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| 3D harmonic oscillator with stable numerical solution |
| Received:September 12, 2018 Revised:November 19, 2018 |
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| DOI：10.7511/jslx20180912001 |
| KeyWord:dynamic simulations dissipative dynamical systems nonlinear dynamics numerical integrals leapfrog integration |
| Author | Institution |
| 肖国峰 |
中国科学院 武汉岩土力学研究所 岩土力学与工程国家重点试验室, 武汉 |
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| Abstract: |
| The harmonic oscillator is widely used in the description of physical system and numerical simulation of physical phenomena.However,due to the high sensitivity of the harmonic oscillator to the system parameters,initial conditions and boundary conditions,many physical processes cannot be numerically solved by dynamic simulations.In recent years,the meshless method,the material point method and the peridynamics method have all bypassed the quantitative description of the natural structure of solid materials.In this paper,a 3D dissipative harmonic oscillator is proposed by using the constant dissipative term and the spring dissipation term,considering the random perturbation effect,and a numerical integration algorithm based on the leapfrog method and the boundary relaxation technique is constructed.Three models,dissipative spring pendulum,simplified string and simplified beam,are constructed by using 3D harmonic oscillator,and 13 definite solution problems are set up to dynamical simulation.The results of numerical experiments show that the 3D harmonic oscillator is stable.Based on the simplified string model,three problems of the bounded string vibrations such as plucking,release and heavy chord are simulated,in which the problem of heavy string simulates the phenomenon of micro-amplitude oscillation in horizontal direction of catenary.Based on the simplified beam model,the tensile,shearing and torsional behavior of a 3D beam is simulated,and the description ability of the 3D harmonic oscillator for the nonlinear large deformation problem is validated,and its high speed response to external action is verified.This work can provide a feasible way to simulate the string vibration problem and the nonlinear large deformation problem of material mechanics. |
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