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IMPROVED SEGMENTED-DIRECT-INTEGRATION METHOD FOR NONLINEAR DYNAMIC EQUATIONS

Haibo Wang

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Abstract

The present segmented-direct-integration method is improved for nonlinear dynamic systems governed by the equation v = H ? v +f ( v , t), and new predict formulas are proposed. As a precise integration method with explicit, predict-correct, self-starting and four order accuracy, the improved method is not necessary to differentiate f ( v,t). Numerical examples show that the improved method is suitable for multi-degrees of freedom, strongly nonlinear and non-conservative dynamic systems, even effective in studying stability of solution. Moreover, the improved method has higher accuracy than the present segmented-direct-integration method as well as classical Runge-Kutta integration method.

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What this paper is about

The present segmented-direct-integration method is improved for nonlinear dynamic systems governed by the equation v = H ? v +f ( v , t), and new predict formulas are proposed. As a precise integration method with explicit, predict-correct, self-starting and four order accuracy, the improved method is not necessary to differentiate f ( v,t). Numerical examples show that the improved method is suitable for multi-degrees of freedom, strongly nonlinear and non-conservative dynamic systems, even effective in studying stability of solution. Moreover, the improved method has higher accuracy than the present segmented-direct-integration method as well as classical Runge-Kutta integration method.

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Available abstract

The present segmented-direct-integration method is improved for nonlinear dynamic systems governed by the equation v = H ? v +f ( v , t), and new predict formulas are proposed. As a precise integration method with explicit, predict-correct, self-starting and four order accuracy, the improved method is not necessary to differentiate f ( v,t). Numerical examples show that the improved method is suitable for multi-degrees of freedom, strongly nonlinear and non-conservative dynamic systems, even effective in studying stability of solution. Moreover, the improved method has higher accuracy than the present segmented-direct-integration method as well as classical Runge-Kutta integration method.

Key concepts: Direct integration of a beam, Nonlinear system, Numerical integration, Dynamic equation, Stability (learning theory), Runge–Kutta methods, Applied mathematics, Mathematics

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