Search results for: classical plate theory

Authors: Jixiao Tao, Xiaoqiao He

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The present study deals with the finite element (FE) analysis of thermally-induced bistable plate using various plate elements. The quadrilateral plate elements include the 4-node conforming plate element based on the classical laminate plate theory (CLPT), the 4-node and 9-node Mindlin plate element based on the first-order shear deformation laminated plate theory (FSDT), and a displacement-based 4-node quadrilateral element (RDKQ-NL20). Using the von-Karman’s large deflection theory and the total Lagrangian (TL) approach, the nonlinear FE governing equations for plate under thermal load are derived. Convergence analysis for four elements is first conducted. These elements are then used to predict the stable shapes of thermally-induced bistable plate. Numerical test shows that the plate element based on FSDT, namely the 4-node and 9-node Mindlin, and the RDKQ-NL20 plate element can predict two stable cylindrical shapes while the 4-node conforming plate predicts a saddles shape. Comparing the simulation results with ABAQUS, the RDKQ-NL20 element shows the best accuracy among all the elements.

Keywords: Bistable, finite element method, geometrical nonlinearity, quadrilateral plate elements

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Authors: R. Pilafkan, M. Kaffash Irzarahimi, S. F. Asbaghian Namin

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The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into classical plate theory (CLPT). A Generalized Differential Quadrature Method (GDQM) approach is utilized and numerical solutions for the critical buckling loads are obtained. Then, molecular dynamics (MD) simulations are performed for a series of zigzag SLGSs with different side-lengths and with various boundary conditions, the results of which are matched with those obtained by the nonlocal plate model to numerical the appropriate values of nonlocal parameter relevant to each type of boundary conditions.

Keywords: biaxial buckling, single-layered graphene sheets, nonlocal elasticity, molecular dynamics simulation, classical plate theory

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Authors: S. Madhu, V. V. Subba Rao

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In the implementation of carbon nanotube reinforced polymer matrix composites in structural applications, deflection and stress analysis are important considerations. In the present study, a multi scale analysis of deflection and stress analysis of carbon nanotube (CNT) reinforced polymer composite plates is presented. A micromechanics model based on the Mori-Tanaka method is developed by introducing straight CNTs aligned in one direction. The effect of volume fraction and diameter of CNTs on plate deflection and the stresses are investigated using Classical Laminate Plate Theory (CLPT). The study is primarily conducted with the intention of observing the suitability of CNT reinforced polymer composite plates under static loading for structural applications.

Keywords: carbon nanotube, micromechanics, composite plate, multi-scale analysis, classical laminate plate theory

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Authors: Badr Alsulami, Ahmed S. Elamary

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This paper summarizes and presents main results of an in-depth numerical analysis dealing with the shear buckling resistance of aluminum plate girders. The studies conducted have permitted the development of a simple design expression to determine the critical shear buckling stress in aluminum web panels. This expression takes into account the effects of reduction of strength in aluminum alloys due to the welding process. Ultimate shear resistance (USR) of plate girders can be obtained theoretically using Cardiff theory or Hӧglund’s theory. USR of aluminum alloy plate girders predicted theoretically using BS8118 appear inconsistent when compared with test data. Theoretical predictions based on Hӧglund’s theory, are more realistic. Cardiff theory proposed to predict the USR of steel plate girders only. Welded aluminum alloy plate girders studied experimentally by others; the USR resulted from tests are reviewed. Comparison between the test results with the values obtained from Hӧglund’s theory, BS8118 design method, and Cardiff theory performed theoretically. Finally, a new equation based on Cardiff tension-field theory proposed to predict theoretically the USR of aluminum plate girders.

Keywords: shear resistance, aluminum, Cardiff theory, Hӧglund's theory, plate girder

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Authors: Saeid Sahmani

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Due to size-dependent behavior of nanostrustures, the classical continuum models are not applicable for the analyses at this submicrion size. Surface stress effect is one of the most important matters which make the nanoscale structures to have different properties compared to the conventional structures due to high surface to volume ratio. In the present study, free vibration characteristics of nanoplates are investigated including surface stress effects. To this end, non-classical plate model based on Gurtin-Murdoch elasticity theory is proposed to evaluate the surface stress effects on the vibrational behavior of nanoplates subjected to different boundary conditions. Generalized differential quadrature (GDQ) method is employed to discretize the governing non-classical differential equations along with various edge supports. Selected numerical results are given to demonstrate the distinction between the behavior of nanoplates predicted by the classical and present non-classical plate models that leads to illustrate the great influence of surface stress effect. It is observed that this influence quite depends on the magnitude of the surface elastic constants which are relevant to the selected material.

