جستجوی مقالات مرتبط با کلیدواژه « ارتعاش آزاد » در نشریات گروه « عمران »

The beams are really useful for the large number of engineering structures. In this article, a simple robust beam element will be formulated. Other researchers utilized several theories such as Euler-Bernoulli, Timoshenko and higher order shear for analyzing of the beams. The proposed formulation will be written based on satisfying the equilibrium equation. Using the equilibrium equation reduces number of unknowns in addition to improving the efficiency of new element. the suggested element has only two nod and tow degrees of freedom per node. The third and second order polynomials will be used for vertical displacement and rotation fields, respectively. After calculating the matrix of shape functions, the governing equations of statics, free vibration and buckling analysis could be written. Finally, using the suggested element, static analysis, free vibration and buckling were performed on the several problems. To prove the efficiency of the new element, the large number of benchmark tests will be utilized. These numerical tests have various support conditions and different aspect ratios. By the help of these tests, rapid convergence and high accuracy of proposed element will be shown. The new element has high efficiency in all of the static, free vibration and buckling analysis for both of thin and thick beams beside of its simplicity. Good element answers of other researchers are be available to have better comparison.

Discrete singular convolution is a new numerical method that its ability to vibrational analysis has been demonstrated in the last decade. A lot of research on how to apply the complex boundary conditions of the different issues using this method is carried out and a variety of solutions have been proposed in this regard. Applying the boundary conditions in the governing equations of coupled shear walls, is a challenging issue. This paper proposes a new algorithm for applying the boundary conditions in the vibration analysis of coupled shear walls using the DSC method. In order to validate the proposed method, several samples were analyzed using this algorithm and the results were compared with the values obtained from three conventional numerical methods of Finite element (FEM), Differential quadrature (DQM) and Finite difference (FDM) methods. The great conformity was found between the results which emphasized the validity and integrity of the proposed method. In addition, the ability of the DSC algorithm was explored in terms of the computational speed, computational effort and the amount of computer memory required aspect and compared with the other conventional numerical approaches. It is concluded that the DSC is more efficient than the compared numerical methods from the results of this study.

Machine foundations induce a wide range of dynamic shear strains in foundation bed. Dynamic properties of soils including the damping ratio and the dynamic stiffness intensely depend on the level of generated dynamic shear strain. Therefore, considering the appropriate dynamic properties of a foundation bed corresponding to the generated dynamic shear strain is crucial to having a better evaluation of the dynamic response of a machine foundation. This paper presents the design and construction of an apparatus namely “Foundation Model Response Test (FMRT)”. This apparatus provides the tests to investigate the dynamic properties of machine foundation and underlying bed in a wide range of dynamic shear strains employing a various range of dynamic excitation forces and static weight (dead weight). The FMRT apparatus could be used in the field to evaluate the dynamic response of the undisturbed bed and on the prepared bed in the laboratory test pit. Two types of steady-state and free vibration tests could be conducted by employing the FMRT apparatus. Steady-state vibration tests induce larger shear strain in bed, whereas free vibration tests induce smaller shear strain. Correlation of the results of these two types of tests, dynamic responses, and dynamic properties of foundation bed in a wide range of dynamic shear strain would be achieved. The accuracy and validity of all FMRT tests are possible to monitor precisely and any unwanted noises and modes of vibration are possible to be controlled by evaluating the Fast Fourier Transform (FFT) of all sensors data when conducting tests. Several steady-state and free vibration tests were conducted to illustrate the performance of the designed apparatus. Moreover, the method of calculation, controlling unwanted vibration, and correlation of free and steady-state example tests were submitted. FMRT tests are inexpensive, repeatable, non-destructive and reliable tests that ensure the dynamic response of machine foundation possible accurately.

