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Showing 27 results for Free Vibration
Vibration of graphene sheets with axial force effect in elastic medium based on nonlocal elasticity and third-order shear deformation theory
Ahmad Ghasemi Ghalebahman, Ali Khakbaz,
Volume 18, Issue 4 (8-2018)
Abstract
This study aims to investigate the transverse vibration of single- and double-layered graphene sheets embedded in an elastic medium based on the third-order shear deformation theory considering the axial force effect within the framework of Eringen’s nonlocal elasticity theory, where the governing equations of motion are obtained using Hamilton’s principle. The superiority of the studied non-local continuum model to its local counterpart is to consider the effect of size on the mechanical behavior of the structure. The results from a natural frequency analysis are obtained for different conditions such as the effect of size and aspect ratio, axial force, nonlocal coefficient, and change in the stiffness properties of the surrounding elastic medium by using the Navier-type solution for simply supported boundary conditions. Given that in a double-layered graphene sheet, the system has an in-phase vibrational mode and anti-phase vibrational mode with 180-degrees phase difference, the effect of van der Waals force on both vibrational modes is attempted to be investigated and it is shown that the van der Waals force has no effect on in-phase vibrational mode and by increasing it, the anti-phase frequency increases. It is also demonstrated that the nonlocal parameter is not a constant parameter but its value depends on the size and atomic structure, like chiral and zigzag configurations, and even on the type of boundary conditions.
Experimental and numerical analysis of Free Vibration of smart two-layered Aluminum/Piezoelectric cylindrical panel
Mahdi Saadatfar, Ali Soleimani, Arash Karimpoor Soumedel, Siamak Esmaeilzade Khadem,
Volume 18, Issue 5 (9-2018)
Abstract
Piezoelectric materials, in different shapes such as rectangular plate, annular plate, circular plate and cylindrical shell, have increasing application in industries in order to create smart structures. In this article, experimental and numerical analysis of free vibration of a two-layered cylindrical panel with metal and piezoelectric layer in different boundary condition is carried out. First, a single PZT-4 layer is polarized in radial direction. Using the Piezoelectric layer and an Aluminum layer, a two-layered smart panel is prepared. Then, the first natural frequency of the hybrid panel with free boundary condition is measured experimentally in three different ways. The hybrid panel is simulated in a finite element software (Abaqus). Results show good agreement between different experimental methods, as well as, between finite element model and experimental results. The accuracy, limitations and merits of different experimental methods are discussed completely. The results show that the natural frequency can be achieved accurately by excitation of actuator layer. Finally, the influence of different boundary conditions as well as geometrical parameter such as radios, length and thickness of smart cylindrical panel are investigated using the finite element software.
Free Vibration analysis of designed FML circular cylindrical shell based on optimum fiber orientation
Ali Nazari, , Ali Asghar Naderi,
Volume 18, Issue 7 (11-2018)
Abstract
The big deformation of composite structures under dynamic loads is one of the most disadvantages of these structures that cause to loss of stiffness of them. The using of fiber metal laminated shell that named FML in abbreviation is one of the ways to decrease the adverse effect of dynamic load. In this study the optimum fiber orientation of composite layers of the FML circular cylindrical shells are determined to more decrease the adverse effect of dynamic loads. For this purpose the fiber orientation of composite layers of the FML circular cylindrical shells are changed frequently and each cases being subjected to axial compressive load and with use of ABAQUS program the tension of all composite layers are calculated for all cases. Then with use of MATLAB program the fiber orientation that cause to maximum stiffness based on maximum tension fracture criterion is selected. The free vibration analysis is used for determination the accuracy and performance of design process. The results of free vibration analyses show that determination of the optimum fiber orientation cause to improvement of the FML shell natural frequency. Energy method and high order shear deformation theory is used to define the equation of motion. Full Calculus method is used for optimization in order to apply the exact result.
Free Vibration Analysis of Functionally Graded Magneto-electro-elastic Plates Resting on Elastic Foundations with Considering Interfacial Imperfections
N. Cheraghi , M. Lezgy-Nazargah, E. Etemadi ,
Volume 19, Issue 3 (3-2019)
Abstract
In this study, a three-dimensional (3D) Peano series solution is presented for the dynamic analysis of functionally graded (FG). Layered magneto-electro-elastic (MEE) plates resting on elastic foundations with considering imperfect interfacial bonding and the interfacial imperfection is modeled using a generalized spring layer method. Regardless of the number of layers, the equations of motion, Gauss’ equations (for electrostatics and magnetostatics), and the boundary and interface conditions are satisfied exactly. In this method, no assumptions on deformations, stresses, magnetic and electric fields along the thickness direction are introduced. Finally, the governing partial differential equations are solved using state-space method. The proposed formulation is validated through comparison with other available results. Effects of a two-parameter elastic foundation, gradient index, bonding imperfection, applied mechanical and electrical loads on the dynamic response of the functionally graded magneto-electro-elastic (FGMEE) plate are discussed The obtained exact solution can be used to assess the accuracy of the theorems for layered FGMEE plates and validating finite element codes.

