Force Equilibrium Approach for Linearization of Constrained Mechanical System Dynamics

The purpose of this study is to derive a linearized form of dynamic equations for constrained mechanical systems. The governing equations for constrained mechanical systems are generally expressed in terms of Differential-Algebraic Equations (DAEs). Conventional methods of linearization are based on the perturbation of the nonlinear DAE, where small amounts of perturbations are taken to guarantee linear characteristics of the equations. On the other hand, the proposed linearized dynamic equations are derived directly from a force equilibrium condition, not from the DAEs, with small motion assumption. This approach is straightforward and simple compared to conventional perturbation methods, and can be applicable to any constrained mechanical systems that undergo small displacement under external forces. The modeling procedure and formulation of linearized dynamic equations are demonstrated by the example of a vehicle suspension system, a typical constrained multibody system. The solution is validated by comparison with conventional nonlinear dynamic analysis and modal test results.