Thermal analysis of viscoelastic multibody systems

Thermal analysis of the transient motion of a multibody system, consisting of interconnected rigid, elastic, and viscoelastic components is presented. The configuration of each elastic or viscoelastic body is identified using three sets of modes, rigid-body, reference and normal modes. Rigid-body modes describe translations and large rotations of the body reference. The finite element method is employed to describe body deformations, and reference conditions are imposed in order to define a unique displacement field. Accordingly, normal modes of vibrations of flexible components can be used to reduce the number of elastic coordinates, thus eliminating high-frequency modes of vibration. The system equations of motion are formulated using Lagrange's equation, and nonlinear algebraic equations, describing constraints between adjacent bodies, are coupled to the equations of motion using a Lagrange multiplier technique.