Keywords: nanomechanics, surface stress, free vibration, GDQ method, small scale effect

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Authors: Ahmed S. Elamary

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Ultimate shear resistance (USR) of slender plate girders can be predicted theoretically using Cardiff theory or Hӧglund theory. This paper will be concerned with predicting the USR using Hӧglund theory and EC3. Two main factors can affect the USR, the panel width “b” and the web depth “d”, consequently, the panel aspect ratio (b/d) has to be identified by limits. In most of the previous study, there is no limit for panel aspect ratio indicated. In this paper theoretical analysis has been conducted to study the effect of (b/d) on the USR. The analysis based on ninety-six test results of steel plate girders subjected to shear executed and collected by others. New formula proposed to predict the percentage of the distance between the plastic hinges form in the flanges “c” to panel width “b”. Conservative limits of (c/b) have been suggested to get a consistent value of USR.

Keywords: ultimate shear resistance, plate girder, Hӧglund’s theory, EC3

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Authors: Yu T. Tsai, Jin H. Huang

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In this paper, the specific sound transmission loss (TL) of the laminated composite plate (LCP) with different material properties in each layer is investigated. The numerical method to obtain the TL of the LCP is proposed by using elastic plate theory. The transfer matrix approach is novelty presented for computational efficiency in solving the numerous layers of dynamic stiffness matrix (D-matrix) of the LCP. Besides the numerical simulations for calculating the TL of the LCP, the material properties inverse method is presented for the design of a laminated composite plate analogous to a metallic plate with a specified TL. As a result, it demonstrates that the proposed computational algorithm exhibits high efficiency with a small number of iterations for achieving the goal. This method can be effectively employed to design and develop tailor-made materials for various applications.

Keywords: sound transmission loss, laminated composite plate, transfer matrix approach, inverse problem, elastic plate theory, material properties

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Authors: Munawwar Mohabuth, Andrei Kotousov, Ching-Tai Ng

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On the basis of the finite deformation theory, the effect of homogeneous stress on the propagation of Lamb waves in an initially isotropic hyperelastic plate is analysed. The equations governing the propagation of small amplitude waves in the prestressed plate are derived using the theory of small deformations superimposed on large deformations. By enforcing traction free boundary conditions at the upper and lower surfaces of the plate, acoustoelastic dispersion equations for Lamb wave propagation are obtained, which are solved numerically. Results are given for an aluminum plate subjected to a range of applied stresses.

Keywords: acoustoelasticity, dispersion, finite deformation, lamb waves

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Authors: Meng Koon Lee, Mohammad Hosseini Fouladi, Satesh Narayana Namasivayam

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Research is focused on the response of soundboards of Classical guitars at frequencies up to 5 kHz as the soundboard is a major contributor to acoustic radiation at high frequencies when compared to the bridge and sound hole. A thin rectangular plate of variable thickness that is simply-supported on all sides is used as an analytical model of the research. This model is used to study the response of the guitar soundboard as the latter can be considered as a modified form of a rectangular plate. Homotopy Perturbation Method (HPM) is selected as a mathematical method to obtain an analytical solution of the 4th-order parabolic partial differential equation of motion of the rectangular plate of constant thickness viewed as a linear problem. This procedure is generalized to the nonlinear problem of the rectangular plate with variable thickness and an analytical solution can also be obtained. Sound power is used as a parameter to investigate the acoustic radiation of soundboards made from spruce using various bracing patterns. The sound power of soundboards made from Malaysian softwood such as damar minyak, sempilor or podo are investigated to determine the viability of replacing spruce as future materials for soundboards of Classical guitars.

