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A systematic approach on computational analysis and optimization design: for a nonlinear coupling shock absorber

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Abstract

The aim of this article is to provide a systematic approach to perform computational simulation and optimization design of parameters matching selection for a nonlinear coupling shock absorber. A theoretical mathematical model with nonlinear coupling for shock absorber is induced based on relative literature. The model considers the coupling of quadratic damping, viscosity damping, coulomb damping and nonlinear spring. Approximate computational solution is deduced by introducing harmonic balance method and Fourier transform method. These approximate theoretical solutions include output response of the system, absolute acceleration transmissibility in vibration or impact, and the maximum relative displacement in impact process, etc. The approximate computational results are compared with those obtained by numerical integration to confirm the validity of the mathematical model. In the meantime, an optimization design model for parameters is built. The design example is illustrated to confirm the validity of the modeling method and the theoretical solution.

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Abbreviations

ω0 :

Natural frequency of the shock absorber

ω:

Excitation frequency

a 0 :

Amplitude of excitation acting on the base

c 1 :

Quadratic damping coefficient

c 2 :

Viscous damping coefficient

c f :

Columb damping force

k 3 :

Cubic stiffness coefficient

k 1 :

Linear-stiffness coefficient

b 0 :

Amplitude of impact excitation acting on base

τ:

Impulse time

T c :

Absolute acceleration transmissibility in impact

T f :

Absolute acceleration transmissibility in vibration

z(t):

Relative displacement between mass block and base

x(t):

Displacement excitation on base

\({\ddot{z}}(t)\) :

Relative acceleration between mass block and base

y(t):

Output displacement on mass block

\({\dot{z}}(t)\) :

Relative velocity between mass block and base

\({\ddot{x}}(t)\) :

Acceleration excitation on base

\({\ddot{y}}(t)\) :

Output acceleration on mass block

λ m :

Maximum non-dimensional relative displacement between base and mass block in impact process

z m :

Maximum relative displacement between base and mass block in impact process

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Acknowledgments

The author would like to acknowledge the support of National Natural Science Foundation of China, National Defense Natural Science Foundation of China (No.00J16.2.5.DZ0502), Special Science Foundation for Middle-Young academic leader of Jiangsu high education in China (Qinglan Gongcheng Project), the support of Natural Science Foundation of Gangxi province of China (No. 0339037), the Natural Science Foundation for Qualified Personnel of Jiangsu University (04JDG027) and the Science Foundation of Jiangsu Higher Education Institution (06KJD460044), Special Science Foundation for Middle-Young academic leader of Guangxi high education in China during the course of this work.

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Authors and Affiliations

  1. Laboratory of Advanced Design and Manufacturing, School of Mechanical Engineering, Jiangsu University, Zhenjiang, 212013, People’s Republic of China

    Ping Yang

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  1. Ping Yang
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Correspondence to Ping Yang.

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Yang, P. A systematic approach on computational analysis and optimization design: for a nonlinear coupling shock absorber. Engineering with Computers 24, 87–96 (2008). https://doi.org/10.1007/s00366-007-0074-x

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  • DOI: https://doi.org/10.1007/s00366-007-0074-x

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