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Research Papers

A Linearization Method of Piecewise Linear Systems Based on Frequency Domain Characteristics With Application to Semi-Active Control of Vibration

[+] Author and Article Information
Tudor Sireteanu

Institute of Solid Mechanics,
Romanian Academy,
15 Constantin Mille,
Bucharest 010141, Romania

Ovidiu Solomon

Institute of Solid Mechanics,
Romanian Academy,
15 Constantin Mille,
Bucharest 010141, Romania;
Department of Applied Mathematics,
The Bucharest University of Economic Studies,
6 Romana Square,
Bucharest 010374, Romania

Ana-Maria Mitu

Institute of Solid Mechanics,
Romanian Academy,
15 Constantin Mille,
Bucharest 010141, Romania

Marius Giuclea

Institute of Solid Mechanics,
Romanian Academy,
15 Constantin Mille,
Bucharest 010141, Romania;
Department of Applied Mathematics,
The Bucharest University of Economic Studies,
6 Romana Square,
Bucharest 010374, Romania
e-mail: marius.giuclea@csie.ase.ro

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 9, 2018; final manuscript received March 30, 2018; published online May 7, 2018. Assoc. Editor: Stefano Lenci.

J. Vib. Acoust 140(6), 061006 (May 07, 2018) (14 pages) Paper No: VIB-18-1011; doi: 10.1115/1.4039933 History: Received January 09, 2018; Revised March 30, 2018

In this paper, a new approach is presented for linearization of piecewise linear systems with variable dry friction, proportional with absolute value of relative displacement. The transmissibility factors of considered systems, defined in terms of root-mean-square (RMS) values, are obtained by numerical time integration of motion equations for a set of harmonic inputs with constant amplitude and different frequencies. A first-order linear differential system is attached to the considered piecewise linear system such as the first component of solution vector of attached system to have the same transmissibility factor as the chosen output of nonlinear system. This method is applied for the semi-active control of vibration with balance logic strategy. Applications to base isolation of rotating machines and vehicle suspensions illustrate the effectiveness of the proposed linearization method.

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References

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Figures

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Fig. 1

Schematic of vibration isolation systems with controllable dry friction

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Fig. 2

Nonlinear and linear equivalent hysteresis loops

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Fig. 3

Transmissibility factor of the RMS absolute acceleration for two different values of input amplitude

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Fig. 5

Time histories of input and absolute accelerations of nonlinear and attached linear systems

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Fig. 4

Transmissibility factors of RMS acceleration: A x¨1 (⋅⋅⋅)—nonlinear system, A x¨1lin (—)—attached linear system, and A x¨1e (—)—linear equivalent system

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Fig. 8

(a) Time history of input, (b) the acceleration output of semi-active system for b=ω n, (c) the acceleration output of attached linear systems for b=ωn, and (d) the acceleration output of attached linear systems for b=ω n

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Fig. 7

(a) Time history of input, (b) the acceleration output of semi-active system for b=ω e, (c) the acceleration output of attached linear systems for b=ω e, and (d) the acceleration output of passive systems for b=ωe

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Fig. 6

The one-sided spectral density of simulated inputs

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Fig. 9

(a) The time history of the transmitted acceleration before and after switching-off time, (b) the time history of the transmitted acceleration for balance logic control, (c) the time history of the transmitted acceleration for attached linear system, and (d) the time history of the transmitted acceleration for passive system

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Fig. 11

Transmissibility factors Ax1(ω) and Ax2(ω) for different values of input amplitude

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Fig. 12

Simulated (—) and fitted (⋅⋅⋅) transmissibility factors of absolute displacements

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Fig. 10

Schematic of quarter car model of semi-active suspension

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Fig. 17

The power spectral densities of unsprung mass absolute displacements for nonlinear and attached linear systems

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Fig. 13

The target and the simulated spectral densities

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Fig. 14

(a) Time history of sprung mass absolute displacement of nonlinear system and (b) time histories of sprung mass absolute displacement of attached linear system

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Fig. 15

(a) Time history of unsprung mass absolute displacement of nonlinear system and (b) time histories of unsprung mass absolute displacement of attached linear system

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Fig. 16

The power spectral densities of sprung mass absolute displacements for nonlinear and attached linear systems

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