Journal of Solid Mechanics
http://jsm.iau-arak.ac.ir/
Journal of Solid Mechanicsendaily1Tue, 01 Jun 2021 00:00:00 +0430Tue, 01 Jun 2021 00:00:00 +0430On The Free Vibration of Doubly Clamped Single-Walled Coiled Carbon Nanotubes: A Novel Size Dependent Continuum Model
http://jsm.iau-arak.ac.ir/article_682454.html
In this paper, the size dependent vibration behavior of doubly clamped single-walled coiled carbon nanotubes (CCNTs) is investigated using nonlocal helical beam model. This model is based on Washizu&rsquo;s beam theory so that all displacement components of CCNT in the equations of motion are defined at the centroidal principal axis and transverse shear deformations are considered. After deriving the nonlocal free vibration equations, they are solved by the generalized differential quadrature method (GDQM). Then, the natural frequencies and corresponding mode shapes are determined for the clamped-clamped boundary conditions (BCs). After that, a parametric study on the effect of different parameters, including the helix cylinder to the tube diameters ratio , the number of pitches, the helix pitch angle, and the nonlocal parameter on the natural frequencies is conducted. It is worth noting that the results of the proposed method would be useful in the practical applications of CCNTs such as using in nanoelectromechanical systems. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Dynamic Response of Bi-Directional Functionally Graded Materials (BDFGMs) Beams Rested on Visco-Pasternak Foundation Under Periodic Axial Force
http://jsm.iau-arak.ac.ir/article_678358.html
Since the temperature or stress distribution in some advanced machines such as modern aerospace shuttles and craft develops in two or three directions, the need for a new type of FGMs is felt whose properties vary in two or three directions. On the other hand, dynamic buckling behavior of structures is a complicated phenomenon which should be investigated through the response of equations of motion. In this paper, dynamic response of beams composed of bi-directional functionally graded materials (BDFGMs) rested on visco-Pasternak foundation under periodic axial force is investigated. Material properties of BDFGMs beam vary continuously in both the thickness and longitudinal directions based on the two types of analytical functions (e.g. exponential and power law distributions). Hamilton's principle is employed to derive the equations of motion of BDFGMs beam according to the Euler-Bernoulli and Timoshenko beam theories. Then, the generalized differential quadrature (GDQ) method in conjunction with the Bolotin method is used to solve the differential equations of motion under different boundary conditions. It is observed that a good agreement between the present work and the literature result. Various parametric investigations are performed for the effects of the gradient index, length-to-thickness ratio and viscoelastic foundation coefficients on the dynamic stability region of BDFGMs beam. The results show that the influence of gradient index of material properties along the thickness direction is greater than gradient index along the longitudinal direction on the dynamic stability of BDFGMs beam for both exponential and power law distributions.Comparative Analysis of Energy Absorption Capacity of Single and Nested Metal Matrix Composite Tubes Under Quasi-Static Lateral and Axial Loading
http://jsm.iau-arak.ac.ir/article_682340.html
In this paper the behavior of nested tube systems under quasi-static compressive loading is investigated. Two nested tube systems with metal matrix composite&nbsp; are subjected to compressive loads so that in the system A the exterior and interior tubes are under axial and lateral loads, respectively but in the system B the exterior and interior tubes are under lateral and axial loads, respectively. Furthermore, these systems behavior are studied numerically. The results show that energy absorption capacity for both of nested tube systems is greater than the sum of energy absorption capacities of two constitutive tubes when loaded individually. Also, it is shown that the absorbed energy for system A is greater than that of system B. In this research the effects of section geometry and the condition of loading (axial or lateral)of thin-walled tubes on energy absorption capacity and the value of the peak load are studied both experimentally and numerically.Study on Vibration Band Gap Characteristics of a Branched Shape Periodic Structure Using the GDQR
http://jsm.iau-arak.ac.ir/article_678297.html