Keywords: rectangular plates, analytical solution, homotopy perturbation, natural frequencies

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Authors: Amir R. Askari, Masoud Tahani

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The objective of the present paper is to investigate the effect of size on the vibrational behavior of fully clamped rectangular micro-plates based on the modified couple stress theory (MCST). To this end, a size-dependent Kirchhoff plate model is considered and the equation of motion which accounts for the effect of residual and couple stress components is derived using the Hamilton's principle. The eigenvalue problem associated with the free vibrations of fully clamped micro-plates is extracted and solved analytically using the extended Kantorovich method (EKM). The present findings are compared and validated by available results in the literature and an excellent agreement between them is observed. A parametric study is also conducted to show the significant effects of couple stress components on natural frequencies of fully clamped micro-plates. It is found that the ratio of MCST natural frequencies to those obtained by the classical theory (CT) only depends on the Poisson's ratio of the plate and is totally independent of plate's aspect ratio for cases with no residual stresses.

Keywords: vibrational analysis, modified couple stress theory, fully clamped rectangular micro-plates, extended Kantorovich method.

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Authors: Mahmoudi Noureddine

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In this study the use of two variable refined plate theories of laminated composite plates to static response of laminated plates. The plate theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The validity of the present theory is demonstrated by comparison with solutions available in the literature and finite element method. The result is presented for the static response of simply supported rectangular plates under uniform sinusoidal mechanical loadings.

Keywords: bending, composite, laminate, plates, fem

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

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In this paper, the non-linear free axisymmetric vibration of a thin annular plate made of functionally graded material (FGM) has been studied by using the energy method and a multimode approach. FGM properties vary continuously as well as non-homogeneity through the thickness direction of the plate. The theoretical model is based on the classical plate theory and the Von Kármán geometrical non-linearity assumptions. An approximation has been adopted in the present work consisting of neglecting the in-plane deformation in the formulation. Hamilton’s principle is used to derive the governing equation of motion. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to 1.5 times the plate thickness. The numerical results are given for the first axisymmetric non-linear mode shape for a wide range of vibration amplitudes and they are presented either in tabular form or in graphical form to show the effect that the vibration amplitude and the variation in material properties have significant effects on the frequencies and the bending stresses in large amplitude vibration of the functionally graded annular plate.

Keywords: non-linear vibrations, annular plates, large amplitudes, functionally graded material

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Authors: Hamed Khani Arani, Mohammad Shariyat, Armaghan Mohammadian

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In this research, the free vibration of a rectangular sandwich nano-plate (SNP) made of three smart layers in the visco Pasternak foundation is studied. The core of the sandwich is a piezo magnetic nano-plate integrated with two layers of piezoelectric materials. First-order shear deformation plate theory is utilized to derive the motion equations by using Hamilton’s principle, piezoelectricity, and modified couple stress theory. Elastic medium is modeled by visco Pasternak foundation, where the damping coefficient effect is investigated on the stability of sandwich nano-plate. These equations are solved by the differential quadrature method (DQM), considering different boundary conditions. Results indicate the effect of various parameters such as aspect ratio, thickness ratio, shear correction factor, damping coefficient, and boundary conditions on the dimensionless frequency of sandwich nano-plate. The results are also compared by those available in the literature, and these findings can be used for automotive industry, communications equipment, active noise, stability, and vibration cancellation systems and utilized for designing the magnetostrictive actuator, motor, transducer and sensors in nano and micro smart structures.

Keywords: free vibration, modified couple stress theory, sandwich nano-plate, visco Pasternak foundation

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Authors: Yang Zhong, Meijie Xu

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The explicit solutions for the natural frequencies and mode shapes of the orthotropic rectangular plate with four clamped edges are presented by the double finite cosine integral transform method. In the analysis procedure, the classical orthotropic rectangular thin plate is considered. Because only are the basic dynamic elasticity equations of the orthotropic thin plate adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by this paper is reasonable and theoretical. Finally, an illustrative example is given and the results are compared with those reported earlier. This method is found to be easier and effective. The results show reasonable agreement with other available results, but with a simpler and practical approach.

Keywords: rectangular orthotropic plate, four clamped edges, natural frequencies and mode shapes, finite integral transform

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Authors: Mokhtar Bouazza

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In this paper, the simplified theory will be used to predict the thermoelastic buckling behavior of rectangular functionally graded plates. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The simplified theory is used to obtain the buckling of the plate under different types of thermal loads. The thermal loads are assumed to be uniform, linear, and non-linear distribution through the thickness. Additional numerical results are presented for FGM plates that show the effects of various parameters on thermal buckling response.

