A Class of Synchronized Nonlinear Two-Dof Systems With Closed Form Solution

Abstract

Nonlinear dynamic behavior of structural systems has a signi cant role in many engineering applications. Related analysis methods are typically numerical. Accordingly, to verify and test their accuracy, availability of nonlinear systems with exact closedform solutions is important. In this paper, a three-parameter system, with an exact analytical solution, consisting of two synchronized colliding mass-spring-dashpot systems, is introduced, and the validity of the exact solutions is demonstrated. Simplicity of the system and its exact response, and the capability to control the frequency content, as well as the severity of the oscillatory behavior are addressed as the main features of the introduced system. The potential future works are outlined.

Test of an Idea for Setting the Nonlinearity Tolerance in Nonlinear Response History Analyses According to Procedures Originated in the Seismic Code of New Zealand NZS 1170.5:2004

“…Two different earthquake records are considered as the excitations in two separate studies (see Fig. 4; where, t f Δ is the step of digitization), and three severities of nonlinear behavior [7,[63][64][65] are considered in three separate studies, by applying the following three scales to the two excitations:…”