An Integration Method With Controllable Numerical Damping Dissipation for Structural Dynamic Equations

Numerical dissipation is an important characteristic of numerical integration methods, which directly affects the accuracy of numerical simulation results. Numerical dissipation can improve numerical simulation results for dynamic systems with spurious high-frequency vibrations, but it can also cause distorted calculation results for dynamic systems with real high-frequency vibrations. A 2-sub-step implicit numerical integration method was proposed with controllable numerical damping dissipation to solve structural dynamic systems. Through theoretical derivations, the numerical properties of the new integration method, including the spectral radii, stability, amplitude decay, and period elongation, were introduced in detail. The new implicit integration method can utilize algorithm parameter α to control the numerical dissipation of spurious high-frequency vibration, with a corresponding dissipation ratio of 1-|α|, where -1≤α≤1. The advantages of the new method in terms of the computational accuracy, the high-frequency numerical dissipation, and the nonlinear solving ability were demonstrated through 3 typical examples of a 1-DOF dynamic system, a high-frequency spurious vibration system, and a multi-DOF nonlinear spring-mass system.