دانلود رایگان مقاله انگلیسی تحلیل حساسیت و بهینه سازی سیستم های دینامیکی هیسترتیک با میراگرهای ویسکوز غیرخطی - اشپرینگر 2018

Abstract

In this paper we discuss the adjoint sensitivity analysis and optimization of hysteretic systems equipped with nonlinear viscous dampers and subjected to transient excitation. The viscous dampers are modeled via the Maxwell model, considering at the same time the stiffening and the damping contribution of the dampers. The timehistory analysis adopted for the evaluation of the response of the systems relies on the Newmark-β time integration scheme. In particular, the dynamic equilibrium in each timestep is achieved by means of the Newton-Raphson and the Runge-Kutta methods. The sensitivity of the system response is calculated with the adjoint variable method. In particular, the discretize-then-differentiate approach is adopted for calculating consistently the sensitivity of the system. The importance and the generality of the sensitivity analysis discussed herein is demonstrated in two numerical applications: the retrofitting of a structure subject to seismic excitation, and the design of a quarter-car suspension system. The MATLAB code for the sensitivity analysis considered in the first application is provided as “Supplementary Material”.

5 Conclusions

In this paper we discussed the adjoint sensitivity analysis and optimization for nonlinear dynamic systems coupled with nonlinear fluid viscous dampers. The dampers are modeled with the Maxwell’s model for visco-elasticity. It is thus possible to account for the stiffening and damping contributions of the device. The systems are subject to transient excitations, and their response is calculated with the Newmark-β method. In particular, the equilibrium in each time-step is iteratively achieved by means of the Newton-Raphson and Runge-Kutta methods. The heart of the discussion of this paper focuses on the adjoint sensitivity analysis of these systems, and its application to two different design cases. The sensitivity of a generic response function is in fact consistently calculated with detail through the discretize-then-differentiate version of the adjoint variable method. The generic framework is then applied to the optimization-based design of an added damping system for seismic retrofitting, and to the optimization-based design of a quarter-car suspension system. Both applications show the importance of the adjoint sensitivity analysis discussed herein in the context of optimization-based design of hysteretic dynamic systems with nonlinear viscous dampers. The results presented could be extended and applied to different design cases, where we expect the methodology discussed here to promote the use of computationally efficient design procedures based on optimization.