In this study, a new periodic structure with special vibration band gap properties is introduced. This structure consists of a main beam and several cantilever beam elements connected to this main beam in the branched shape. Two models with different number of beam elements and geometrical parameters are considered for this periodic structure. The transverse vibrations of beams are solved using the generalized differential quadrature rule (GDQR) method to calculate the first four band gaps of each model. Investigating the influences of geometrical parameters on the band gaps shows that some bands are close to each other for specific ranges of geometrical parameters values. Furthermore, as the number of beam elements increases, the number of close band gaps increases. Having more than two close band gaps means that this periodic structure has a relatively wide band gap in total. Furthermore, this wide band can move to low frequency ranges by changing the geometrical parameters. Absorbing vibrations over a wide band gap at low frequency ranges makes this periodic structure a good vibration absorber. Verification of the analytical method using ANSYS software shows that the GDQR method can be used for vibration analysis of beam-like structures with high accuracy.Linear and Nonlinear Free Vibration of a Two-Dimensional Multiferroic Composite Plate Subjected to Magneto-Electro-Thermo-Aerodynamic Loading
http://jsm.iau-arak.ac.ir/article_682341.html
Vibration response of a two-dimensional magneto-electro-elastic plate is investigated in this paper. The considered multi-phase plate is rectangular and simply-supported resting on an elastic foundation. The plate is under aerodynamic pressure and subjected to temperature change. It is also assumed that the magneto-electro-elastic body is poled along the z direction and subjected to electric and magnetic potentials between the upper and lower surfaces. The nonlinear vibrational analysis of the described plate is considered as an innovation of the present paper,&nbsp;which had not been done before. To model this problem, third-order shear deformation theory along with Gauss&rsquo;s laws for electrostatics and magnetostatics, first-order piston theory, and Galerkin and multiple times scale methods are used. After validating the presented method, effects of several parameters on the natural frequency, time history, backbone curve, and phase plane diagram of this smart composite plate are obtained. It is found that for plates with constant a/h ratio, electric and magnetic potentials have noticeable effects on the time histories, phase plane diagrams and backbone curves of the plates with smaller thicknesses. In addition, the numerical results of this research indicate that some parameters have considerable effect on the vibration behavior of presented plate. Elastic parameters of the foundation, applied electric and magnetic potentials, and environment temperature are important parameters in this analysis.Investigation of Stress State of the Layered Composite with a Longitudinal Cylindrical Cavity
http://jsm.iau-arak.ac.ir/article_683397.html
The article presents the study of the stress state of a two-layer composite with a cylindrical cavity located parallel to the surfaces of the layers. Displacements are set on the cavity and the upper and lower boundaries of the upper and lower layers, respectively. The three-dimensional elasticity solution has been obtained by the analytical-numerical generalized Fourier method with respect to the system of Lame equations in local cylindrical coordinates associated with cavity and Cartesian coordinates associated with boundaries of the layers. The infinite systems of linear algebraic equations resulting from satisfying the boundary conditions are solved by the reduction method. As a result, displacements and stresses have been obtained at various points of the elastic body. We have compared the stress-strain state of a two-layer structure with a cylindrical cavity located in either of the layers. The analysis included various geometrical parameters and boundary functions; the results obtained were compared with a single-layer holed structure.Size-Dependent Vibration Problem of Two Vertically-Aligned Single-Walled Boron Nitride Nanotubes Conveying Fluid in Thermal Environment Via Nonlocal Strain Gradient Shell Model
http://jsm.iau-arak.ac.ir/article_682264.html
The free vibration behavior of two fluid-conveying vertically-aligned single-walled boron nitride nanotubes are studied in the present paper via the nonlocal strain gradient piezoelectric theory in conjunction with the first-order shear deformation shell assumption in thermal environments. It is supposed that the two adjacent boron nitride nanotubes are coupled with each other in the context of linear deformation by van der Waals interaction according to Lennard&ndash;Jones potential function. To achieve a more accurate modeling for low-scale structures, both hardening and softening effects of materials are considered in the nonlocal strain gradient approach. The&nbsp;motion equations and associated boundary conditions are derived by means of Hamilton&rsquo;s variational principle, then solved utilizing differential quadrature method. Numerical studies are done to reveal the effect of different boundary conditions, size scale parameters, aspect ratio, inter-tube distance, and temperature change on the variations of dimensionless eigenfrequency and critical flow velocity.Free Vibration Analysis of Composite Grid Stiffened Cylindrical Shells Using A Generalized Higher Order Theory
http://jsm.iau-arak.ac.ir/article_681359.html
