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حرية الوصول المقاله
1 - Finite element formulation for the free vibration analysis of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory
Milad Hemmatnezhad Reza AnsariAbstractThe present paper is concerned with the free vibration analysis of double-walled carbon nanotubes embedded in an elastic medium and based on Eringen's nonlocal elasticity theory. The effects of the transverse shear deformation and rotary inertia are included acc أکثرAbstractThe present paper is concerned with the free vibration analysis of double-walled carbon nanotubes embedded in an elastic medium and based on Eringen's nonlocal elasticity theory. The effects of the transverse shear deformation and rotary inertia are included according to the Timoshenko beam theory. The governing equations of motion which are coupled with each other via the van der Waals interlayer forces have been derived using Hamilton's principle. The thermal effect is also incorporated into the formulation. Using the statically exact beam element with displacement fields based on the first order shear deformation theory, the finite element method is employed to discretize the coupled governing equations which are then solved to find the natural frequencies. The effects of the small scale parameter, boundary conditions, thermal effect, changes in material constant of the surrounding elastic medium, and geometric parameters on the vibration characteristics are investigated. Furthermore, our analysis includes nonlocal double-walled carbon nanotubes with different boundary conditions between inner and outer tubes which seem to be scarcely considered in the literature, and the corresponding given results for this case can be considered as a benchmark for further studies. Comparison of the present numerical results with those from the open literature shows an excellent agreement. تفاصيل المقالة -
حرية الوصول المقاله
2 - Modelling of Non-Uniform Piezoelectric Micro-Cantilever in Different Environments
Mitra Taghizade A. H. Korayem M. H. KorayemIn recent years, Atomic Force Microscopy (AFM) has been known as a powerful and efficient tool for surface imaging in different environment. To enhance image quality and more precise prediction of Micro-cantilever (MC) behaviour, accuracy in the MC modeling and simulati أکثرIn recent years, Atomic Force Microscopy (AFM) has been known as a powerful and efficient tool for surface imaging in different environment. To enhance image quality and more precise prediction of Micro-cantilever (MC) behaviour, accuracy in the MC modeling and simulation and detecting the MC sensitivity to geometric parameters has great importance. To model the vibration motion of the AFM non-uniform piezoelectric MC, Timoshenko beam theory is used in order to consider the effect of shear effect in air and liquid environment. In addition, the effect of the forces imposed by the ambient and sample surface is considered. Frequency response has been studied in the air and different liquid environments and the obtained results have been compared with experiential results as well as with results obtained from Euler-Bernoulli beam theory that is reflective of higher precision exercised in the modeling in respect to Euler-Bernoulli beam theory. Efast statistical method, which is found efficient and quick in the survey of linear and nonlinear models and takes the inter-parameter coupling effect into consideration besides calculating the sensitivities unique to each of the factors, has been applied in order to analyse the geometrical parameters’ effects on the MC natural frequencies in the air and water environments. تفاصيل المقالة -
حرية الوصول المقاله
3 - Vibration Analysis of Rotary Tapered Axially Functionally Graded Timoshenko Nanobeam in Thermal Environment
N Shafiei M Hamisi M GhadiriIn this paper, vibration analysis of rotary tapered axially functionally graded (AFG) Timoshenko nanobeam is investigated in a thermal environment based on nonlocal theory. The governing equations of motion and the related boundary conditions are derived by means of Ham أکثرIn this paper, vibration analysis of rotary tapered axially functionally graded (AFG) Timoshenko nanobeam is investigated in a thermal environment based on nonlocal theory. The governing equations of motion and the related boundary conditions are derived by means of Hamilton’s principle based on the first order shear deformation theory of beams. The solution method is considered using generalized differential quadrature element (GDQE) method. The accuracy of results are validated by other results reported in other references. The effect of various parameters such as AFG index, rate of cross section change, angular velocity, size effect and boundary conditions on natural frequencies are discussed comprehensively. The results show that with increasing angular velocity, non-dimensional frequency is increased and it depends on size effect parameter. Also, in the zero angular velocity, it can be seen with increasing AFG index, the frequencies are reducing, but in non-zero angular velocity, AFG index shows complex behavior on frequency. تفاصيل المقالة -
حرية الوصول المقاله
4 - Nonlinear Modeling of Bolted Lap Jointed Structure with Large Amplitude Vibration of Timoshenko Beams
