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, axisymmetric free vibration analysis of a circular Nano-plate having variable thickness was studied. The variation in thickness of plate was considered as a linearly in radial direction. Nonlocal elasticity theory was utilized to take into account size-dependent effects. Ritz functions was utilized to obtain the frequency equations for simply supported and clamped boundary. To verify accuracy of Ritz method, differential transform method (DTM) also used to drive the size dependent natural frequencies of circular nano-plates. The validity of solutions was performed by comparing present results with those of the literature for both classical plate and nano plate. Effect of nonlocal parameter, mode number and taper parameter on the natural frequency are investigated. Results showed that taper parameter has significant effect on the non-dimensional frequency and its effects on the clamped boundary condition is more than simply support.

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.

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.