scholarly journals The Elliptic Harmonic Balance Method for the Performance Analysis of a Two-Stage Vibration Isolation System with Geometric Nonlinearity

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Weilei Wu ◽  
Bin Tang

This study develops a modified elliptic harmonic balance method (EHBM) and uses it to solve the force and displacement transmissibility of a two-stage geometrically nonlinear vibration isolation system. Geometric damping and stiffness nonlinearities are incorporated in both the upper and lower stages of the isolator. After using the relative displacement of the nonlinear isolator, we can numerically obtain the steady-state response using the first-order harmonic balance method (HBM1). The steady-state harmonic components of the stiffness and damping force are modified using the Jacobi elliptic functions. The developed EHBM can reduce the truncation error in the HBM1. Compared with the HBM1, the EHBM can improve the accuracy of the resonance regimes of the amplitude-frequency curve and transmissibility. The EHBM is simple and straightforward. It can maintain the same form as the balancing equations of the HBM1 but performs better than it.

2016 ◽  
Vol 87 (1) ◽  
pp. 633-646 ◽  
Author(s):  
Xinlong Wang ◽  
Jiaxi Zhou ◽  
Daolin Xu ◽  
Huajiang Ouyang ◽  
Yong Duan

2011 ◽  
Vol 3 (6) ◽  
pp. 689-701
Author(s):  
Malik Mamode

AbstractThe exact analytical expression of the period of a conservative nonlinear oscillator with a non-polynomial potential, is obtained. Such an oscillatory system corresponds to the transverse vibration of a particle attached to the center of a stretched elastic wire. The result is given in terms of elliptic functions and validates the approximate formulae derived from various approximation procedures as the harmonic balance method and the rational harmonic balance method usually implemented for solving such a nonlinear problem.


2016 ◽  
Vol 14 (2) ◽  
pp. 343-361
Author(s):  
Wei Huang ◽  
Jian Xu ◽  
Dayong Zhu ◽  
Cheng Liu ◽  
Jianwei Lu ◽  
...  

Purpose The purpose of this paper is to propose a novel strategy of optimal parameters configuration and placement for sensitive equipment. Design/methodology/approach In this study, clamped thin plate is considered as the foundation form, and a novel composite system is proposed based on the two-stage isolation system. By means of the theory of mechanical four-pole connection, the displacement amplitude transmissibility from the thin plate to precision equipment is derived. For the purpose of performing optimal design of the composite system, a novel multi-objective idea is presented. Multi-objective particle swarm optimization (MOPSO) algorithm is adopted as an optimization technique, which can achieve a global optimal solution (gbest), and selecting the desired solution from an equivalent Pareto set can be avoided. Maximum and variance of the four transmitted peak displacements are considered as the fitness functions simultaneously; the purpose is aimed at reducing the amplitude of the multi-peak isolation system, meanwhile pursuing a uniform vibration as far as possible. The optimization is mainly organized as a combination of parameter configuration and placement design, and the traversal search of discrete plate is performed in each iteration for the purpose of achieving the global optimum. Findings An important transmissibility based on the mechanical four-pole connection is derived, and a composite vibration isolation system is proposed, and a novel optimization problem is also defined here. This study reports a novel optimization strategy combined with artificial intelligence for parameters and placement design of precision equipment, which can promote the traditional view of two-stage vibration isolation. Originality/value Two-stage vibration isolation systems are widely applied to the vibration attenuation of precision equipment, but in these traditional designs, vibration participation of foundation is often ignored. In this paper, participation of foundation of equipment is considered, and a coherent new strategy for equipment isolation and foundation vibration is presented. This study shows a new vision of interdisciplinary including civil engineering, mechanical dynamics and computational science.


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