Determination of effective mass for continuous contact models in multibody dynamics

Continuous contact models have been popular in representing contact forces between impacting bodies of a multibody system. These models consider the contact force to be the result of a logical spring-damper element between the contacting bodies that exists for a very short period. The simplified and approximated model for generating the contact force is then assumed to be a mass-spring-damper system. Therefore, three common parameters that these models require are the spring stiffness, damping coefficient, and the so-called effective mass. For systems containing one degree-of-freedom, classical methods based on the kinetic energy have commonly been used to determine the effective mass. However, for multiple-degree-of-freedom multibody systems that contain kinematic joints, the determination of the effective mass has not been adequately addressed in the literature. This paper proposes a simple method for computing the effective mass based on the concept of impulse–momentum balance. This approach is applicable to both constrained and unconstrained equations of motion regardless of the multibody system’s number of degrees-of-freedom.