Computational Method for Dynamic Analysis of Multibody Systems with Deformable Elements

The paper presents a comprehensive method for the elastodynamic analysis of mobile mechanical systems, based on the finite element method. Using Kane’s algorithm, which is employed in the dynamic analysis of mechanical systems with rigid bodies, a method is developed that, by superimposing the rigid body motion over the one of a deformable body, allows to identify the kinematic and dynamic components of the matrices involved in the motion equations namely, the mass matrix, stiffness matrix, damping matrix, and the force vector acting on the system. The method is applied to a high-speed mechanism used for actuating an internal combustion engine with three in-line pistons. Within this method, each kinematic link is considered as a finite element, with corresponding reference frames for which the kinematic and dynamic components of the matrices involved in the motion equations are determined. To solve the differential equations system, a modal superposition method is applied, which enables the decoupling of the equations and to identify the time-varying diagrams for nodal displacements, both longitudinal and transversal displacements, and consequently to determine the accelerations of the kinematic links, which are useful in vibration analysis. The strength force is considered the force exerted by the gas on the piston head, which was experimentally determined under laboratory conditions. The theoretical results obtained are validated through virtual prototyping and experimental tests.