This paper presents a Nonlinear analytical model for silicon micromechanical ring resonators with bulk-mode vibrations. A distributed element model has been developed to describe the dynamic behavior of the micromechanical ring resonator. This model shows the Nonlinear effects in a silicon ring resonator focusing on the effect of large amplitudes around the resonance frequency, material and electrical Nonlinearities. Through the combination of geometrical and material Nonlinearities, closed-form expressions for thirdorder Nonlinearity in mechanical stiffness of bulk-mode ring resonators are obtained. Using the perturbation method and the method of harmonic balance, the expressions for describing the effect of Nonlinearities on the resonance frequency and stability are derived.The results, which show the effect of varying the AC-drive voltage, initial gap spacing, DC-bias voltage and the quality factor on the frequency Response and resonant frequencies, are discussed in detail. The Nonlinear model introduces an appropriate method in the field of bulk-mode ring resonator design for achieving sufficient power handling and low motional resistance.

Design sensitivity analysis is a necessary task for optimization of structures. Methods of sensitivity analysis for linear systems have been developed and well documented in the literature; however there are a few such research works for Nonlinear systems. Nonlinear sensitivity analysis of structures under seismic loading is very complicated. This paper presents an analytical sensitivity technique for Reinforcement Concrete Moment Resisting Frames (RCMRF) that accounts for both material and geometric Nonlinearity under pushover analysis. The results of proposed method are compared with the results of finite difference method. A three-story, two bays moment frame example is used to illustrate the efficiency of the method. This technique can be very useful and efficient for optimal performance-based design of RC buildings.

Nowadays, controlling vibration of a structure in earthquakes and reducing the structural Responses are of great importance. Dampers are a type of systems controlling the absorption of the earthquake energy and dissipating it in order to reduce the structural Responses. The main objective of this paper is to find the optimal characteristics of the Nonlinear viscose dampers placed at all storeys in a three-storey single bay concrete frame. It is assumed that the structure is subjected to the Elcentro and Gazli earthquakes; and both linear and Nonlinear behaviors are considered for the structure during the earthquakes. OpenSees software is used to model the concrete frame and Nonlinear viscous dampers. The structural Responses are calculated at different time steps, using Newmark's numerical method. A series of constraints which are considered during the optimization process include the limits for parameters of Nonlinear viscous damper (Viscous coefficient, axial stiffness and damper exponent) and the maximum absolute value for base shear. The objective is to find optimal values for these parameters in such a way that the maximum absolute value would be minimized for the roof displacement during the earthquake load. The results show that the Nonlinear viscous damper is very suitable to control the structure Responses when it has linear behavior. In fact, when the structure is subjected to the Elcentro earthquake, the maximum absolute value of the roof displacement and base shear decrease by 37. 51% and 43. 39%, respectively. The Nonlinear behavior of the concrete frame does not improved considerably when the Nonlinear viscous dampers are used to control the Nonlinear Response of the structure in the earthquake.

Recently, the application of Composite Steel Plate Shear Walls (CSPSWs) and Steel Plate Shear Walls (SPSWs) as lateral load-resisting systems has been developed. These systems should be resistant enough, ductile, and stiffened to support against different types of excitations. In this work, the seismic performance of these two systems is investigated under different near-and far-field inputs. Strip elements are employed to model the CSPSW and SPSW in SAP2000. An experimental result of CSPSW is first verified. A six story building frame equipped with both systems is then modeled and six different far and near field seismic records are applied to the building frame. Nonlinear Time History Analyses (NTHAs) are conducted based on different maximum ground acceleration levels. Based on the results, appropriate seismic performance of CSPSWs can be clearly observed. CSPSW are also able to decrease relative story displacements more than SPSW More precisely, CSPSWs experience Life Safety (LS) performance level or at least Collapse Prevention (CP) performance level while SPSWs fully collapse.