The present study analyzes the free vibration of multi-layered composite cylindrical shells and perforated composite cylindrical shells via a modified version of Reddy&rsquo;s third-order shear deformation theory (TSDT) under simple support conditions. An advantage of the proposed theory over other high-order theories is the inclusion of the shell section trapezoidal form coefficient term in the displacement field and strain equations to improve the accuracy of results. The non-uniform stiffness and mass distributions across reinforcement ribs and the empty or filled bays between the ribs in perforated shells were addressed via a proper distribution function. For integrated perforated cylindrical shells, the results were validated by comparison to other studies and the numerical results obtained via ABAQUS. The proposed theory was in good consistency with numerical results and the results of previous studies. It should be noted that the proposed theory was more accurate than TSDT.&nbsp;Response of Two-Temperature on the Energy Ratios at Elastic-Piezothermoelastic Interface
http://jsm.iau-arak.ac.ir/article_682387.html
In the present investigation the reflection and transmission phenomenon of plane waves between two half spaces elastic and orthotropic piezothermoelastic with two-temperature theory is discussed. A piezothermoelastic solid half space is assumed to be loaded with an elastic half space. Due to the phenomenon, four qausi waves are obtained; quasi longitudinal (qP) wave, quasi transverse (qS) wave, quasi thermal (qT) wave and electric potential wave (eP). It is found that the amplitude ratios of various reﬂected and refracted waves are functions of angle of incidence, frequency of incident wave and are inﬂuenced by the piezothermoelastic properties of media. The energy ratios are computed numerically using amplitude ratios for a particular model of graphite and cadmium selenide (CdSe). The variations of energy ratios with angle of incidence are shown graphically depicting the effect of two-temperature. The conservation of energy across the interface is justiﬁed. A particular case of interest is also deduced from the present investigation. &nbsp;Thermoelastic Analysis of Annular Sector Plate Under Restricted Boundaries Amidst Elastic Reaction
http://jsm.iau-arak.ac.ir/article_683353.html
An analytical framework is developed for the thermoelastic analysis of annular sector plate whose boundaries are subjected to elastic reactions. The exact expression for transient heat conduction with internal heat sources is obtained using a classical method. The fourth-order differential equation for the thermally induced deflection is obtained by developing a new integral transformation in accordance with the simply supported elastic supports that are subjected to elastic reactions. Here it is supposed that the movement of the boundaries is limited by an elastic reaction, that is, (a) shearing stress is proportional to the displacement, and (b) the reaction moment is proportional to the rate of change of displacement with respect to the radius. Finally, the maximum thermal stresses distributed linearly over the thickness of the plate are obtained in terms of resultant bending momentum per unit width. The calculation is obtained for the steel, aluminium and copper material plates using Bessel's function can be expressed in infinite series form, and the results are depicted using a few graphs.&nbsp;Photothermoelastic Investigation of Semiconductor Material Due to Distributed Loads
http://jsm.iau-arak.ac.ir/article_683153.html
A dynamic mathematical model of photothermoelastic (semiconductor) medium is developed to analyze the deformation due to inclined loads. The governing equations for photothermoelastic with dual phase lag model are framed for two dimensional case and are further simplified by using potential function. Appropriate transforms w.r.t time (Laplace) and w.r.t space variables (Fourier) are employed on the resulting equations which convert the system of equations into differential equation. The problem is examined by deploying suitable mechanical boundary conditions. Specific types of distributed loads as uniformly distributed force and Linearly distributed force are taken to examine the utility of the model. The analytic expressions like displacements, stresses, temperature distribution and carrier density are obtained in the new domain (transformed).To recover the quantities in the physical domain, numerical inversion technique is employed. Numerical computed results with different angle of inclination vs distance are analyzed with and without dual phase lag theories of thermoelasticity in the form of visual representations. It is seen that physical field quantities are sensitive towards photothermoelastic and phase lag parameters.Study of the Mechanical Behavior of Municipal Solid Waste Landfill Using a Viscoplastic Constitutive Model
http://jsm.iau-arak.ac.ir/article_683354.html
