Modal analysis of continuous systems by replacing displacement excitation with equivalent excitation force and fixed boundary

This paper describes the theoretical modal analysis of continuous systems that are subjected to displacement excitation. Because vibration modes of continuous systems whose boundaries actively move are unknown, we proposed an equivalent replacement method of displacement excitation with an excitatio...

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Autores principales:	Keisuke YAMADA, Hideo UTSUNO
Formato:	article
Lenguaje:	EN
Publicado:	The Japan Society of Mechanical Engineers 2020
Materias:	continuous system displacement excitation modal analysis wave equation bending vibration acoustic field beam plate Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/51455d484d6e4be1ae5f27fac86fec7b
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spelling	oai:doaj.org-article:51455d484d6e4be1ae5f27fac86fec7b2021-11-29T05:59:27ZModal analysis of continuous systems by replacing displacement excitation with equivalent excitation force and fixed boundary2187-974510.1299/mej.20-00003https://doaj.org/article/51455d484d6e4be1ae5f27fac86fec7b2020-06-01T00:00:00Zhttps://www.jstage.jst.go.jp/article/mej/7/4/7_20-00003/_pdf/-char/enhttps://doaj.org/toc/2187-9745This paper describes the theoretical modal analysis of continuous systems that are subjected to displacement excitation. Because vibration modes of continuous systems whose boundaries actively move are unknown, we proposed an equivalent replacement method of displacement excitation with an excitation force and fixed boundary. We can easily derive the vibration modes of the continuous system because the excitation boundaries are fixed by this replacement method. Using the proposed replacement method and modal analysis, we can derive a certain vibration mode independently. In other words, the number of degrees of freedom can be decreased using the proposed method even when continuous systems are subjected to displacement excitation. The equivalent replacement methods for ‘one-dimensional and multi-dimensional continuous systems whose equation of motion is a wave equation’, and ‘one-dimensional and two-dimensional continuous systems whose equation of motion is a fourth-order partial differential equation’ were proposed in this research. As a representative, an acoustic tube and a cuboidal room were used as the analytical models for the one-dimensional and multi-dimensional continuous systems whose equation of motion is a wave equation. In contrast, an Euler-Bernoulli beam and a Kirchhoff-Love plate were used as the analytical models for the one-dimensional and two-dimensional continuous systems whose equation of motion is a fourth-order partial differential equation. The correctness of the proposed methods was mathematically proved. In addition, the effectiveness of the proposed method was verified through numerical simulations.Keisuke YAMADAHideo UTSUNOThe Japan Society of Mechanical Engineersarticlecontinuous systemdisplacement excitationmodal analysiswave equationbending vibrationacoustic fieldbeamplateMechanical engineering and machineryTJ1-1570ENMechanical Engineering Journal, Vol 7, Iss 4, Pp 20-00003-20-00003 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	continuous system displacement excitation modal analysis wave equation bending vibration acoustic field beam plate Mechanical engineering and machinery TJ1-1570
spellingShingle	continuous system displacement excitation modal analysis wave equation bending vibration acoustic field beam plate Mechanical engineering and machinery TJ1-1570 Keisuke YAMADA Hideo UTSUNO Modal analysis of continuous systems by replacing displacement excitation with equivalent excitation force and fixed boundary
description	This paper describes the theoretical modal analysis of continuous systems that are subjected to displacement excitation. Because vibration modes of continuous systems whose boundaries actively move are unknown, we proposed an equivalent replacement method of displacement excitation with an excitation force and fixed boundary. We can easily derive the vibration modes of the continuous system because the excitation boundaries are fixed by this replacement method. Using the proposed replacement method and modal analysis, we can derive a certain vibration mode independently. In other words, the number of degrees of freedom can be decreased using the proposed method even when continuous systems are subjected to displacement excitation. The equivalent replacement methods for ‘one-dimensional and multi-dimensional continuous systems whose equation of motion is a wave equation’, and ‘one-dimensional and two-dimensional continuous systems whose equation of motion is a fourth-order partial differential equation’ were proposed in this research. As a representative, an acoustic tube and a cuboidal room were used as the analytical models for the one-dimensional and multi-dimensional continuous systems whose equation of motion is a wave equation. In contrast, an Euler-Bernoulli beam and a Kirchhoff-Love plate were used as the analytical models for the one-dimensional and two-dimensional continuous systems whose equation of motion is a fourth-order partial differential equation. The correctness of the proposed methods was mathematically proved. In addition, the effectiveness of the proposed method was verified through numerical simulations.
format	article
author	Keisuke YAMADA Hideo UTSUNO
author_facet	Keisuke YAMADA Hideo UTSUNO
author_sort	Keisuke YAMADA
title	Modal analysis of continuous systems by replacing displacement excitation with equivalent excitation force and fixed boundary
title_short	Modal analysis of continuous systems by replacing displacement excitation with equivalent excitation force and fixed boundary
title_full	Modal analysis of continuous systems by replacing displacement excitation with equivalent excitation force and fixed boundary
title_fullStr	Modal analysis of continuous systems by replacing displacement excitation with equivalent excitation force and fixed boundary
title_full_unstemmed	Modal analysis of continuous systems by replacing displacement excitation with equivalent excitation force and fixed boundary
title_sort	modal analysis of continuous systems by replacing displacement excitation with equivalent excitation force and fixed boundary
publisher	The Japan Society of Mechanical Engineers
publishDate	2020
url	https://doaj.org/article/51455d484d6e4be1ae5f27fac86fec7b
work_keys_str_mv	AT keisukeyamada modalanalysisofcontinuoussystemsbyreplacingdisplacementexcitationwithequivalentexcitationforceandfixedboundary AT hideoutsuno modalanalysisofcontinuoussystemsbyreplacingdisplacementexcitationwithequivalentexcitationforceandfixedboundary
_version_	1718407584483901440

Modal analysis of continuous systems by replacing displacement excitation with equivalent excitation force and fixed boundary

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