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TECHNICAL PAPERS

Steady-State Dynamic Response of Preisach Hysteretic Systems

[+] Author and Article Information
P. D. Spanos

R. B. Ryon Chair in Engineering, Rice University, Houston TXspanos@rice.edu

A. Kontsos

Department of Mechanical Engineering & Materials Science,Rice Universityakontsos@rice.edu

P. Cacciola

Dipartimento di Construzioni e Tecnologie Avanzate, University of Mesina, Italycacciola@ingegneria.unime.it

J. Vib. Acoust 128(2), 244-250 (Nov 02, 2005) (7 pages) doi:10.1115/1.2159041 History: Received May 02, 2005; Revised November 02, 2005

The goal of this paper is to study the steady-state dynamic response of an oscillator involving a hysteretic component and exposed to harmonic excitation. This is accomplished by using the Preisach formalism in the description of the contribution of the hysteretic component. Two cases are considered. In the first one, the hysteretic component is modeled using a series of “Jenkin’s elements,” while in the second one the same component is modeled by a zero-memory plus a purely hysteretic term. The steady-state amplitude of the response is determined analytically by using the equivalent linearization technique which involves input-output relationships for the equivalent linear system, the stiffness and damping coefficients of which are response-amplitude dependent. The derived results are compared with pertinent numerical data obtained by integrating the nonlinear equation of motion of the oscillator. The analytical and the numerical results are found in excellent agreement and supplement the findings of certain previous studies.

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Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic representation of an oscillator with a hysteretic component

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Figure 2

A series of elastoplastic elements and corresponding force-displacement plot

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Figure 3

Typical force-displacement plot of a SMA device

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Figure 4

A typical hysteretic operator

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Figure 5

The Preisach plane. T designates the limiting triangle and is the support of the Preisach function

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Figure 7

Representative response of the SDOF system and corresponding hysteretic loop both computed numerically for ω=3rad∕s and r=0.4(k=c=fy,min=0)

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Figure 8

The steady-state amplitude A for a range of frequencies (k=c=0 and fy,min=0)

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Figure 9

Representative hysteretic loops (ω=3rad∕s and r=0.8 in all cases): (i) k=c=fy,min=0, (ii) k=4, c=0.04, and fy,min=0, (iii) k=4, c=0.04, fy,min=2

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Figure 10

The steady-state amplitude A for a range of frequencies (k=16, c=0.4, and P0=1)

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Figure 11

Representative response of the hysteretic system, corresponding loop (left top and bottom), and comparison with the loop obtained when the SMA device is removed from the system (right top and bottom)

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Figure 6

An example of an input history where αi and βi represent local maxima and minima

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