As long as there is the need for disposal of&nbsp; household&nbsp; waste there will be the need to understand&nbsp; the phenomena taking place in storage facilities for nonhazardous waste (municipal solid waste landfill). The understanding of landfill technology is of great importance because of its ever-changing state, whether mechanical, chemical or hydrological. In this context, there is a need to better understand the stress-strain behavior evolution with time of the landfilled waste. Based on triaxial and oedometric compression tests of municipal solid waste samples&nbsp; ranging from fresh&nbsp; to degraded waste, a viscoplastic constitutive model (Burgers creep-viscoplastic model) is used to describe the behavior of the municipal solid waste under loading. This model is able to adequately capture the stress-strain and pore water pressure response of the municipal solid waste at different ages. To illustrate its applicability, settlements due to the incremental loading of waste with time are predicted for a typical municipal solid waste landfill. The proposed model predicts the total settlement of a storage facilityin a range similar to results published in the literature. An extension of the studied municipal solid waste landfill was also investigated.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Analysis of Nanoplate with a Central Crack Under Distributed Transverse Load Based on Modified Nonlocal Elasticity Theory
http://jsm.iau-arak.ac.ir/article_683156.html
In this paper, using the complete modified nonlocal elasticity theory, the deflection and strain energy equations of rectangular nanoplates, with a central crack, under distributed transverse load were overwritten. First, the deflection of nanoplate was obtained using Levy's solution and consuming it; strain energy of nanoplate was found. As regards nonlocal elasticity theory wasn&rsquo;t qualified for predicting the static behavior of nanoplates under distributed transverse load, using modified nonlocal elasticity theory, the deflection of nanoplate with a central crack for different values of the small-scale effect parameter was achieved. It was gained with the convergence condition for the complete modified nonlocal elasticity theory. To verify the result, the results for the state of the small-scale effect parameter were placed equal to zero (plate with macro-scale) and then were compared with the numerical results as well as the classical analytical solution results available in the valid references. It was shown that the complete modified nonlocal elasticity theory does not show any singularity at the crack-tip unlike the classical theory; therefore, the method presented is a suitable method for analysis of the nanoplates with a central crack.The Frequency Response of Intelligent Composite Sandwich Plate under Biaxial In-Plane Forces
http://jsm.iau-arak.ac.ir/article_673985.html
This 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&rsquo;s principle. These equations are solved by the differential quadrature method. The analysis performed by the third-order shear deformation theory (Reddy&rsquo;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.Isogeometric Analysis for Topology Optimisation of Two Dimensional Planar and Laminated Composite Plate Continuum Structures
http://jsm.iau-arak.ac.ir/article_682224.html
Isogeometric analysis is the recent development in the field of engineering analysis with high performance computing and greater precision.&nbsp; This current research has opened a new door in the field of structural optimisation.&nbsp; The main focus of this research study is to perform topology optimisation of continuum structures in civil engineering using Isogeometric analysis. The continuum structures analysed here in this study are reinforced concrete, steel and laminated composite plates.&nbsp; Reinforced concrete is a rational union of concrete and steel.&nbsp; Topology optimisation of reinforced concrete structures is an emerging area of study to determine the optimal layout of material in the concrete domain.&nbsp; Laminated structures are made of several layers of material and bonded to achieve high stiffness and low weight to strength ratio. The deformed shape at the optimal state can be determined with topology optimisation of laminated composites.&nbsp; The formulation for composite plates is done using kirchoff thin plate theory without any shear contribution.&nbsp; B-splines are used to model the geometry.&nbsp; The objective is to optimise the energy of the structure and optimality criteria is used to calculate the newer values of relative densities.&nbsp; First order sensitivity analysis is performed to determine the newer values of objective function.&nbsp; The code is written in MatLab&reg; and a few problems have been solved with different domains.&nbsp; The results are verified and have shown a good agreement with those in the literature.Magneto-Rheological Response in Vibration of Intelligent Sandwich Plate with Velocity Feedback Control
http://jsm.iau-arak.ac.ir/article_674337.html
