In this paper, we have considered a new class of critical technique that called the He's Variational Approach (VA) to solve the nonlinear vibration of an electrostatically actuated microbeam. It has been indicated that the Variational Approach (VA) is quickly convergence and does not demand small perturbation and also sufficiently accurate to both linear and nonlinear problems in engineering. The obtained results show that the approximate solutions are uniformly legitimate on the whole solution field.

This review features a survey of some recent developments in asymptotic techniques and new developments, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the achieved approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to over-come the shortcomings.In this review we have applied different powerful analytical methods to solve high nonlinear problems in engineering vibrations. Some patterns are given to illustrate the effectiveness and convenience of the methodologies.

A vast amount of published work can be found in the field of beam vibrations dealing with analytical and numerical techniques. This paper deals with analysis of the nonlinear free vibrations of beams. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of tapered beams. A new implementation of the ancient Chinese method called the Max-Min Approach (MMA) and Homotopy Perturbation Method (HPM) are presented to obtain natural frequency and corresponding displacement of tapered beams. The effect of vibration amplitude on the non-linear frequency is discussed. In the end to illustrate the effectiveness and convenience of the MMA and HPM, the obtained results are compared with the exact ones and shown in graphs and in tables. Those approaches are very effective and simple and with only one iteration leads to high accuracy of the solutions. It is predicted that those methods can be found wide application in engineering problems, as indicated in this paper.

The usefulness of supplementary energy dissipation devices is now quite well-known in earthquake structural engineering for reducing the earthquake-induced response of structural systems. The seismic behavior of structures with supplemental ADAS devices is concerned in this study. In this paper, the ratio of the hysteretic energy to input energy is compared in different structural systems. The main purpose of this paper is to evaluate the behavior of structures equipped with yielding dampers (ADAS), located in far fields based on energy concepts. In order to optimize their seismic behavior, the codes and solutions are also presented. Three cases including five, ten and fifteen-story three-bay Concentric Braced Frames (CBF) with and without ADAS were selected. The PERFORM 3D.V4 software along with three earthquake records (Northridge, Imperial Valley and Tabas) is used for nonlinear time history analysis and the conclusions are drawn upon energy criterion. The effect of PGA variation and height of the frames are also considered in the study. Finally, to increase the energy damping ability and reduce the destructive effects in structures on an earthquake event, so that a great amount of induced energy is damped and destruction of the structure is prevented as much as possible by using ADAS dampers.

The behavior of braced steel frame structures is of special importance due to its extensive use. Also the application of active and semi-active control systems, regarding to their benefits in obtaining better seismic performance has increased significantly. The majority of the works on steel structures and steel connections has been done under far field records, and the behavior of steel frame structures equipped with yielding dampers under these circumstances has not yet been fully analyzed. The main purpose of this paper is to determine the behavior of structures equipped with yielding dampers, located in near field based on energy concepts. In order to optimize their seismic behavior, the codes and solutions are also presented.The selected system is a braced steel frame system which is equipped with yielding dampers and the analysis is performed using the "Perform 3D V.4" software and the conclusions are drawn upon energy criterion. The effect of PGA variation and height of the frames are also considered in the study .Finally, using the above mentioned results, a proper solution is presented for typical systems in order to increase the energy damping ability and reduce the destructive effects in structures on an earthquake event, so that a great amount of induced energy is damped and destruction of the structure is prevented as much as possible.