Keywords: buckling, functionally graded, plate, simplified higher-order deformation theory, thermal loading

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Authors: Arne Fagerstrom, Gary Cunningham, Fredrik Hartwig

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In this paper, a theory of sustainable enterprises, sustainable enterprise theory (SET), is developed. The sustainable enterprise theory can only be a valid theory if knowledge about life and nature is complete. Knowledge limitations should not stop enterprises from doing business with a goal of better long-term life on earth. Life demands stewardship of the resources used during one’s lifetime. This paper develops a model influenced by (the classical) enterprise theory and resource theory that includes more than money in the business activities of an enterprise. The sustainable enterprise theory is then used in an analysis of accountability and in discussions about sustainable businesses.

Keywords: sustainable business, sustainability reporting, sustainable values, theory of the firm

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Authors: Mustafa Reşit Haboğlu, Ali Kurşun , Şafak Aksoy, Halil Aykul, Numan Behlül Bektaş

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A thermal elastic stress analysis of steel fiber reinforced aluminum laminated composite plate is investigated. Four sides of the composite plate are clamped and subjected to a uniform temperature load. The analysis is performed both analytically and numerically. Laminated composite is manufactured via hot pressing method. The investigation of the effects of the orientation angle is provided. Different orientation angles are used such as [0°/90°]s, [30°/-30°]s, [45°/-45°]s and [60/-60]s. The analytical solution is obtained via classical laminated composite theory and the numerical solution is obtained by applying finite element method via ANSYS.

Keywords: laminated composites, thermo elastic stress, finite element method.

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Authors: Bakur Gulua

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In this work, we consider some boundary value problems for the plate. The plate is the elastic material with voids. The state of plate equilibrium is described by the system of differential equations that is derived from three-dimensional equations of equilibrium of an elastic material with voids (Cowin-Nunziato model) by Vekua's reduction method. Its general solution is represented by means of analytic functions of a complex variable and solutions of Helmholtz equations. The problem is solved analytically by the method of the theory of functions of a complex variable.

Keywords: the elastic material with voids, boundary value problems, Vekua's reduction method, a complex variable

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Authors: Gholamreza Koochaki

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This paper presents the buckling analysis of functionally graded beams with various boundary conditions. The first order shear deformation beam theory (Timoshenko beam theory) and the classical theory (Euler-Bernoulli beam theory) of Reddy have been applied to the functionally graded beams buckling analysis The material property gradient is assumed to be in thickness direction. The equilibrium and stability equations are derived using the total potential energy equations, classical theory and first order shear deformation theory assumption. The temperature difference and applied voltage are assumed to be constant. The critical buckling temperature of FG beams are upper than the isotropic ones. Also, the critical temperature is different for various boundary conditions.

Keywords: buckling, functionally graded beams, Hamilton's principle, Euler-Bernoulli beam

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Authors: Djamal Hamadi, Sifeddine Abderrahmani, Toufik Maalem, Oussama Temami

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In recent years many finite elements have been developed for plate bending analysis. The formulated elements are based on the strain based approach. This approach leads to the representation of the displacements by higher order polynomial terms without the need for the introduction of additional internal and unnecessary degrees of freedom. Good convergence can also be obtained when the results are compared with those obtained from the corresponding displacement based elements, having the same total number of degrees of freedom. Furthermore, the plate bending elements are free from any shear locking since they converge to the Kirchhoff solution for thin plates contrarily for the corresponding displacement based elements. In this paper the efficiency of the strain based approach compared to well known displacement formulation is presented. The results obtained by a new formulated plate bending element based on the strain approach and Kirchhoff theory are compared with some others elements. The good convergence of the new formulated element is confirmed.