This study deals with the free vibration of the sandwich plate made of two smart magnetostrictive face sheets and an electro-rheological fluid core. Electro-rheological fluids are polymer-based material that changes its viscosity under the applied electric field. A feedback control system follows the magnetization effect on the vibration characteristics of the sandwich plate when subjected to the magnetic field. It is assumed that there is no slip between layers, so the stress-strain relations of each layer are separately considered. Energy method is utilized in order to derive the five coupled equations of motion. These equations are solved by differential quadrature method (DQM). Results of this study show the rheology response of fluid in presence of electric field where the core gets hard and the dimensionless frequency increases. Also, the significant effect of thickness and aspect ratios and velocity feedback gain are discussed in detail. Such intelligent structures can replace in many of the systems used in automotive, aerospace and building industries as the detector, warning, and vibration absorber etc.Thermodynamic Stability of Sandwich Micro-Beam with Honeycomb Core and Piezoelectric / Porous Viscoelastic Graphene Facesheets
http://jsm.iau-arak.ac.ir/article_677554.html
Thermodynamic stability of sandwich micro beam with honeycomb core and piezoelectric / porous visco graphene sheets resting on visco Pasternak. In order to consider size effect, strain gradient theory is utilized. Using energy method and zigzag theory, final motion equations of sandwich micro beam are derived and solved by Galerkin method. The effects of parameters such as small scale, temperature changes, core to face sheets ratio, intensity of electric fields and elastic medium on the thermal dynamic stability of sandwich micro beam are investigated. Results indicated that by increasing temperature changes, the origins of the instability regions moves to lower excitation frequencies and decreases the width of the instability region of sandwich micro beam at a certain dynamic load factor. In addition, increasing porosity indexes leads to increase excitation frequencies and consequently cause to more stable system . The results of present work can be used to optimum design and control of micro-thermal/electro-mechanical devices.Analytical solutions of Finite Wedges Coated by an Orthotropic Coating Containing Multiple Cracks and Cavities
http://jsm.iau-arak.ac.ir/article_682153.html
This paper presents a general formulation for an isotropic wedge reinforced by an orthotropic coating involving multiple arbitrarily oriented defects under out of plane deformation. The exact closed form solution of the problem weakened by a screw dislocation in the isotropic wedge is obtained by making use of finite Fourier cosine transform. Also, the closed-form solutions of the out of plane stress and displacement fields are obtained. After that, by making use of a distributed dislocation approach, a set of singular integral equations of the domain involving smooth cavities and cracks subjected to out of plane external loading are achieved. The cracks and cavities are considered to be only in the isotropic wedge. The presented integral equations have Cauchy singularity and must be evaluated numerically. Multiple numerical examples will be presented to show the applicability and efficiency of the presented solution. The geometric and point load singularities of the stress components are obtained and compared with the available data in the literature.Anisotropic and isotropic elasticity applied for the study of elastic fields generated by interfacial dislocations in a heterostructure of InAs/(001)GaAs semiconductors
http://jsm.iau-arak.ac.ir/article_682342.html
This work is a study of the elastic fields&rsquo; effect (stresses and displacements) caused by dislocations networks at a heterostructure interface of a InAs / GaAs semiconductors thin system in the cases of isotropic and anisotropic elasticity. The numerical study of this type of heterostructure aims to predict the behavior of the interface with respect to these elastic fields satisfying the boundary conditions. The method used is based on a development in Fourier series. The deformation near the dislocation is greater than the other locations far from the dislocationA Comparison Between the Linear and Nonlinear Dynamic Vibration Absorber for a Timoshenko Beam
http://jsm.iau-arak.ac.ir/article_683324.html
Dynamic vibration absorbers (DVAs) play an important role in the energy dissipation of a vibrating system. Undesirable vibrations of structures can be reduced by using the absorbers. This paper investigates the effect of an attached energy sink on the energy dissipation of a simply supported beam subjected to harmonic excitation. The aim is to design an optimal linear energy sink (LES) and a nonlinear energy sink (NES) and then compare them with each other. Each absorber includes a spring, a mass, and a damper. For each absorber, the optimum mass, stiffness, and damping coefficients are obtained in order to minimize the beam&rsquo;s maximum amplitude at the resonant frequencies. The optimization problem is minimizing the maximum amplitude of the beam subjected to an arbitrary harmonic force excitation. For consideration of the effects of rotary inertia and shear deformation, the Timoshenko beam theory is used. The mathematical model of beam with DVA is verified by using the ANSYS WORKBENCH software. Finally, by considering the uncertainty on the DVA parameters it was observed that the LES is more robust than the NES.