Geometrically non-linear free and forced vibration of a shallow arch

The purpose of this present work is to investigate the geometrical non-linearity in free and forced vibration of a shallow arch elastically restrained at the ends. The non-linear governing equilibrium equation of the shallow arch is obtained after the Euler Bernoulli theory and the Von Karman geomet...

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Autores principales:	Omar Outassafte, Ahmed Adri, Yassine El Khouddar, Said Rifai, Rhali Benamar
Formato:	article
Lenguaje:	EN
Publicado:	JVE International 2021
Materias:	free and forced vibration shallow arch newton-raphson hamilton’s principle second formulation initial rise backbone curves Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/f6919096fc7d4024b64a3f291ff46934
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spelling	oai:doaj.org-article:f6919096fc7d4024b64a3f291ff469342021-11-15T19:20:56ZGeometrically non-linear free and forced vibration of a shallow arch1392-87162538-846010.21595/jve.2021.21857https://doaj.org/article/f6919096fc7d4024b64a3f291ff469342021-09-01T00:00:00Zhttps://www.jvejournals.com/article/21857https://doaj.org/toc/1392-8716https://doaj.org/toc/2538-8460The purpose of this present work is to investigate the geometrical non-linearity in free and forced vibration of a shallow arch elastically restrained at the ends. The non-linear governing equilibrium equation of the shallow arch is obtained after the Euler Bernoulli theory and the Von Karman geometrical non-linearity assumptions. After applying the ends conditions, the eigenvalues problem of the generalized trancendant equation have been determined iteratively using the Newton-Raphson algorithm. The kinetic and total strain energy have been discretized into a series of a finite spatial functions which are a combination of linear modes and basic function contribution coefficients. Using Hamilton’s principle energy and spectral analysis, the problem is reduced into a set of non-linear algebraic equations that solved numerically using an approximate explicit method developed previously the so-called second formulation. Considering a multimode approach, the effect of initial rise and concentrated force on non-linear behaviour of system has been illustrated in the backbone curves giving the non-linear amplitude-frequency dependence. The corresponding non-linear deflections and curvatures have been plotted for various vibration amplitudes.Omar OutassafteAhmed AdriYassine El KhouddarSaid RifaiRhali BenamarJVE Internationalarticlefree and forced vibrationshallow archnewton-raphsonhamilton’s principlesecond formulationinitial risebackbone curvesMechanical engineering and machineryTJ1-1570ENJournal of Vibroengineering, Vol 23, Iss 7, Pp 1508-1523 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	free and forced vibration shallow arch newton-raphson hamilton’s principle second formulation initial rise backbone curves Mechanical engineering and machinery TJ1-1570
spellingShingle	free and forced vibration shallow arch newton-raphson hamilton’s principle second formulation initial rise backbone curves Mechanical engineering and machinery TJ1-1570 Omar Outassafte Ahmed Adri Yassine El Khouddar Said Rifai Rhali Benamar Geometrically non-linear free and forced vibration of a shallow arch
description	The purpose of this present work is to investigate the geometrical non-linearity in free and forced vibration of a shallow arch elastically restrained at the ends. The non-linear governing equilibrium equation of the shallow arch is obtained after the Euler Bernoulli theory and the Von Karman geometrical non-linearity assumptions. After applying the ends conditions, the eigenvalues problem of the generalized trancendant equation have been determined iteratively using the Newton-Raphson algorithm. The kinetic and total strain energy have been discretized into a series of a finite spatial functions which are a combination of linear modes and basic function contribution coefficients. Using Hamilton’s principle energy and spectral analysis, the problem is reduced into a set of non-linear algebraic equations that solved numerically using an approximate explicit method developed previously the so-called second formulation. Considering a multimode approach, the effect of initial rise and concentrated force on non-linear behaviour of system has been illustrated in the backbone curves giving the non-linear amplitude-frequency dependence. The corresponding non-linear deflections and curvatures have been plotted for various vibration amplitudes.
format	article
author	Omar Outassafte Ahmed Adri Yassine El Khouddar Said Rifai Rhali Benamar
author_facet	Omar Outassafte Ahmed Adri Yassine El Khouddar Said Rifai Rhali Benamar
author_sort	Omar Outassafte
title	Geometrically non-linear free and forced vibration of a shallow arch
title_short	Geometrically non-linear free and forced vibration of a shallow arch
title_full	Geometrically non-linear free and forced vibration of a shallow arch
title_fullStr	Geometrically non-linear free and forced vibration of a shallow arch
title_full_unstemmed	Geometrically non-linear free and forced vibration of a shallow arch
title_sort	geometrically non-linear free and forced vibration of a shallow arch
publisher	JVE International
publishDate	2021
url	https://doaj.org/article/f6919096fc7d4024b64a3f291ff46934
work_keys_str_mv	AT omaroutassafte geometricallynonlinearfreeandforcedvibrationofashallowarch AT ahmedadri geometricallynonlinearfreeandforcedvibrationofashallowarch AT yassineelkhouddar geometricallynonlinearfreeandforcedvibrationofashallowarch AT saidrifai geometricallynonlinearfreeandforcedvibrationofashallowarch AT rhalibenamar geometricallynonlinearfreeandforcedvibrationofashallowarch
_version_	1718426881375600640

Geometrically non-linear free and forced vibration of a shallow arch

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