Basic characteristics of differential quadrature method for dynamic response of structures

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (5) : 214-221.

MEI Yuchen, LI Hongjing, SUN Guangjun

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Abstract

Based on basic numerical mode of the differential quadrature (DQ) method for dynamic response of structures, the numerical stability and numerical dissipation of DQ method were investigated when time point distributions were uniform distribution, Chebyshev one and Chebyshev-Gauss-Lobatto (CGL) one, respectively within a time step.The algebraic accuracy order number of DQ method was strictly deduced with the equivalent first-order model.The study showed that the method’s numerical stability is closely related to time point distributions within a time step, non-uniform modes are obviously better than uniform ones, but the system damping ratio has large influence on the method’s stability; the method’s algebraic accuracy depends on number of discrete time points, higher numerical accuracy can be realized generally; DQ methods with time points’ two non-uniform distribution modes of Chebyshev distribution and CGL one, respectively have excellent numerical dissipation.

Key words

dynamic response of structures / differential quadrature (DQ) / numerical stability / algebraic accuracy / numerical dissipation

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MEI Yuchen, LI Hongjing, SUN Guangjun. Basic characteristics of differential quadrature method for dynamic response of structures[J]. Journal of Vibration and Shock, 2020, 39(5): 214-221

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