Vibration of damped plate-oscillator systems

James W. Nicholson, Lawrence Bergman

Research output: Contribution to journalArticle

Abstract

A classical method for obtaining the exact natural frequencies, natural modes, orthogonality relation and response due to arbitrary loading of undamped beam-oscillator systems presented earlier by the writers is extended to viscously damped plate-oscillator systems. The natural modes are expressed in terms of the Green's function for the vibrating plate. Damping is present in both the plate and oscillators. Modal analysis allows the determination of a closed form expression for the system response to arbitrary loading. Oscillators attached to a simply supported rectangular plate have been considered, but the method is applicable to any plate-oscillator system, provided the Green's function for the undamped vibrating plate is known. An example involving a single oscillator attached to the plate shows the natural frequencies, natural modes and response due to two special types of loading.

Original languageEnglish (US)
Pages (from-to)14-30
Number of pages17
JournalJournal of Engineering Mechanics
Volume112
Issue number1
DOIs
StatePublished - Jan 1 1986

Fingerprint

Green's function
Natural frequencies
Modal analysis
Damping

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Vibration of damped plate-oscillator systems. / Nicholson, James W.; Bergman, Lawrence.

In: Journal of Engineering Mechanics, Vol. 112, No. 1, 01.01.1986, p. 14-30.

Research output: Contribution to journalArticle

Nicholson, James W. ; Bergman, Lawrence. / Vibration of damped plate-oscillator systems. In: Journal of Engineering Mechanics. 1986 ; Vol. 112, No. 1. pp. 14-30.
@article{cf6c55fadb1b45ad9c424ecce90b3e1f,
title = "Vibration of damped plate-oscillator systems",
abstract = "A classical method for obtaining the exact natural frequencies, natural modes, orthogonality relation and response due to arbitrary loading of undamped beam-oscillator systems presented earlier by the writers is extended to viscously damped plate-oscillator systems. The natural modes are expressed in terms of the Green's function for the vibrating plate. Damping is present in both the plate and oscillators. Modal analysis allows the determination of a closed form expression for the system response to arbitrary loading. Oscillators attached to a simply supported rectangular plate have been considered, but the method is applicable to any plate-oscillator system, provided the Green's function for the undamped vibrating plate is known. An example involving a single oscillator attached to the plate shows the natural frequencies, natural modes and response due to two special types of loading.",
author = "Nicholson, {James W.} and Lawrence Bergman",
year = "1986",
month = "1",
day = "1",
doi = "10.1061/(ASCE)0733-9399(1986)112:1(14)",
language = "English (US)",
volume = "112",
pages = "14--30",
journal = "Journal of Engineering Mechanics - ASCE",
issn = "0733-9399",
publisher = "American Society of Civil Engineers (ASCE)",
number = "1",

}

TY - JOUR

T1 - Vibration of damped plate-oscillator systems

AU - Nicholson, James W.

AU - Bergman, Lawrence

PY - 1986/1/1

Y1 - 1986/1/1

N2 - A classical method for obtaining the exact natural frequencies, natural modes, orthogonality relation and response due to arbitrary loading of undamped beam-oscillator systems presented earlier by the writers is extended to viscously damped plate-oscillator systems. The natural modes are expressed in terms of the Green's function for the vibrating plate. Damping is present in both the plate and oscillators. Modal analysis allows the determination of a closed form expression for the system response to arbitrary loading. Oscillators attached to a simply supported rectangular plate have been considered, but the method is applicable to any plate-oscillator system, provided the Green's function for the undamped vibrating plate is known. An example involving a single oscillator attached to the plate shows the natural frequencies, natural modes and response due to two special types of loading.

AB - A classical method for obtaining the exact natural frequencies, natural modes, orthogonality relation and response due to arbitrary loading of undamped beam-oscillator systems presented earlier by the writers is extended to viscously damped plate-oscillator systems. The natural modes are expressed in terms of the Green's function for the vibrating plate. Damping is present in both the plate and oscillators. Modal analysis allows the determination of a closed form expression for the system response to arbitrary loading. Oscillators attached to a simply supported rectangular plate have been considered, but the method is applicable to any plate-oscillator system, provided the Green's function for the undamped vibrating plate is known. An example involving a single oscillator attached to the plate shows the natural frequencies, natural modes and response due to two special types of loading.

UR - http://www.scopus.com/inward/record.url?scp=0022546274&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022546274&partnerID=8YFLogxK

U2 - 10.1061/(ASCE)0733-9399(1986)112:1(14)

DO - 10.1061/(ASCE)0733-9399(1986)112:1(14)

M3 - Article

VL - 112

SP - 14

EP - 30

JO - Journal of Engineering Mechanics - ASCE

JF - Journal of Engineering Mechanics - ASCE

SN - 0733-9399

IS - 1

ER -