Keywords: displacement fields, finite elements, plate bending, Kirchhoff theory, strain based approach

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Authors: Junaid Kameran Ahmed

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A laminated plate composite of graphite/epoxy has been analyzed dynamically in the present work by using a quadratic element (8-node diso-parametric), and by depending on 1^st order shear deformation theory, every node in this element has 6-degrees of freedom (displacement in x, y, and z axis and twist about x, y, and z axis). The dynamic analysis in the present work covered parametric studies on a composite laminated plate (square plate) to determine its effect on the natural frequency of the plate. The parametric study is represented by set of changes (plate thickness, number of layers, support conditions, layer orientation), and the plates have been simulated by using ANSYS package 12. The boundary conditions considered in this study, at all four edges of the plate, are simply supported and fixed boundary condition. The results obtained from ANSYS program show that the natural frequency for both fixed and simply supported increases with increasing the number of layers, but this increase in the natural frequency for the first five modes will be neglected after 10 layers. And it is observed that the natural frequency of a composite laminated plate will change with the change of ply orientation, the natural frequency increases and it will be at maximum with angle 45 of ply for simply supported laminated plate, and maximum natural frequency will be with cross-ply (0/90) for fixed laminated composite plate. It is also observed that the natural frequency increase is approximately doubled when the thickness is doubled.

Keywords: laminated plate, orthotropic plate, square plate, natural frequency (free vibration), composite (graphite / epoxy)

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Authors: Mustafa Arda, Metin Aydogdu

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Carbon nanotubes (CNTs) have many possible application areas because of their superior physical properties. Nonlocal Theory, which unlike the classical theories, includes the size dependency. Nonlocal Stress and Strain Gradient approaches can be used in nanoscale static and dynamic analysis. In the present study, torsional vibration of CNTs was investigated according to nonlocal stress and strain gradient theories. Effects of the small scale parameters to the non-dimensional frequency were obtained. Results were compared with the Molecular Dynamics Simulation and Lattice Dynamics. Strain Gradient Theory has shown more weakening effect on CNT according to the Stress Gradient Theory. Combination of both theories gives more acceptable results rather than the classical and stress or strain gradient theory according to Lattice Dynamics.

Keywords: torsional vibration, carbon nanotubes, nonlocal gradient theory, stress, strain

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Authors: Prathmesh Vikas Patil, Yashaswini Lomte Patil

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Laminated composite materials have considerable attention in various engineering applications due to their exceptional strength-to-weight ratio and mechanical properties. The analysis of laminated composite plates in three-dimensional (3D) elasticity is a complex problem, as it requires accounting for the orthotropic anisotropic nature of the material and the interactions between multiple layers. Conventional approaches, such as the classical plate theory, provide simplified solutions but are limited in performing exact analysis of the plate. To address such a challenge, the state space method emerges as a powerful numerical technique for modeling the behavior of laminated composites in 3D. The state-space method involves transforming the governing equations of elasticity into a state-space representation, enabling the analysis of complex structural systems in a systematic manner. Here, an effort is made to perform a 3D elasticity analysis of plates with cross-ply and angle-ply laminates using the state space approach. The state space approach is used in this study as it is a mixed formulation technique that gives the displacements and stresses simultaneously with the same level of accuracy.

Keywords: cross ply laminates, angle ply laminates, state space method, three-dimensional elasticity analysis

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Authors: Seyyed Feisal Asbaghian Namin, Reza Pilafkan, Mahmood Kaffash Irzarahimi

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TThis paper considers vibration of single-layered graphene sheets using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), an open source software, is used to obtain fundamental frequencies. On the other hand, governing equations are derived using nonlocal elasticity and first order shear deformation theory (FSDT) and solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in governing equations of motion by nonlocal parameter. The effect of different side lengths, boundary conditions and nonlocal parameter are inspected for aforementioned methods. Results are obtained from MD simulations is compared with those of the nonlocal elasticity theory to calculate appropriate values for the nonlocal parameter. The nonlocal parameter value is suggested for graphene sheets with various boundary conditions. Furthermore, it is shown that the nonlocal elasticity approach using classical plate theory (CLPT) assumptions overestimates the natural frequencies.

Keywords: graphene sheets, molecular dynamics simulations, fundamental frequencies, nonlocal elasticity theory, nonlocal parameter

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Authors: Mei-Jie Xu, Yang Zhong

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Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: Parveen K. Saini, Mayank Kushwaha

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The influence of material property variation on stress concentration factor (SCF) due to the presence of a circular hole in a functionally graded material (FGM) plate is studied in this paper. A numerical method based on complex variable theory of elasticity is used to investigate the problem. To achieve the material property, variation plate is decomposed into a number of rings. In this research work, Young's modulus is assumed to be varying exponentially and it is found that stress concentration factor can be reduced by increasing Young’s modulus progressively away from the hole.

