Adjoint sensitivity analysis and optimization of hysteretic dynamic systems with nonlinear viscous dampers

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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 time-history 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 time-step 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”.

Original languageEnglish
Pages (from-to)2273-2289
Number of pages17
JournalStructural and Multidisciplinary Optimization
Issue number6
StatePublished - 1 Jun 2018


  • Adjoint sensitivity analysis
  • Gradient-based optimization
  • Nonlinear dynamic systems
  • Viscous dampers

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Software
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization


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