Symplectic Runge-Kutta Method for Structural Dynamics

GUO Jing; XING Yu-feng

doi:10.3879/j.issn.1000-0887.2014.01.002

Volume 35 Issue 1

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GUO Jing, XING Yu-feng. Symplectic Runge-Kutta Method for Structural Dynamics[J]. Applied Mathematics and Mechanics, 2014, 35(1): 12-21. doi: 10.3879/j.issn.1000-0887.2014.01.002

Citation:

GUO Jing, XING Yu-feng. Symplectic Runge-Kutta Method for Structural Dynamics[J]. Applied Mathematics and Mechanics, 2014, 35(1): 12-21. doi: 10.3879/j.issn.1000-0887.2014.01.002

Citation:

GUO Jing, XING Yu-feng. Symplectic Runge-Kutta Method for Structural Dynamics[J]. Applied Mathematics and Mechanics, 2014, 35(1): 12-21. doi: 10.3879/j.issn.1000-0887.2014.01.002

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Symplectic Runge-Kutta Method for Structural Dynamics

doi: 10.3879/j.issn.1000-0887.2014.01.002

GUO Jing^1,2,
XING Yu-feng²

¹Science and Technology on Reliability and Environment Engineering Laboratory, Beijing Institute of Structure and Environment Engineering, Beijing 100076, P.R.China;²The Solid Mechanics Research Center, Beihang University, Beijing 100191, P.R.China

Funds: The National Natural Science Foundation of China(11172046;11172028;11372021)

Received Date: 2013-07-15
Rev Recd Date: 2013-10-21
Publish Date: 2014-01-15

Abstract

Abstract

An explicit and efficient implementation of the symplectic implicit Gauss-Legendre Runge-Kutta (RK) method of stage s and order 2s,was presented for solution of the dynamical ordinary differential equation with physical damping and external loads. The analytical explicit spectral radii and single-step phase errors of the implicit Gauss-Legendre RK method were given and compared with those of the explicit classical RK method of stage 4 and order 4. Numerical comparisons through the dynamical solution of a linear multi-degree-of-freedom (MDOF) system and a nonlinear Rayleigh system were made to validate the present study and showed the advantages of the symplectic RK method over the classical RK method with numerical dissipation, especially in aspects of the kinematic properties and long time numerical simulation.
- symplectic,
- Runge-Kutta method,
- spectral radii,
- artificial damping,
- phase error

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References(36)

References

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