’s modulus of carbon nanotube (CNT) - reinforcement polymer composite in the axial direction is investigated via a structural model in ANSYS software. Their high strength can be affected by the MoreIn this article, the influence of various vacancy defects on the Young’s modulus of carbon nanotube (CNT) - reinforcement polymer composite in the axial direction is investigated via a structural model in ANSYS software. Their high strength can be affected by the presence of defects in the nanotubes used as reinforcements in practical nanocomposites. Molecular structural mechanics (MSM)/finite element (FE) Multiscale modeling of carbon nanotube/polymer composites with linear elastic polymer matrix is used to study the effect of CNT vacancy defects on the mechanical properties. The nanotube is modeled at the atomistic scale using MSM, where as the interface we assumed to be bonded by Vander Waals interactions based on the Lennar-Jonze potential at the interface and polymer matrix. A nonlinear spring is used for modeling of interactions. It is studied for zigzag and armchair Nanotubes with various aspect ratios (Length/Diameter). Finally, results of the present structural model show good agreement between our model and the experimental work. Manuscript profile -
Open Access Article
6 - A Generalized Thermo-Elastic Diffusion Problem in a Functionally Graded Rotating Media Using Fractional Order Theory
K Paul B MukhopadhyayIssue 2 , Vol. 12 , Spring 2020A generalized thermo-elastic diffusion problem in a functionally graded isotropic, unbounded, rotating elastic medium due to a periodically varying heat source in the context of fractional order theory is considered in our present work. The governing equations of the th MoreA generalized thermo-elastic diffusion problem in a functionally graded isotropic, unbounded, rotating elastic medium due to a periodically varying heat source in the context of fractional order theory is considered in our present work. The governing equations of the theory for a functionally graded material with GNIII model are established. Analytical solution of the problem is derived in Laplace-Fourier transform domain. Finally, numerical inversions are used to show the effect of rotation, non-homogeneity and fractional parameter on stresses, displacement, chemical potential, mass distribution, temperature, etc. and those are illustrated graphically. Manuscript profile -
Open Access Article
7 - Analysis of Viscoelastic Functionally Graded Sandwich Plates with CNT Reinforced Composite Face Sheets on Viscoelastic Foundation
A Ghorbanpour Arani M Emdadi H Ashrafi M Mohammadimehr S Niknejad A.A Ghorbanpour Arani A HosseinpourIssue 4 , Vol. 11 , Autumn 2019In this article, bending, buckling, and free vibration of viscoelastic sandwich plate with carbon nanotubes reinforced composite facesheets and an isotropic homogeneous core on viscoelastic foundation are presented using a new first order shear deformation theory. Accor MoreIn this article, bending, buckling, and free vibration of viscoelastic sandwich plate with carbon nanotubes reinforced composite facesheets and an isotropic homogeneous core on viscoelastic foundation are presented using a new first order shear deformation theory. According to this theory, the number of unknown’s parameters and governing equations are reduced and also the using of shear correction factor is not necessary because the transverse shear stresses are directly computed from the transverse shear forces by using equilibrium equations. The governing equations obtained using Hamilton’s principle is solved for a rectangular viscoelastic sandwich plate. The effects of the main parameters on the vibration characteristics of the viscoelastic sandwich plates are also elucidated. The results show that the frequency significantly decreases with using foundation and increasing the viscoelastic structural damping coefficient as well as the damping coefficient of materials and foundation. Manuscript profile -
Open Access Article
8 - Influence of the Imperfect Interface on Love-Type Mechanical Wave in a FGPM Layer