M Jamal-Omidi F AdelThis paper aims at investigating the nonlinear behavior of a system which is consisting of two free-free beams which are connected by a nonlinear joint. The nonlinear system is modelled as an in-extensional beam with Timoshenko beam theory. In addition, large amplitude أکثرThis paper aims at investigating the nonlinear behavior of a system which is consisting of two free-free beams which are connected by a nonlinear joint. The nonlinear system is modelled as an in-extensional beam with Timoshenko beam theory. In addition, large amplitude vibration assumption is taken into account in order to obtain exact results. The nonlinear assumption in the system necessities existence of the curvature-related and inertia-related nonlinearities. The nonlinear partial differential equations of motion for the longitudinal, transverse, and rotation are derived using the Hamilton’s principle. A set of coupled nonlinear ordinary differential equations are further obtained with the aid of Galerkin method. The frequency-response curves are presented in the section of numerical results to demonstrate the effect of the different dimensionless parameters. It is shown that the nonlinear bolted-lap joint structure exhibits a hardening-type behavior. Furthermore, it is found that by adding a nonlinear spring the system exhibits a stronger hardening-type behavior. In addition, it is found that the system shows nonlinear behavior even in the absence of the nonlinear spring due to the nonlocal nonlinearity assumption. Moreover, it is shown that considering different engineering beam theories lead to different results and it is found that the Euler-Bernoulli beam theory over-predict the resonance frequency of the structure by ignoring rotary inertia and shear deformation. تفاصيل المقالة -
حرية الوصول المقاله
5 - A Nonlocal First Order Shear Deformation Theory for Vibration Analysis of Size Dependent Functionally Graded Nano beam with Attached Tip Mass: an Exact Solution
M Ghadiri A JafariIn this article, transverse vibration of a cantilever nano- beam with functionally graded materials and carrying a concentrated mass at the free end is studied. Material properties of FG beam are supposed to vary through thickness direction of the constituents according أکثرIn this article, transverse vibration of a cantilever nano- beam with functionally graded materials and carrying a concentrated mass at the free end is studied. Material properties of FG beam are supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM). The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on Timoshenko beam theory in order to consider the effect of shear deformation and rotary inertia. Hamilton’s principle is applied to obtain the governing differential equation of motion and boundary conditions and they are solved applying analytical solution. The purpose is to study the effects of parameters such as tip mass, small scale, beam thickness, power-law exponent and slenderness on the natural frequencies of FG cantilever nano beam with a point mass at the free end. It is explicitly shown that the vibration behavior of a FG Nano beam is significantly influenced by these effects. The response of Timoshenko Nano beams obtained using an exact solution in a special case is compared with those obtained in the literature and is found to be in good agreement. Numerical results are presented to serve as benchmarks for future analyses of FGM cantilever Nano beams with tip mass. تفاصيل المقالة -
حرية الوصول المقاله
6 - Non Uniform Rational B Spline (NURBS) Based Non-Linear Analysis of Straight Beams with Mixed Formulations
R Ranjan J.N ReddyDisplacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element أکثرDisplacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation , and/or shear strain , as well as the variational method used (e.g., collocation, weak form Galerkin, or least-squares). When nonlinear shear deformation theories are used, the displacement finite element models experience membrane and shear locking. The present study is concerned with development of alternative beam finite elements using both uniform and non-uniform rational b-splines (NURBS) to eliminate shear and membrane locking in an hpk finite element setting for both the Euler-Bernoulli beam and Timoshenko beam theories. Both linear and non-linear analysis are performed using mixed finite element models of the beam theories studied. Results obtained are compared with analytical (series) solutions and non-linear finite element and spectral/hp solutions available in the literature, and excellent agreement is found for all cases. تفاصيل المقالة -
حرية الوصول المقاله
7 - Nonlinear Finite Element Analysis of Bending of Straight Beams Using hp-Spectral Approximations
R RanjanDisplacement finite element models of various beam theories have been developed using traditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions). Various finite element models of beams differ from each other in the choice of the in أکثرDisplacement finite element models of various beam theories have been developed using traditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation φ and/or shear strain γxz, or in the integral form used (e.g., weak form or least-squares) to develop the finite element model. The present study is concerned with the development of alternative beam finite elements using hp-spectral nodal expansions to eliminate shear and membrane locking. Both linear and non-linear analysis are carried out using both displacement and mixed finite element models of the beam theories studied. Results obtained are compared with both analytical (series) solutions and non-linear finite element solutions from literature, and excellent agreement is found for all cases. تفاصيل المقالة -
