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Influence of Nonviscous Modes on Transient Response of Lumped Parameter Systems With Exponential Damping

[+] Author and Article Information
Jon García-Barruetabeña1

Department of Mechanical Engineering,  Mondragon Unibertsitatea, Loramendi 4, 20500, Mondragon, Spainjgarcia@eps.mondragon.edu, jmabete@eps.mondragon.edu

Fernando Cortés

Deusto Institute of Technology (DeustoTech), Faculty of Engineering,  University of Deusto, Avenida de las Universidades 24, 48007, Bilbao, Spainfernando.cortes@deusto.es

José Manuel Abete

Department of Mechanical Engineering,  Mondragon Unibertsitatea, Loramendi 4, 20500, Mondragon, Spainjgarcia@eps.mondragon.edu, jmabete@eps.mondragon.edu

1

Corresponding author.

J. Vib. Acoust 133(6), 064502 (Nov 28, 2011) (8 pages) doi:10.1115/1.4005004 History: Received February 25, 2011; Accepted July 12, 2011; Revised July 12, 2011; Published November 28, 2011; Online November 28, 2011

This paper is aimed at investigating the influence of nonviscous modes on the vibrational response of viscoelastic systems. Thus, exponential damping models are considered. Provided that nonviscous modes disappear with time, they have influence on only the transient response of the system. Thus, the system response is obtained by means of modal superposition in order to examine the contribution of each mode. The analysis is carried out on two lumped parameter systems; systems involving a single degree and three degrees of freedom are studied. For the former, the analytic solution is derived via modal superposition and Laplace transformation. For the latter, the analytic response is contrasted with that provided via two numerical direct methods. From this investigation, it can be concluded that the system may present no oscillations, even if elastic modes are underdamped modes.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 2

Representation of a viscoelastic material model using relaxation functions

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Figure 3

Single dof system (a) using a Zener model and (b) using relaxation functions

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Figure 4

Response for the 1 dof system. (a) Total response u(t). (b) Contribution of the first elastic mode ue1(t) to the total response u(t). (c) Contribution of the second elastic mode ue2(t) to the total response u(t). (d) Contribution of the nonviscous mode unv(t) to the total response u(t).

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Figure 5

N dof system using a Zener model

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Figure 6

Three dofs system (a) using a Zener model and (b) using relaxation functions

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Figure 7

Response for the 3 dofs system. (a) Response u1(t). (b) Response u2(t). (c) Response u3(t).

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