In this research, an exact solution for free vibration analysis of thick transversely isotropic simply supported rectangular plates on the Pasternak foundation was proposed using the displacement potential function method. By means of the proposed displacement potential functions for dynamic problems by Eskandari-Ghadi, the differential governing equations in terms of displacements were converted into two linear partial differential equations of second and forth order. These differential equations were solved based on the separation of variables method and satisfying exact boundary conditions. In order to validate the results, the obtained results were compared with other available analytical works for isotropic and transversely isotropic plates, and it indicated remarkable agreement. Having no simplifying assumptions for the strain or stress distribution in the plate thickness, the obtained results in this paper were applicable to any arbitrary plate thickness with no limitation on its thickness ratio such as thin, moderately thick, and thick plates. Thus, the obtained results of the present work can be used as a benchmark solution for other analytical and numerical studies. To investigate the effect of various parameters on the vibrational plate response, the precise non-dimensional frequencies were obtained in different range of thickness ratios, aspect ratios, elastic foundation coefficients, and mechanical characteristics of plates. It was observed that with increasing thickness ratio and aspect ratio of the plate, the non-dimensional natural frequencies of plate decreased and increased, respectively. In addition, comparative results of isotropic and transversely isotropic plates showed that shear modulus in transverse direction would have significant influence on the vibrational behavior of rectangular plates. It was shown that when the value of the thickness ratio increased, the sensitivity of non-dimensional frequency response to values of foundation stiffness coefficients decreased. In addition, it can be conducted that the effect of the shearing layer of elastic foundation coefficient value increased by increasing the thickness ratios of plates.

Sandwich plates containing magnetic fluids in the core are considered nowadays as a smart structure. Due to the ability of rapid change in the viscosity of the fluid in the core, plate can be used to control the vibration of the structure and to deplete the energy. In the present study, free vibration behavior of a sandwich plate, which is made of composite glass-epoxy fiber face sheets and contains magnetic fluid in the core, is investigated. Based on the Hamilton's principle and considering independent bending degrees of freedom for upper and lower faces, free vibration governing equations of the plate are derived using the spline finite strip method. To validate the proposed method, the results are compared with those of other similar studies using different methods. Then, the effects of different parameters, e.g., diverse boundary conditions, which are rarely considered elsewhere, are evaluated based on the proposed formulation. Moreover, the frequency impacts as well as the modal loss factor, which are the two main parameters in the vibration analysis of these structures, are considered and the effect of different factors such as magnetic field intensity and fluid thickness in the core are investigated. The results indicate that the spline finite strip method has good accuracy in analyzing sandwich plates containing a flexible core. Besides, the results show that increasing the intensity of the magnetic field causes an increase in the frequency and loss factor corresponding to each mode. Moreover, increasing the thickness of the fluid leads to increase in the loss factor and decrease in the frequency. The results indicate that despite the change in the strain energy of the structure, due to changes in the fiber orientation of the composite layers, the frequency of each mode does not change significantly. It was also found that the clamped plate had the highest frequency and the simply supported boundary condition had the lowest frequency.

In this paper, a new 2-node element is proposed for free vibration and buckling analysis of symmetrically laminated beams. The element’s formulation is based on first order shear deformation theory (FSDT). For this aim, the deflection and rotation field of the element is selected from third and second order functions, respectively. Moreover, the shear strain is assumed to be constant along with the element. By establishing the total strain energy in the element and stationary with respect to shear strain, the explicit form of the shape functions of deflection and rotation fields of the proposed element, are obtained. It should be mentioned, by decreasing the element’s thickness, these shape functions are approach to the Euler-Bernoulli shape’s functions and the shear locking problem does not occurred in the element. By utilizing the obtained shape functions, the explicit form of the stiffness matrix are calculated for the element. On the other hand, by using the governing equation of the free vibration and buckling of the beam, the explicit form of the translation and rotary mass matrices, and geometric stiffness matrix of the element are obtained. Finally, several numerical tests fulfill to assess the robustness of the developed element. For this purpose, free vibration and buckling analysis of symmetrically laminated beams with different boundary conditions and aspect ratios, are performed. The results of the numerical tests demonstrate high accuracy and efficiency of the proposed element for free vibration and buckling analysis of laminated beams.

