Multi-body System Dynamics Simulation Differential Quadrature Method

Mutibody system is a complex system in which multiple objects(rigid body,elastic/soft body,mass point,etc.)are interconnected in a certain way.With the rapid development of computers and the wide application of multibody systems in the fields of mechanics,aviation,aerospace,weapons,vehicles,robotics and biomechanics,multibody system dynamics has become one of the important contents of modern mechanics,many research focus on the simulation of the multibody system dynamics.The simulation model is usually in the form of ordinary differential equations or differential algebraic equations.Numerical solutions of those differential equations are great important for the simulation theory and application.Compared with traditional methods,differential quadrature method has the advantages of simple mathematics principle,less computation time,and high precision.In this paper,the differential quadrature method is introduced in the simulation of multibody system dynamics.Based on the principle of differential quadrature method,the determination of the weight coefficient matrix,the selection of node formulas,and the processing of boundary conditions are discussed in detail.In order to get a better numerical solution,the uniform nodes or Chebyshev polynomial roots are used to divide the time domain,the Lagrange basis function is used to determine the weight coefficient matrix,and the boundary conditions are dealt with by the equation substitution method.Based on the model of nonlinear ordinary differential equations or differential algebraic equations of multibody system dynamics,the differential quadrature method is used in the time domain to obtain the nonlinear algebraic equations with unknown values of function values at each time node.The function values at each time node are obtained by Newton iterative method,and the numerical solutions are gotten finally to satisfy the engineering applications.The planar two-link is used to verify the methods presented in this paper.Compared with the Runge-Kutta method,the results show that this method has the advantages of simple formula derivation,high precision and easy programming.It is an effective method for the simulation of multibody system dynamics.