The Free undamped Vibration analysis of a shell of general shape is formulated with a degenerated curved lagrangian finite element, without neglecting shear deformations and z/R with consistent mass matrix. The shell element with nine nodes and 45 degree of Freedoms (three transverse and two rotations) is applicable for both thin and thick shell analysis. The accuracy and efficiency of this proposed finite element are illustrated by examples and the results are compared with those obtained by other analytical and numerical methods. The comparisons show that the method yields very good results with a relatively small number of elements.

The Free Vibration characteristics, such as fundamental frequency and mode shape of stiffened plates employing standardfinite element analysis, are investigated in this paper. The parametric study is presented for Free Vibration characteristics ofstiffened plates with various parameters, such as type, orientation and number of stiffeners, boundary conditions and aspectratio of plates and stiffener depth to plate thickness ratio. Typical mode shapes are also presented for clamped square eccentricallystiffened plates. Finally, design charts with non-dimensional parameters are proposed to determine the fundamentalfrequency of commonly adopted clamped stiffened plates in construction. These charts will be very much useful for designersfor obtaining the fundamental frequencies of the stiffened plates of different dimensions without doing much complicatedanalysis or using standard computer codes.

Shell structures have various applications in Civil and Mechanical engineering. Shells, like other types of structure, are subject to damage and deterioration, such as development and propagation of cracks. In this research, the effect of a full penetration non - propagating macro crack, with various parameters, on natural Vibration frequencies and mode shapes, is investigated. For this purpose, 400 cracked shell models have been created. These shells are grouped into cylindrical panels and full cylindrical shells and the effect of various parameters, such as crack length, crack orientation, thickness, poison ratio, shell height and panel's central angle, on the Vibration frequencies and mode shapes of the shells, has been investigated.

This article deals with the Free in-plane Vibration analysis of a frame with four arbitrary inclined members by differential transform method. Based on four differential equations and sixteen boundary and compatibility conditions, the related structural eigenvalue problem will be analytically formulated. The frequency parameters and mode shapes of the frame will be calculated for various values of the structural properties, such as joint angles, springs' stiffness and flexural rigidity of members. Finally, the obtained solution by the proposed method will be verified by authors' finite element program.

This study based on Free Vibration analysis and study the behavior of framed structure under different frequency of Vibration using ANSYS software and shaking table. A small scale uni-axial shaking table was prepared in laboratory, which can produce lower to moderate Vibration, regarding frequency and velocity. Moment resisting framed structures constructed with connecting beam and column elements of mild steel wire of different dimensions were tested in shaking table and analyzed using ANSYS software. The effect of masses and stiffness of structures on its natural frequency and deflection under certain ground Vibration also studied and discussed. The test results showed that, this shaking table is satisfying the general concept of Free Vibration. The height of structures has an inverse effect on its natural frequency for same lateral stiffness. After several shaking, structure’ s natural frequency started to decreases with their decreasing stiffness. Therefore, the fabricated shaking table can used in Free Vibration analysis.

In this paper, the nonlinear bending Vibration of a Free-Free beam is analyzed using the perturbation theory. The nonlinear part of the equation of motion is obtained using two separate approaches i.e. the invariant manifold approach, and the perturbation theory. By application of the multiple scale method, the nonlinear differential equation of motion with necessary boundary conditions is solved and the Vibrational mode shapes are obtained. The advantage of using perturbation method with regard to the well known numerical approaches is the possibility of simulating analytically the effect of magnitude changes of nonlinear part in the final solution. The result shows that magnitude changes of nonlinear part causes noticeable changes in the Vibrational mode shapes of the beam. Also, it is shown that in the higher modes, the effect of the nonlinear part will increase dramatically.

In this paper, Free Vibration analysis of orthotropic functionally graded material (FGM) cylinders was carried out by a Mesh-Free method. In this analysis, moving least squares shape functions are used for approximation of displacement field in the weak form of equilibrium equation. Essential boundary conditions are imposed by transformation method. In this simulation, an axisymmetric model is used. The orthotropic FGM cylinders are assumed to be a mixture of two isotropic materials as fiber and matrix. The volume fraction of the fiber is changed in the radial direction. Consequently, mechanical properties of these cylinders are changed in the radial direction. Free Vibration analysis of orthotropic FGM cylinders with any arbitrary combination of boundary conditions is possible by the proposed model. Natural frequencies obtained from the presented model are in good agreement with results of finite element simulation and other results from literature. Effects of various types of boundary conditions, geometrical parameters, and mechanical properties on the natural frequencies are studied.