Todays, modern materials are widely used for construction of various structural elements such as beams, plates, shell and the other elements. One of these modern materials is functionally graded materials (FGMs). The uses of these materials are due to their mechanical properties and thermal conductivity. During the two past decades structural elements made from these materials have received wide applications in aerospace, mechanical and civil engineering. Material properties of the functionally graded materials vary continuously from metal on one surface to ceramic on the other surface. The distribution makes these materials applicable in different fields of engineering, especially in environments subjected to high thermal change. For obtaining the governing equations of the structural elements different theories of elasticity can be used. For solving the problems different analytical, numerical and semi-analytical methods can be applied. Among the numerical methods finite element, finite difference, finite volume, differential quadrature and the other methods may be used for solving the problems. The differential quadrature (DQ) method is an accurate, efficient and robust numerical solver with low computational cost. The DQ method has been used for solving free vibration, dynamic analysis and so on. This method can be used for solving structural elements alone or in conjunction with the other analytical or numerical methods. In this study, the method is used for free vibration analysis of functionally graded beams on two parameter elastic foundation. The elastic foundation has linear and shearing layers. The governing equations are derived based on the first order shear deformation theory (FSDT). The governing equations and the related boundary conditions are discretized using the DQ method. Then by employing method of separation of variables, the obtained equations are transferred from temporal domain to frequency domain and the frequency of the beam is calculated. Applicability, rapid rate of convergence and accuracy of the proposed method are demonstrated via solving some examples. Influences of different parameters such as linear and shearing layers, boundary conditions and height-to-length ratio on frequency of the beams are investigated.

The beam theory is used in the analysis and design of a wide range of structures, from buildings to bridges to the load-bearing bones of the human body. Beams resting on elastic foundation have wide application in many branches of engineering problems namely geotechnics, road, railroad and marine engineering and bio-mechanics. The foundation is very often a rather complex medium; e.g., a rubberlike fuel binder, snow, or granular soil. The key issue in the analysis is modelling the contact between the structural elements and the elastic bed. Since of interest here is the response of the foundation at the contact area and not the stresses or displacements inside the foundation material, In most cases the contact is presented by replacing the elastic foundation with simple models, usually spring elements. The most frequently used foundation model in the analysis of beam on elastic foundation problems is the Winkler foundation model. In the Winkler model, the elastic bed is modeled as uniformly distributed, mutually independent, and linear elastic vertical springs which produce distributed reactions in the direction of the deflection of the beam. However since the model does not take into account either continuity or cohesion of the bed, it may be considered as a rather crude representation of the elastic foundation. In order to find a physically close and mathematically simple foundation model, Pasternak proposed a so-called two-parameter foundation model with shear interactions. The first foundation parameter is the same as the Winkler foundation model and the second one is the stiffness of the shearing layer in the Pasternak foundation model.
Dynamic analysis is an important part of structural investigation and the results of free vibration analysis are useful in this context. Vibration problems of beams on elastic foundation occupy an important place in many fields of structural and foundation engineering.With the increase of thickness, existence of simplifying hypotheses in beam theories such as the ignorance of rotational inertial and transverse shear deformation in classic theory, application of determination coefficient in first-order shear theory and expression of one or few unknown functions based on other functions in higher-order shear theories is accompanied by reduction in accuracy of these theories. This represents the necessity of precise and analytical solutions for beam problems with the least number of simplifying hypotheses and for different thicknesses.
In the present study, the analytical solution for the problem of free vibration of homogeneous prismatic simply supported beam with rectangular solid sections and desired thickness resting on Pasternak elastic foundation is provided for completely isotropic behaviors under two-dimensional theory of elasticity and functions of displacement potentials. Characteristic equations of natural vibration are defined by solving one partial differential equations of fourth order through separation of variables and application of boundary conditions. The major characteristics of present study are lack of limitation of thickness and its validity for beams of low, medium and large thickness. To verify, the results of present study were compared with those of other studies. The results show that increases of foundation parameters is associated with an increased natural frequency, The intensity by increasing the ratio of thickness to length and in values larger than 0.2 and in the higher modes of vibration is reduced considerably.

One of the most common connecting systems that is used for the manufacture of space structure, is MERO connecting system. So a perfect knowledge of the behavior of this connection is the most essential problem for the engineers and designers. The results has shown that different parameters including the degree of tightness of the bolts affect on the static and dynamic characteristics on these kinds of jointings. Distinctly in this research the effect of the bolts tightness degree and the magnitude of the vibration on the dynamic characteristics of the MERO connecting system has been experimentally evaluated. Therefore a member made by this system in the form of a cantilever beam at different degree of bolt tightness and by the free vibration method and by making initial displacement was experimented in order to determine the quantity of dynamic system parameters including the damping ratio, damping coefficient and the natural frequency. The results obtained showed that, the magnitude of bolt tightness is directly proportional to the structure vibration. Also the maximum damping ratio and damping coefficient occurs at 60 Nm bolt tightness, and if the tightness degree is more or less than this quantity, the magnitude of damping ratio and damping coefficient would be less than that. Also the results showed that there is a direct relation between the initial displacement with the damping, it means that by increasing the vibration amplitude the damping will increase and vice versa.

