Differential Quadrature Method for Partial Differential Dynamic Equations of Beam-Ring Structure.

The partial differential equations of a circular truss beam-ring structure with antenna extended and locked are studied. The differential quadrature method is used to discretize the differential equations and boundary conditions in a spatial domain. The method of equation substitution and the method of boundary conditions are directly substituted into the internal discrete equations and are used to deal with the boundary conditions. The natural frequency of the beam-ring structure is calculated and verified by the natural frequency obtained by Galerkin's method in paper (Wu et al., "Vibration Frequency Analysis of Beam-Ring Structure for Circular Deployable Truss Antenna," International Journal of Structural Stability and Dynamics, Vol. 19, No. 2, 2019, Paper 1950012). To solve the problem when there are multiple mixed boundary conditions at a point, the method of replacing the internal discrete equation with boundary conditions is not unique and the solution accuracy is low, so the differential algebraic equations are used to replace the boundary conditions directly into the internal discrete equation, and the iterative scheme is established. Finally, the fourth-order-Runge-Kutta method is used to solve the problem. Based on the numerical results, the two methods are compared by using a 200s time history diagram, 10,000s displacement constraint diagram, 10,000s velocity constraint diagram, etc. The results show that the mixed boundary conditions can be solved more accurately by using differential algebraic equations, and the stability of constraints can be maintained under long-time simulation. [ABSTRACT FROM AUTHOR]