Efficient algorithm for the dynamic analysis of large civil structures with a small number of nonlinear components

Abstract

Nonlinear vibration analysis of complex structures is still a challenging topic due to limitations of existing algorithms. This paper proposes a highly efficient method to address this problem where the structure has only a portion of components with geometric or material nonlinearity under service load. Incremental harmonic balance (IHB) method serves as the main tool. The linear and nonlinear parts of the structure are separated with the introduction of interface forces at the boundaries. The analysis of the linear and nonlinear parts is interacting via the interface forces with the compatibility condition. Two numerical examples are analyzed for illustration of the method, i.e. a frame with base isolation system and a suspension bridge model. Various resonances are noted in the vibration of the structures suggesting the need of analyzing the nonlinear vibration of any structure with nonlinear components. The accuracy of the proposed method is validated with comparison the obtained results with that by Runge-Kutta method. Results show that the proposed method provides a neat and efficient tool for this purpose, when the nonlinear components are far less than the linear components in the system.