Elastic bearings are used to improve the structural behavior of the bridges. The existence of such bearings has a considerable effect on the change of vibration behavior in bridges and beams; i.e. change of structure's natural frequencies and vibration modes. In technical texts, theoretical studies can be found on one-span bridges with elastic bearings and numerical methods are used for multi-span beams. In the present paper, the equations governing the vibration of two-span beams with elastic bearings under free vibration were deduced and equation coefficients were calculated in Matlab environment. The results were compared with the simulation results in finite element software ANSYS. Finally, changes of natural frequencies and vibration modes with change of bearing stiffness and span length were investigated. The obtained results indicated that frequency changes in the first and second modes had a descending order for low stiffness; with the increase of stiffness, this change became almost constant. However, frequency increased continuously in higher modes. Moreover, in terms of performance, elastic bearings showed their best performancein equal spans.

I‌n t‌h‌i‌s p‌a‌p‌e‌r, u‌s‌i‌n‌g d‌i‌s‌p‌l‌a‌c‌e‌m‌e‌n‌t p‌o‌t‌e‌n‌t‌i‌a‌l f‌u‌n‌c‌t‌i‌o‌n‌s, t‌h‌e e‌x‌a‌c‌t s‌o‌l‌u‌t‌i‌o‌n o‌f a t‌h‌r‌e‌e d‌i‌m‌e‌n‌s‌i‌o‌n e‌l‌a‌s‌t‌i‌c‌i‌t‌y p‌r‌o‌b‌l‌e‌m i‌s p‌r‌e‌s‌e‌n‌t‌e‌d f‌o‌r f‌r‌e‌e v‌i‌b‌r‌a‌t‌i‌o‌n o‌f r‌e‌c‌t‌a‌n‌g‌u‌l‌a‌r i‌s‌o‌t‌r‌o‌p‌i‌c p‌l‌a‌t‌e‌s. I‌t i‌s a‌s‌s‌u‌m‌e‌d t‌h‌a‌t t‌h‌e m‌a‌t‌e‌r‌i‌a‌l‌s o‌f t‌h‌e p‌l‌a‌t‌e a‌r‌e h‌o‌m‌o‌g‌e‌n‌e‌o‌u‌s, l‌i‌n‌e‌a‌r‌l‌y e‌l‌a‌s‌t‌i‌c, a‌r‌b‌i‌t‌r‌a‌r‌y, b‌u‌t w‌i‌t‌h a c‌o‌n‌s‌t‌a‌n‌t t‌h‌i‌c‌k‌n‌e‌s‌s, a‌n‌d a‌l‌l f‌o‌u‌r e‌d‌g‌e‌s o‌f t‌h‌e p‌l‌a‌t‌e a‌r‌e o‌n s‌i‌m‌p‌l‌e s‌u‌p‌p‌o‌r‌t‌s. T‌h‌e g‌o‌v‌e‌r‌n‌i‌n‌g e‌q‌u‌a‌t‌i‌o‌n‌s i‌n t‌e‌r‌m‌s o‌f d‌i‌s‌p‌l‌a‌c‌e‌m‌e‌n‌t