Technical Brief

On the Performance of a Two-Stage Vibration Isolation System Which has Geometrically Nonlinear Stiffness

[+] Author and Article Information
Zeqi Lu

Power and Energy Engineering College,
Harbin Engineering University,
Nangtong Street No. 145,
Harbin 150001, China
e-mail: luzeqi@aliyun.com

Tiejun Yang

Power and Energy Engineering College,
Harbin Engineering University,
Nangtong Street No. 145,
Harbin 150001, China
e-mail: yangtiejun@hrbeu.edu.cn

Michael J. Brennan

Departamento de Engenharia Mecânica,
Universidade Estadual Paulista (UNESP),
Av. Brasil Centro,
Ilha Solteira (SP) 56-15385-000, Brasil
e-mail: mjbrennan0@btinternet.com

Xinhui Li

Power and Energy Engineering College,
Harbin Engineering University,
Nangtong Street No. 145,
Harbin 150001, China
e-mail: linxinhui_sd@aliyun.com

Zhigang Liu

Power and Energy Engineering College,
Harbin Engineering University,
Nangtong Street No. 145,
Harbin 150001, China
e-mail: liuzhigang@hrbeu.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 18, 2014; final manuscript received August 18, 2014; published online September 11, 2014. Assoc. Editor: Guilhem Michon.

J. Vib. Acoust 136(6), 064501 (Sep 11, 2014) (5 pages) Paper No: VIB-14-1051; doi: 10.1115/1.4028379 History: Received February 18, 2014; Revised August 18, 2014

Linear single-stage vibration isolation systems have a limitation on their performance, which can be overcome passively by using linear two-stage isolations systems. It has been demonstrated by several researchers that linear single-stage isolation systems can be improved upon by using nonlinear stiffness elements, especially for low-frequency vibrations. In this paper, an investigation is conducted into whether the same improvements can be made to a linear two-stage isolation system using the same methodology for both force and base excitation. The benefits of incorporating geometric stiffness nonlinearity in both upper and lower stages are studied. It is found that there are beneficial effects of using nonlinearity in the stiffness in both stages for both types of excitation. Further, it is found that this nonlinearity causes the transmissibility at the lower resonance frequency to bend to the right, but the transmissibility at the higher resonance frequency is not affected in the same way. Generally, it is found that a nonlinear two-stage system has superior isolation performance compared to that of a linear two-stage isolator.

Copyright © 2014 by ASME
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Grahic Jump Location
Fig. 1

Comparison of the transmissibility of a single-stage linear isolator and a two-stage linear isolator as a function of nondimensional frequency. The mass ratio is 0.2, the upper stiffness is equal to the lower stiffness, and the damping ratio for the upper and lower stages is 0.01. Single-stage linear isolator, red solid line; two-stage linear isolator, blue dashed line.

Grahic Jump Location
Fig. 2

Schematic of the two-stage nonlinear isolation system. (a) Actual system and (b) equivalent lumped parameter model. The mass m1 is the suspended (primary) mass and m2 is the intermediate (secondary) mass.

Grahic Jump Location
Fig. 3

Illustration of the HBM and numerical solution for force and displacement transmissibility when the upper and lower horizontal stiffness are fixed at k∧h1 = k∧h2 = 1.17 and l∧ = 0.7, F∧e = F∧emax, X∧e = X∧emax, μ = 0.2, k∧v2 = 1, and ζ1 = ζ2 = 0.01. HBM solution: force transmissibility (blue solid line), displacement transmissibility (red dashed line). Numerical solution obtained by direct numerical integration of Eqs. (2) and (8) (decreasing frequency: black and green “+”; increasing frequency: black and green “o”).

Grahic Jump Location
Fig. 4

Plots of force and displacement transmissibilities of the two-stage nonlinear isolator with the same parameters as in Fig. 3, showing the effects of changing the horizontal stiffness, k∧h1 and k∧h2. (a) and (b) Force transmissibility, (c) and (d) displacement transmissibility: (a) and (c), Effects of setting k∧h1 = 0 and adjusting k∧h2: red dashed line, k∧h2 = 0; black dashed–dotted line, k∧h2 = 0.7; green dotted line, k∧h2 = 1; blue solid line, k∧h2 = 1.17; (b) and (d), Effect of fixing k∧h2 = 1.17 and adjusting k∧h1: blue solid line, k∧h1 = 0; green dotted line, k∧h1 = 0.7; black dashed–dotted line, k∧h1 = 1; red dashed line, k∧h1 = 1.17.




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