Free Vibrations of Elastically Connected Stretched Beams with Applications To Carbon Nanotubes

Bibliographic Details
Main Author:	Srinivas, Shirish
Language:	English
Published:	University of Akron / OhioLINK 2008
Subjects:	Mechanical Engineering mode shapes
Online Access:	http://rave.ohiolink.edu/etdc/view?acc_num=akron1226671765

id	ndltd-OhioLink-oai-etd.ohiolink.edu-akron1226671765
record_format	oai_dc
spelling	ndltd-OhioLink-oai-etd.ohiolink.edu-akron12266717652021-08-03T05:25:36Z Free Vibrations of Elastically Connected Stretched Beams with Applications To Carbon Nanotubes Srinivas, Shirish Mechanical Engineering mode shapes A general theory for the determination of natural frequencies and mode shapes for a set of elastically connected axially loaded Euler-Bernoulli beams is developed. A normal mode solution is applied to a set of non-dimensional coupled partial differential equations. The natural frequencies are the eigenvalues of a matrix of differential operators. The matrix operator is shown to be self adjoint leading to an orthogonality condition for the mode shapes. In the special case of identical beams, it is shown that the natural frequencies are organized into sets of intramodal frequencies in which each mode shape is a product of a spatial mode and a discrete mode. An exact solution is available for the general case. However the natural frequencies and mode shapes are then determined using a complicated numerical method. A Rayleigh-Ritz method using mode shapes of the corresponding unstretched beams is developed as an alternative. The Rayleigh-Ritz method is applied to a continuous model of multi-walled carbon nanotubes in which the van der Waals forces between atoms in the tubes aremodeled by a elastic layers connecting the tubes. 2008 English text University of Akron / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=akron1226671765 http://rave.ohiolink.edu/etdc/view?acc_num=akron1226671765 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection	NDLTD
language	English
sources	NDLTD
topic	Mechanical Engineering mode shapes
spellingShingle	Mechanical Engineering mode shapes Srinivas, Shirish Free Vibrations of Elastically Connected Stretched Beams with Applications To Carbon Nanotubes
author	Srinivas, Shirish
author_facet	Srinivas, Shirish
author_sort	Srinivas, Shirish
title	Free Vibrations of Elastically Connected Stretched Beams with Applications To Carbon Nanotubes
title_short	Free Vibrations of Elastically Connected Stretched Beams with Applications To Carbon Nanotubes
title_full	Free Vibrations of Elastically Connected Stretched Beams with Applications To Carbon Nanotubes
title_fullStr	Free Vibrations of Elastically Connected Stretched Beams with Applications To Carbon Nanotubes
title_full_unstemmed	Free Vibrations of Elastically Connected Stretched Beams with Applications To Carbon Nanotubes
title_sort	free vibrations of elastically connected stretched beams with applications to carbon nanotubes
publisher	University of Akron / OhioLINK
publishDate	2008
url	http://rave.ohiolink.edu/etdc/view?acc_num=akron1226671765
work_keys_str_mv	AT srinivasshirish freevibrationsofelasticallyconnectedstretchedbeamswithapplicationstocarbonnanotubes
_version_	1719419975794425856

Free Vibrations of Elastically Connected Stretched Beams with Applications To Carbon Nanotubes

Similar Items