S Chaudhary A Singhal S.A SahuIssue 1 , Vol. 11 , Winter 2019In this study, we consider the propagation of the Love-type wave in piezoelectric gradient covering layer on an elastic half-space having an imperfect interface between them. Dispersion relation has been obtained in the form of determinant for both electrically open and MoreIn this study, we consider the propagation of the Love-type wave in piezoelectric gradient covering layer on an elastic half-space having an imperfect interface between them. Dispersion relation has been obtained in the form of determinant for both electrically open and short cases. The effects of different material gradient coefficients of functionally graded piezoelectric material (FGPM) and imperfect boundary on the phase velocity of Love-type waves are discussed. Also, the influence of mechanically and electrically imperfect interface on the surface wave phase velocity is obtained and shown graphically. The dispersion curves are plotted and the effects of material properties of both FGPM and orthotropic material are studied. Moreover, dispersion relation of the considered microstructure depends substantially on the material gradient coefficients and width of the guiding plate. Numerical results are highlighted graphically and are validated with existing literature. The present study is the prior attempt to show the interfacial imperfection influence with the considered structure on wave phase velocity. The outcomes are widely applicable and useful for the development and characterization of Love-type mechanical waves in FGPM-layered media, SAW devices and other piezoelectric devices. Manuscript profile -
Open Access Article
9 - New Two 20-Node High-Order Finite Elements Based on the SFR Concept for Analyzing 3D Elasticity Problems
H Djahara K Meftah L Sedira A AyadiIssue 2 , Vol. 14 , Spring 2022This paper proposes conforming and nonconforming 20-node hexahedral finite elements. The elements’ formulation stems from the so-called Space Fiber Rotation (SFR) concept, allowing a spatial rotation of three-dimensional virtual fiber within the elements. Adding r MoreThis paper proposes conforming and nonconforming 20-node hexahedral finite elements. The elements’ formulation stems from the so-called Space Fiber Rotation (SFR) concept, allowing a spatial rotation of three-dimensional virtual fiber within the elements. Adding rotational degrees of freedom results in six degrees of freedom per node (three rotations and three translations) which enhances the approximation of the classical displacement field. The incompatible modes approach has been adopted in the nonconforming element formulation in order to avoid numerical deficiencies associated with the Poisson’s ratio locking phenomenon. The accuracy of the proposed elements is examined through a series of three-dimensions linear elastic benchmarks including beam, plates, and shell structures. The proposed elements were shown to give better results than the standard 20-node hexahedron especially when mesh distortion is applied. This confirms that the two proposed elements are less sensitive to mesh distortion. The elements also show good performance when compared with analytical and numerical solutions from the literature. Manuscript profile -
Open Access Article
10 - Analysis of Nonlinear Vibrations of Slightly Curved Tripled-Walled Carbon Nanotubes Resting on Elastic Foundations in a Magneto-Thermal Environment
M.G Sobamowo J.O Akanmu O.A Adeleye A.A YinusaIssue 2 , Vol. 12 , Spring 2020In this work, nonlocal elasticity theory is applied to analyze nonlinear free vibrations of slightly curved multi-walled carbon nanotubes resting on nonlinear Winkler and Pasternak foundations in a thermal and magnetic environment. With the aid of Galerkin decomposition MoreIn this work, nonlocal elasticity theory is applied to analyze nonlinear free vibrations of slightly curved multi-walled carbon nanotubes resting on nonlinear Winkler and Pasternak foundations in a thermal and magnetic environment. With the aid of Galerkin decomposition method, the systems of nonlinear partial differential equations are transformed into systems of nonlinear ordinary differential equations which are solved using homotopy perturbation method. The influences of elastic foundations, magnetic field, temperature rise, interlayer forces, small scale parameter and boundary conditions on the frequency ratio are investigated. It is observed form the results that the frequency ratio for all boundary conditions decreases as the number of walls increases. Also, it is established that the frequency ratio is highest for clamped-simple supported and lowest for clamped-clamped supported. Further investigations on the controlling parameters of the phenomena reveal that the frequency ratio decreases with increase in the value of spring constant (k1) temperature and magnetic field strength. It is hoped that this work will enhance the applications of carbon nanotubes in structural, electrical, mechanical and biological applications especially in a thermal and magnetic environment. Manuscript profile