حرية الوصول المقاله
8 - A Comparative Study of Least-Squares and the Weak-Form Galerkin Finite Element Models for the Nonlinear Analysis of Timoshenko Beams
W Kim J.N ReddyIn this paper, a comparison of weak-form Galerkin and least-squares finite element models of Timoshenko beam theory with the von Kármán strains is presented. Computational characteristics of the two models and the influence of the polynomial orders used on أکثرIn this paper, a comparison of weak-form Galerkin and least-squares finite element models of Timoshenko beam theory with the von Kármán strains is presented. Computational characteristics of the two models and the influence of the polynomial orders used on the relative accuracies of the two models are discussed. The degree of approximation functions used varied from linear to the 5th order. In the linear analysis, numerical results of beam bending under different types of boundary conditions are presented along with exact solutions to investigate the degree of shear locking in the newly developed mixed finite element models. In the nonlinear analysis, convergences of nonlinear finite element solutions of newly developed mixed finite element models are presented along with those of existing traditional model to compare the performance. تفاصيل المقالة -
حرية الوصول المقاله
9 - Theoretical Formulations for Finite Element Models of Functionally Graded Beams with Piezoelectric Layers
J.N Reddy S Doshi A MulianaIn this paper an overview of functionally graded materials and constitutive relations of electro elasticity for three-dimensional deformable solids is presented, and governing equations of the Bernoulli–Euler and Timoshenko beam theories which account for through- أکثرIn this paper an overview of functionally graded materials and constitutive relations of electro elasticity for three-dimensional deformable solids is presented, and governing equations of the Bernoulli–Euler and Timoshenko beam theories which account for through-thickness power-law variation of a two-constituent material and piezoelectric layers are developed using the principle of virtual displacements. The formulation is based on a power-law variation of the material in the core with piezoelectric layers at the top and bottom. Virtual work statements of the two theories are also developed and their finite element models are presented. The theoretical formulations and finite element models presented herein can be used in the analysis of piezolaminated and adaptive structures such as beams and plates. تفاصيل المقالة -
حرية الوصول المقاله
10 - Nonlinear Vibration Analysis of Multi-Walled Carbon Nanotubes in Thermal Environment using the Nonlocal Timoshenko Beam Model
ابوالحسن نظری نژاد گیاشی رضا انصاری حبیب رمضان نژاد آزاربنیIn this paper, based on the nonlocal Timoshenko beam theory, a nonlinear model is presented for the vibrational behavior of carbon nanotubes (CNTs) embedded in elastic medium in thermal environment. Using the Timoshenko beam theory and nonlocal elasticity of Eringen, th أکثرIn this paper, based on the nonlocal Timoshenko beam theory, a nonlinear model is presented for the vibrational behavior of carbon nanotubes (CNTs) embedded in elastic medium in thermal environment. Using the Timoshenko beam theory and nonlocal elasticity of Eringen, the influences of rotary inertia, transverse shear deformation and small scale effect are taken into account. To model the interaction forces between walls, whether adjacent or non-adjacent, the van der Waals interlayer interactions are considered. The harmonic balance method (HBM) is used for the solution of the set of nonlinear governing equations and the frequency function of the system for the simply-supported boundary conditions is derived. Compared to the incremental harmonic balance method which has been employed in the previous studies, the HBM is simpler and has a reasonable accuracy. The effects of geometrical parameters of nanotubes such as the number of walls, the ratio of length to outer diameter and environmental conditions such as elastic medium modulus, temperature and also the effect of nonlocal parameter on the nonlinear frequency are investigated. The presented nonlinear vibration analysis is of a general form, so that they are applicable for CNTs with arbitrary number of walls. The obtained results for single-, double- and triple-walled CNTs indicate that with an increase in the number of walls, elastic medium modulus, aspect ratio and temperature, the value of nonlinear frequency tends to that of its linear counterpart. Also, a comparison between the results of the Timoshenko beam theory and those of Euler-Bernoulli beam theory shows that the difference between the frequency responses of these theories is significant for short CNTs, but, as the length increases, the difference between the results becomes negligible. تفاصيل المقالة
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