Frequency analysis on the nonlinear free vibration of a tri-cross string system

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (8) : 186-192.

PAN Bo1,2,XU Zili3,ZHAO Bo1, 2,GE Xiang2

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Abstract

Abstract:Theoretical analysis on the nonlinear free vibration of a tri-cross string system was presented in this work, which is an element of space net-antennas.The governing equations were derived from the Hamilton’s principle and a linearized solution was obtained by the standard perturbation method.The semi-analytical solutions of the governing equations has not been provided referring to the solution of the plate vibrating problem.This analysis reveals that natural frequencies of the tri-cross string depend on the vibration amplitude due to geometrical nonlinearity in the constitutive equation.The geometric parameters, such as the diameters and the lengths of the constituent strings, also affect the frequency through the nonlinearity of the tri-cross string.The nonlinear natural frequency shows coupled characteristic, i.e. the natural frequency of the tri-cross string varies with that of the constituent strings, but the contribution of each constituent string to the natural frequency is in different proportions.

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tri-cross string / nonlinearity / perturbation method / coupling effect

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PAN Bo1,2,XU Zili3,ZHAO Bo1, 2,GE Xiang2. Frequency analysis on the nonlinear free vibration of a tri-cross string system[J]. Journal of Vibration and Shock, 2020, 39(8): 186-192

References

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