Estimating Nonlinear Damping for Mechanical Single‐Degree‐of‐Freedom Systems: A Robust and Effective Approach

ABSTRACT Single‐degree‐of‐freedom (SDOF) systems are a simple but widely used method in engineering to describe mechanical phenomena. Mathematically, a SDOF system can be described by a second‐order differential equation (Newton's second law). In general, the differential equation depends on arbitrary parameters (e.g., spring stiffness, damping, friction), which have to be estimated from measurements. Parameter estimation of such models is still a broad research field, especially for nonlinear systems. A widely used method for parameter estimation is the restoring force method. A robust and computationally effective method for the determination of unknown nonparametric restoring forces (e.g., nonlinear damping) for nonlinear SDOF systems based on measured data will be presented in this work. The parameter estimation problem is formulated as an inverse problem. Inverse problems are almost always ill‐posed. The Inverse problem is transformed into a boundary value problem using the calculus of variation. The ill‐posed problem is then solved efficiently using regularization techniques. Numerical experiments and the derivation of the method showed that a regularization term is necessary to obtain reasonable results. Furthermore, this approach does not require solving a complex and computationally intensive optimization problem. In this work, the method has been successfully demonstrated on a numerical example of a nonlinear SDOF.