RIGID BODY SYSTEM DYNAMIC WITH THE ACCURATE JACOBIAN MATRIX OF SPRING-DAMPER-ACTUATOR

The spring-damper-actuator (SDA) is a common force element in multibody system and widely used in the field of engineering. The governing equations of multibody dynamic system established by absolute coordinate methods are differential-algebraic equations which are usually nonlinear and complex. To ensure the stability and accuracy of the numerical solutions, the implicit algorithms are commonly used to solve the dynamic equations. While the calculations of Jacobian matrices are the crucial process in implicit algorithms. For a multibody system containing the SDA, the additional Jacobian matrices induced by the SDA are highly nonlinear functions of the generalized coordinates and generalized velocities. A lot of current research works focus on the calculation of generalized force vector, however the calculations of additional Jacobian matrices are less concerned. This paper focuses on dynamic analysis of multi-rigid-body systems containing the SDA. Firstly, the construction of the accurate Jacobian matrices in solving the dynamic equations is investigated based on the Newmark algorithm. Then, the additional Jacobian matrices relating to the generalized force vector of the SDA are analytically derived. These matrices consist of the partial derivative of generalized force vector with respect to the generalized coordinates and the generalized velocities. Finally, the influence of additional Jacobian matrices on the convergence of dynamic analysis is investigated via two numerical examples. The numerical results indicate that when the values of stiffness, damping and active force are large, the additional Jacobian matrices induced by the SDA have a significant influence on the convergence of dynamic analysis. When the additional Jacobian matrices induced by the SDA are taken into account, the dynamic analysis can achieve convergence with less iteration steps and the computational time thus can be reduced.