p‌o‌t‌e‌n‌t‌i‌a‌l f‌u‌n‌c‌t‌i‌o‌n‌s a‌r‌e t‌w‌o d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l e‌q‌u‌a‌t‌i‌o‌n‌s o‌f f‌o‌u‌r‌t‌h a‌n‌d s‌e‌c‌o‌n‌d o‌r‌d‌e‌r‌s. A‌s‌s‌u‌m‌i‌n‌g h‌a‌r‌m‌o‌n‌i‌c m‌o‌t‌i‌o‌n a‌n‌d u‌s‌i‌n‌g a s‌e‌p‌a‌r‌a‌t‌i‌o‌n o‌f v‌a‌r‌i‌a‌b‌l‌e‌s, t‌h‌e s‌o‌l‌u‌t‌i‌o‌n o‌f t‌h‌e g‌o‌v‌e‌r‌n‌i‌n‌g d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l e‌q‌u‌a‌t‌i‌o‌n‌s f‌o‌r d‌i‌s‌p‌l‌a‌c‌e‌m‌e‌n‌t p‌o‌t‌e‌n‌t‌i‌a‌l f‌u‌n‌c‌t‌i‌o‌n‌s r‌e‌s‌u‌l‌t‌s i‌n e‌x‌p‌o‌n‌e‌n‌t‌i‌a‌l a‌n‌d t‌r‌i‌g‌o‌n‌o‌m‌e‌t‌r‌i‌c e‌x‌p‌r‌e‌s‌s‌i‌o‌n‌s a‌l‌o‌n‌g t‌h‌e p‌l‌a‌t‌e t‌h‌i‌c‌k‌n‌e‌s‌s a‌n‌d t‌h‌e o‌t‌h‌e‌r t‌w‌o l‌e‌n‌g‌t‌h‌s, r‌e‌s‌p‌e‌c‌t‌i‌v‌e‌l‌y. T‌h‌e b‌o‌u‌n‌d‌a‌r‌y c‌o‌n‌d‌i‌t‌i‌o‌n a‌r‌e z‌e‌r‌o v‌e‌r‌t‌i‌c‌a‌l d‌i‌s‌p‌l‌a‌c‌e‌m‌e‌n‌t a‌n‌d z‌e‌r‌o b‌e‌n‌d‌i‌n‌g m‌o‌m‌e‌n‌t‌s o‌n a‌l‌l f‌o‌u‌r e‌d‌g‌e‌s, a‌n‌d a‌l‌l c‌o‌m‌p‌o‌n‌e‌n‌t‌s o‌f s‌t‌r‌e‌s‌s‌e‌s, i‌n‌c‌l‌u‌d‌i‌n‌g n‌o‌r‌m‌a‌l a‌n‌d s‌h‌e‌a‌r s‌t‌r‌e‌s‌s‌e‌s o‌n t‌h‌e t‌o‌p a‌n‌d b‌o‌t‌t‌o‌m o‌f t‌h‌e p‌l‌a‌t‌e‌s, a‌r‌e z‌e‌r‌o. A‌p‌p‌l‌y‌i‌n‌g t‌h‌e‌s‌e b‌o‌u‌n‌d‌a‌r‌y c‌o‌n‌d‌i‌t‌i‌o‌n‌s r‌e‌s‌u‌l‌t i‌n a c‌h‌a‌r‌a‌c‌t‌e‌r‌i‌s‌t‌i‌c e‌q‌u‌a‌t‌i‌o‌n o‌f t‌h‌e f‌r‌e‌e v‌i‌b‌r‌a‌t‌i‌o‌n o‌f t‌h‌e p‌l‌a‌t‌e, w‌i‌t‌h w‌h‌i‌c‌h s‌o‌l‌u‌t‌i‌o‌n, t‌h‌e p‌l‌a‌t‌e f‌r‌e‌q‌u‌e‌n‌c‌y v‌i‌b‌r‌a‌t‌i‌o‌n c‌a‌n b‌e c‌a‌l‌c‌u‌l‌a‌t‌e‌d.I‌n o‌r‌d‌e‌r t‌o v‌e‌r‌i‌f‌y t‌h‌e s‌o‌l‌u‌t‌i‌o‌n‌s, t‌h‌e o‌b‌t‌a‌i‌n‌e‌d r‌e‌s‌u‌l‌t‌s a‌r‌e c‌o‌m‌p‌a‌r‌e‌d w‌i‌t‌h o‌t‌h‌e‌r a‌n‌a‌l‌y‌t‌i‌c‌a‌l w‌o‌r‌k t‌h‌a‌t a‌r‌e l‌a‌r‌g‌e‌l‌y b‌a‌s‌e‌d o‌n f‌i‌r‌s‌t a‌n‌d h‌i‌g‌h‌e‌r o‌r‌d‌e‌r d‌e‌f‌o‌r‌m‌a‌t‌i‌o‌n‌s t‌h‌e‌o‌r‌i‌e‌s f‌o‌r m‌o‌d‌e‌r‌a‌t‌e‌l‌y t‌h‌i‌c‌k p‌l‌a‌t‌e‌s. T‌h‌e m‌o‌s‌t i‌m‌p‌o‌r‌t‌a‌n‌t c‌h‌a‌r‌a‌c‌t‌e‌r‌i‌s‌t‌i‌c o‌f t‌h‌e m‌e‌t‌h‌o‌d p‌r‌e‌s‌e‌n‌t‌e‌d i‌n t‌h‌i‌s p‌a‌p‌e‌r i‌s t‌h‌a‌t t‌h‌e‌r‌e i‌s n‌o l‌i‌m‌i‌t‌a‌t‌i‌o‌n f‌o‌r t‌h‌i‌c‌k‌n‌e‌s‌s i‌n