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.

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.

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.

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.

The free vibration features of rotating functionally graded microbeams in thermal environmentare presented in this paper. The governing equations are extracted on the basis of the Euler-Bernoulli beam assumptions beside the modified couple stress theory. The finite elementmethod is applied on the weak form of the strain and the kinetic energies to extract the naturalfrequencies and the associated modeshapes. The nonlinear static equations of motion due to therotation and the thermal environment are treated employing the Newton-Raphson technique. Moreover, the natural frequencies are estimated from the linearized equations of motion aboutthe static configuration. After the validation of the present results, the rotation speed, thematerial length scale parameter, the temperature change, the power law exponent and theslenderness ratio impacts on the fundamental natural frequency and the first and the secondmodeshapes are examined. The outcomes indicate the increment of the natural frequency aftera threshold value of the power law exponent depends on a given rotation speed for the rotatingmicrobeams in comparison with the stationary microbeams. Furthermore, the modeshapes ofrotating functionally graded microbeams vary by the power law exponent while for stationaryfunctionally graded microbeams the modeshapes are invariant with respect to the power lawexponent even in the presence of the thermal environment.