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Research Papers

Experimental Investigation of a Two-Stage Nonlinear Vibration Isolation System With High-Static-Low-Dynamic Stiffness

[+] Author and Article Information
Zeqi Lu

Shanghai Institute of
Applied Mathematics and Mechanics,
Shanghai University,
149 Yanchang Road,
Shanghai 200072, China
e-mail: luzeqi@shu.edu.cn

Tiejun Yang

Power and Energy Engineering College,
Harbin Engineering University,
145 Nangtong Street,
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, Brazil
e-mail: mjbrennan0@btinternet.com

Zhigang Liu

Power and Energy Engineering College,
Harbin Engineering University,
145 Nangtong Street,
Harbin 150001, China
e-mail: liuzhigang@hrbeu.edu.cn

Li-Qun Chen

Department of Mechanics,
Shanghai University,
99 Shangda Road,
Shanghai 200444, China;
Shanghai Institute of
Applied Mathematics and Mechanics,
Shanghai University,
149 Yanchang Road,
Shanghai 200072, China;
Shanghai Key Laboratory of
Mechanics in Energy Engineering,
Shanghai University,
149 Yanchang Road,
Shanghai 200072, China
e-mail: lqchen@staff.shu.edu.cn

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 31, 2015; final manuscript received October 14, 2016; published online November 7, 2016. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 84(2), 021001 (Nov 07, 2016) (9 pages) Paper No: JAM-15-1585; doi: 10.1115/1.4034989 History: Received October 31, 2015; Revised October 14, 2016

A novel design of a two-stage nonlinear vibration isolation system, with each stage having a high-static-low-dynamic stiffness (HSLDS), is studied experimentally in this paper. The positive stiffness in each stage is realized by a metallic plate, and the corresponding negative stiffness is realized by a bistable carbon fiber–metal (CF) composite plate. An analytical model is developed as an aid to design a bistable composite plate with the required negative stiffness, and a static test of the plate is conducted to measure the actual stiffness of the plate. Dynamic tests of the two-stage isolator are carried out to determine the effectiveness of the isolator. Two tests are conducted, one with the bistable composite plates removed so that the isolator behaves as a linear device and one with the bistable composite plates fitted. An improvement in the isolator transmissibility of about 13 dB at frequencies greater than about 100 Hz is achieved when the bistable composite plates are added.

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Figures

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Fig. 1

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

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Fig. 2

Comparison of the displacement transmissibility of a two-stage nonlinear isolator (blue dashed line) and a two-stage linear isolator (red solid line)

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Fig. 3

Schematic of the two-stage nonlinear vibration isolation system

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Fig. 4

Bistable plate shapes: (a) the plate flat at curing temperature, (b) unstable state of the plate at room temperature, (c) one of the stable states of the plate at room temperature, and (d) one of the stable states of the plate at room temperature

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Fig. 5

View of the structure of the bistable plate, that is, a regular unsymmetrical laminate (Fs applied)

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Fig. 6

The curvatures of a square laminate in the x and y directions, with the properties given in Table 1, as a function of the size of the laminate (Lx=Ly). The solid blue lines are stable solutions, and the red dashed lines are unstable solutions.

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Fig. 7

Force–displacement and stiffness characteristics of the square bistable composite plate with the properties given in Table 1 (Lx=Ly): (a) force–displacement characteristic and (b) stiffness as a function of displacement of the center of the plate

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Fig. 8

Stiffness characteristics of the square bistable composite plate with the properties given in Table 1 (Lx=Ly=0.1). For a different number of CF layers on each side of the steel plate.

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Fig. 9

Experimental setup to measure the stiffness of the bistable plate

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Fig. 10

Comparison of analytical and experimental force–displacement curve; the distance between the bolts is defined as the effective length, Lx=0.1 m ; three layers of CF. Blue line: analytical result, red “o” points: experiment result, and black dashed line: fitted curve (third order polynomial).

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Fig. 11

Photographs of the two-stage vibration isolator: (a) actual test-rig and (b) test-rig with the bistable plates removed. The cylindrical devices connected to the corners of the plates are to facilitate the lateral sliding conditions (a section through one of them can be seen in Fig. 9).

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Fig. 12

Time history displacement response curves of the upper mass of the nonlinear isolator for two excitation frequencies, (a) excitation frequency of 10 Hz and (b) excitation frequency of 60 Hz. Blue “o,” fundamental harmonic; red line, actual response.

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Fig. 13

The measured transmissibility of the two-stage isolator, with and without the composite bistable plates fitted. Also, shown are the predictions for the nonlinear isolator using the harmonic balance method, and the predictions for the linear isolator. For the nonlinear system, the blue crosses show the measurements for increasing frequency and the blue circles for decreasing frequency; the blue solid line shows the analytical result. For the linear system, the red stars show the measurements, and the red dashed line shows the analytical result.

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