Abstract
The vibrations of a linear discrete mechanical system of n degrees of freedom are governed in physical space by a matrix differential equation of nth order. This means, in general, the solution of an eigenvalue problem of the dimension n. for n ≥3, the eigenvalue problems can generally be solved only numerically, by means of a computer. Only in special cases it is possible to determine the eigencharacteristics of an eigenvalue problem analytically. a uniform oscillator with n equal masses m and n equal linear springs k is an example. Such a system can be thought of, for example, as a simplified discretized model for the longitudinal vibrations of a clamped-free rod. The aim of the present study is to obtain the displacements of the n masses analytically, when the free end is subjected to a force f(t). Then the responses for special forms of f(t) such as the unit-impulse function, the unit-step function and harmonic excitation, are obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 283-288 |
| Number of pages | 6 |
| Journal | Journal of Sound and Vibration |
| Volume | 173 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jun 2 1994 |
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ASJC Scopus subject areas
- Engineering(all)
- Mechanical Engineering
Cite this
Forced response of uniform n-mass oscillators. and an interesting series. / Gurgoze, M.; Ozer, A.
In: Journal of Sound and Vibration, Vol. 173, No. 2, 02.06.1994, p. 283-288.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Forced response of uniform n-mass oscillators. and an interesting series
AU - Gurgoze, M.
AU - Ozer, A.
PY - 1994/6/2
Y1 - 1994/6/2
N2 - The vibrations of a linear discrete mechanical system of n degrees of freedom are governed in physical space by a matrix differential equation of nth order. This means, in general, the solution of an eigenvalue problem of the dimension n. for n ≥3, the eigenvalue problems can generally be solved only numerically, by means of a computer. Only in special cases it is possible to determine the eigencharacteristics of an eigenvalue problem analytically. a uniform oscillator with n equal masses m and n equal linear springs k is an example. Such a system can be thought of, for example, as a simplified discretized model for the longitudinal vibrations of a clamped-free rod. The aim of the present study is to obtain the displacements of the n masses analytically, when the free end is subjected to a force f(t). Then the responses for special forms of f(t) such as the unit-impulse function, the unit-step function and harmonic excitation, are obtained.
AB - The vibrations of a linear discrete mechanical system of n degrees of freedom are governed in physical space by a matrix differential equation of nth order. This means, in general, the solution of an eigenvalue problem of the dimension n. for n ≥3, the eigenvalue problems can generally be solved only numerically, by means of a computer. Only in special cases it is possible to determine the eigencharacteristics of an eigenvalue problem analytically. a uniform oscillator with n equal masses m and n equal linear springs k is an example. Such a system can be thought of, for example, as a simplified discretized model for the longitudinal vibrations of a clamped-free rod. The aim of the present study is to obtain the displacements of the n masses analytically, when the free end is subjected to a force f(t). Then the responses for special forms of f(t) such as the unit-impulse function, the unit-step function and harmonic excitation, are obtained.
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UR - http://www.scopus.com/inward/citedby.url?scp=0028761208&partnerID=8YFLogxK
U2 - 10.1006/jsvi.1994.1547
DO - 10.1006/jsvi.1994.1547
M3 - Article
VL - 173
SP - 283
EP - 288
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
SN - 0022-460X
IS - 2
ER -