Steady-State Response of Nonlinear Systems with Nonlinear Dissipative Elements Using a Bond Graph Symmetry

The analysis of nonlinear systems has always been a challenge. The structure of the mathematical model of a nonlinear physical system often does not allow us to identify how the elements that make up the system are related. A bond graph allows its elements to be classified into fields in such a way that the relationship between them can be determined. This paper proposes a bond graph junction structure with an integral causality assignment for a class of nonlinear systems, through which a mathematical model can be derived. The class of nonlinear systems consists of products of functions of the state variables and nonlinear dissipative elements. The steady-state response of the system can be obtained from a bond graph with an assignment of derivative causality. Depending on the causal connections between the elements, solving a nonlinear algebraic equation is required to determine the contribution of nonlinear resistive elements to the steady state of the state variables. Therefore, a bond graph exhibits symmetry between the modeled system and its mathematical model. A case study is solved using the proposed methodology, and the steady-state response results are verified through bond graph simulation with integral causality.