Keywords: stress concentration, circular hole, FGM plate, bending

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Authors: Behzad Mohammadzadeh, Huyk Chun Noh

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The plate is one of the popular structural elements used in a wide range of industries and structures. They may be subjected to blast loads during explosion events, missile attacks or aircraft attacks. This study is to investigate dynamic responses of the rectangular plate subjected to explosive loads. The effects of material properties and plate thickness on responses of the plate are to be investigated. The compressive pressure is applied to the surface of the plate. Different amounts of thickness in the range from 10mm to 30mm are considered for the plate to evaluate the changes in responses of the plate with respect to the plate thickness. Two different properties are considered for the steel. First, the analysis is performed by considering only the elastic-plastic properties for the steel plate. Later on damping is considered to investigate its effects on the responses of the plate. To do analysis, the numerical method using a finite element based package ABAQUS is applied. Finally, dynamic responses and graphs showing the relation between maximum displacement of the plate and aim parameters are provided.

Keywords: impulsive loaded plates, dynamic analysis, ABAQUS, material nonlinearity

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Authors: Ajmal Hussain

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In Indian music parlance, Rasa denotes a distinct aesthetic experience that builds up in the mind of the listeners while listening to a piece of Indian classical music. The distinction of the experience is rooted in the concept that it gives rise to an enhanced awareness about the Self or God and creates a mental state detached from mundane issues of everyday life. The theory of Rasa was initially proposed in the context of theatre but became a part of Indian musicological discourse roughly two thousand years ago, however, to this day, it remains shrouded in mystery due to its religious associations and connotations. This paper attempts to demystify the theory of Rasa in the light of available scientific knowledge fund particularly in Brain and Mind sciences. The paper initially describes the religious context of the theory of Rasa and then discusses its classical formulations by Bharata and Abhinavagupta including the steps and stages laid down by the latter to explain the creation of musical experience. The classical formulations are then interpreted with reference to the scientific knowledge fund about the human mind and mechanics of perception. The study uses the model of human mind as proposed by Portuguese-American neuroscientist Antonio Damasio in his theory ‘A Nesting Principle’. On the basis of the findings by Damasio, the paper interprets the experience of Rasa from a scientific perspective and clarifies the sequence of steps and stages involved in the making of musical experience. The study concludes that although the classical formulations of Rasa identify key aspects of musical experience, the association of Rasa with religion is misleading. The association with religion does not depend upon musical stimulus but the intellectual orientation of the listener. It further establishes that the function of Rasa is more profound as, from an evolutionary perspective, it can be seen as a catalyst for higher consciousness.

Keywords: aesthetic, consciousness, music, Rasa

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: Babak Safaei, A. M. Fattahi

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Polymer/carbon nanotube nanocomposites have a wide range of promising applications Due to their enhanced properties. In this work, free vibration analysis of single-walled carbon nanotube-reinforced composite plates is conducted in which carbon nanotubes are embedded in an amorphous polyethylene. The rule of mixture based on various types of plate model namely classical plate theory (CLPT), first-order shear deformation theory (FSDT), and higher-order shear deformation theory (HSDT) was employed to obtain fundamental frequencies of the nanocomposite plates. Generalized differential quadrature (GDQ) method was used to discretize the governing differential equations along with the simply supported and clamped boundary conditions. The material properties of the nanocomposite plates were evaluated using molecular dynamic (MD) simulation corresponding to both short-(10,10) SWCNT and long-(10,10) SWCNT composites. Then the results obtained directly from MD simulations were fitted with those calculated by the rule of mixture to extract appropriate values of carbon nanotube efficiency parameters accounting for the scale-dependent material properties. The selected numerical results are presented to address the influences of nanotube volume fraction and edge supports on the value of fundamental frequency of carbon nanotube-reinforced composite plates corresponding to both long- and short-nanotube composites.

Keywords: nanocomposites, molecular dynamics simulation, free vibration, generalized, differential quadrature (GDQ) method

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