Nonlinear Free Vibration Analysis of Composite Plate in Car Body of High Speed Trains
R. Nezami, M. Ghazanfari,
Volume 19, Issue 12 (12-2019)
Abstract

Vibration analysis of the plate is an important topic in high-speed train body design. Because of the dynamic loads on plates which are used in the wagon body of the train, vibration analysis and determination of the amount of deflection and bending of the structure is important in wagon design. A plate which is used in the high-speed train is composite plate. Composite plates are considered because of many advantages relative to the other plates, such as low weight, high strength and cost-effective. In this paper, the nonlinear free vibration analysis of the used plate in the wagon body of high-speed trains has been presented. First, a three layers sandwich plate used for car body of high-speed trains has been transformed into a single layer equivalent orthotropic plate. Von-Karman theory and the Galerkin method have been employed to solving the equations of motion of the equivalent orthotropic plate. The nonlinear natural frequencies of the first four modes of the system have been determined using the numerical and variational iteration methods (VIM). Then the effect of different parameters on the value of nonlinear frequencies of the first four modes has been studied. The Difference lower than 0.1% is observed between the determined natural frequencies by VIM, with initial condition limited to zero, and natural frequencies determined by linear vibration. The results show that natural frequency is increased by increasing elasticity modulus of the face, the thickness of the core and the thickness of the face of the sandwich plate. In addition, because of nonlinearity of plate vibration equations, natural frequencies of composite plate are increased by increasing initial condition.


Thermal Effects on Free Vibration of Functionally Graded Curved Timoshenko Nanobeams Resting on Winkler–Pasternak Elastic Foundation
I. Ghoytasi, O. Rahmani,
Volume 19, Issue 12 (12-2019)
Abstract
In this paper, the effects of unified temperature loading and Winkler-Pasternak elastic foundation on the vibration of functionally graded curved nanobeam have been studied. The proposed model is based on the modified couple stress theory and the Timoshenko beam model. The continuous distribution of material along the thickness of functionally graded curved nanobeam is achieved by changing the gradient index in the volume fraction. The governing equations and related boundary conditions are obtained using the Hamilton principle. By analyzing the quantitative and qualitative results in the tables and figures, influences of geometrical and thermo-physical parameters such as gradient index, aspect ratio, unified temperature difference, the ratio of thickness to length scale parameter and arc angle of functionally graded curved nanobeam on the natural frequency for different vibration mode have been interpreted. There is an excellent agreement between the present results and the results of the previous works. Applied temperature loading increases the sensitivity of the natural frequency to the changes in the aforementioned parameters and also increases the range of its changes. Also, applying the Pasternak elastic foundation changes the behavior of the natural frequency to the temperature changes.

Determining the severity and location of cracks in the Euler-Bernoulli beam, using the time domain signal of Free Vibration response and particle optimization method, under impact load

Volume 21, Issue 2 (5-2021)
Abstract
         In this paper, a crack detection method is presented to detect Euler-Bernoulli beams containing arbitrary number of transverse cracks. The proposed method uses the time domain signal of the free vibration response to provide the position and depth of cracking of the Euler-Bernoulli beam that is modeled with a modified stiffness using the Spring model, with high accuracy and precision. The time history responses used in this paper are nodal computational accelerations at certain points of the beam exposed to impact load. The acceleration of the nodes is calculated with the Newmark beta method at the edge of the elastic beam`s superelements. Initially, using the computational time history of the damaged beam and the analytical model of the Euler-Bernoulli beam, the objective function of the failure detection problem, to be optimized by particle swarm algorithm, is defined and, intensity and location of transverse cracks are calculated by solving the optimization problem in Matlab environment. In order to determine the accuracy of the proposed method, three beam samples with different cracks and loadings are considered. In the first sample, the crack supposed to be in the superelements of beam and the beam considered to be with four elements as superelements. The second one has ten elements and same loading as previous. The third one has twenty elements and the loading is on the second element. All of the loadings are impulse loads. The comparison of the results of a four elements beam with the primitive conditions shows that accuracy of the deducted results were exactly matched. For the ten element beam, the results were satisfying but in the twenty element beam with asymmetric loading, obtained results indicate imprecise match.
To determine the accuracy of the developed model in real environmental conditions, different percentages of noise were added to the data of all three samples. These noise addition to data, contain 1, 3, 5 Percentages of noise.  The results show that the model presented in the presence of noise also provides accurate results and the model is not sensitive to the presence of noise in the data applied to three samples. Considering different number of elements in each sample, no convergence was observed, Also the results were not sensitive to the location of impact load applied on the samples.
The results of this study indicated that asymmetric cracking and loading variation are very effective in predicting beam failure. The results also indicate that variable reduction is very effective on the accuracy of results.
Having more cracks and therefore more elements to analyze will yield to less accurate results. To lessen these inaccuracies, it can be practical to achieve better results by assuming the location of crack is constant in the element length if the depth of crack be the matter of importance.
The number of iterations that have been executed, indicate that the pace of convergences in the developed process is less than when PSO deployed solely. This speed rate for obtaining results makes the developed method practical for solving crack detection problems in structures.

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