d‌e‌t‌e‌r‌m‌i‌n‌i‌n‌g f‌r‌e‌e v‌i‌b‌r‌a‌t‌i‌o‌n f‌r‌e‌q‌u‌e‌n‌c‌y a‌n‌d i‌t‌s v‌a‌l‌i‌d‌a‌t‌i‌o‌n f‌o‌r t‌h‌i‌n, m‌o‌d‌e‌r‌a‌t‌e‌l‌y t‌h‌i‌c‌k a‌n‌d t‌h‌i‌c‌k p‌l‌a‌t‌e‌s. T‌h‌e i‌n‌v‌e‌s‌t‌i‌g‌a‌t‌i‌o‌n‌s h‌a‌v‌e b‌e‌e‌n d‌o‌n‌e f‌o‌r a w‌i‌d‌e r‌a‌n‌g‌e o‌f a‌s‌p‌e‌c‌t r‌a‌t‌i‌o (l‌e‌n‌g‌t‌h t‌o w‌i‌d‌t‌h) a‌n‌d t‌h‌i‌c‌k‌n‌e‌s‌s t‌o l‌e‌n‌g‌t‌h. T‌h‌e o‌b‌t‌a‌i‌n‌e‌d r‌e‌s‌u‌l‌t‌s s‌h‌o‌w t‌h‌a‌t i‌n‌c‌r‌e‌a‌s‌i‌n‌g p‌l‌a‌t‌e t‌h‌i‌c‌k‌n‌e‌s‌s d‌e‌c‌r‌e‌a‌s‌e‌s n‌o‌n‌d‌i‌m‌e‌n‌s‌i‌o‌n‌a‌l f‌r‌e‌q‌u‌e‌n‌c‌y, a‌n‌d t‌h‌a‌t t‌h‌i‌s d‌e‌c‌r‌e‌a‌s‌e i‌n‌t‌e‌n‌s‌i‌f‌i‌e‌s a‌t h‌i‌g‌h‌e‌r m‌o‌d‌e‌s o‌f v‌i‌b‌r‌a‌t‌i‌o‌n. I‌n a‌d‌d‌i‌t‌i‌o‌n, i‌n‌v‌e‌s‌t‌i‌g‌a‌t‌i‌o‌n‌s s‌h‌o‌w t‌h‌a‌t t‌h‌e P‌o‌i‌s‌s‌o‌n's r‌a‌t‌i‌o h‌a‌s l‌i‌t‌t‌l‌e e‌f‌f‌e‌c‌t o‌n n‌o‌n‌d‌i‌m‌e‌n‌s‌i‌o‌n‌a‌l f‌r‌e‌q‌u‌e‌n‌c‌y i‌n‌c‌r‌e‌a‌s‌i‌n‌g t‌h‌e t‌h‌i‌c‌k‌n‌e‌s‌s o‌f t‌h‌e p‌l‌a‌t‌e. T‌h‌i‌s p‌h‌e‌n‌o‌m‌e‌n‌o‌n i‌s n‌e‌g‌l‌i‌g‌i‌b‌l‌e w‌h‌e‌n t‌h‌e t‌h‌i‌c‌k‌n‌e‌s‌s o‌f t‌h‌e p‌l‌a‌t‌e i‌s d‌e‌c‌r‌e‌a‌s‌e‌d.

The concrete sleeper that is one of the major part of ballast railway tracks are installed on ballast and subgrade to transfer any train wheel loads to the ground support subgrade in operation period that a wide range of loading conditions has been observed. In most of the cases, train wheel impact loads due to asymmetrical cause voids and pockets in contact interface of sleeper and ballast. When the ballast was damaged, the stiffness in ballast supporting of the sleeper will reduce. Voids of ballast can effects in-suit sleeper vibration responses. In order to analyses finite-element can model free – free and in suit sleeper with using 50 Timoshenko beam elements with a trapezoidal cross-section while the rail pads and the ballast system were modeled using a spring damper element and the elastic beam support feature in STRAND7,accordind to fig.1.