Stability analysis of laminated beam systems with delay using lyapunov functional

This work is concerned with systems of laminated beams model subject to linear and nonlinear delay feedback. In a dynamic laminated beam, time delay manifests in the form of lags in restoring the desired system stability after perturbations. Four prevalent categories of time delay are considered. Fo...

Full description

Saved in:

Bibliographic Details
Main Author:	Mpungu, Kassimu
Format:	Thesis
Language:	English
Published:	2022
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/101563/1/KassimuMpunguPFS2022.pdf.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-utm-ep.101563
record_format	uketd_dc
spelling	my-utm-ep.1015632023-06-23T02:57:42Z Stability analysis of laminated beam systems with delay using lyapunov functional 2022 Mpungu, Kassimu QA Mathematics This work is concerned with systems of laminated beams model subject to linear and nonlinear delay feedback. In a dynamic laminated beam, time delay manifests in the form of lags in restoring the desired system stability after perturbations. Four prevalent categories of time delay are considered. For laminated beams with relatively high adhesive stiffness, a constant delay feedback is considered for systems made up of individual beams with same elasticity, and neutral delay otherwise. In systems where delay is significantly due to adhesive softening, distributed delay is considered. Lastly, in structures where the mechanism of dissipating energy is nonlinear, a corresponding nonlinear delay effect is investigated. The mechanism of stabilization mainly relies on the intrinsic structural damping, unlike in previous works where researchers introduced additional dampings such as boundary feedback and material damping. The objective of this work is to establish the asymptotic behavior of a vibrating Timoshenko laminated beam using structural or utmost a single frictional damping in presence of different forms of time delay. The energy method for partial differential equations is the main tool used to establish wellposedness results and asymptotic behavior. The existence and uniqueness of the solution is proved using the linear semi group theory, whereas for energy decay properties, the multiplier technique involving constructing a suitable Lyapunov functional equivalent to the energy is utilized. With appropriate assumptions on the delay weight and wave speeds, it is established that the energy of the system at least decays exponentially due to structural damping. Furthermore, a single additional frictional damping guarantees polynomial decay despite the presence of constant or distributed delay feedback. For nonlinear structural damping, with help of some convexity arguments, general decay result is achieved. In summary, depending on the damping mechanism(s), exponential, polynomial, or general decay results of a laminated beam system subject to different forms of delay feedback are established. 2022 Thesis http://eprints.utm.my/id/eprint/101563/ http://eprints.utm.my/id/eprint/101563/1/KassimuMpunguPFS2022.pdf.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:150566 phd doctoral Universiti Teknologi Malaysia Faculty of Science - Mathematics
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Mpungu, Kassimu Stability analysis of laminated beam systems with delay using lyapunov functional
description	This work is concerned with systems of laminated beams model subject to linear and nonlinear delay feedback. In a dynamic laminated beam, time delay manifests in the form of lags in restoring the desired system stability after perturbations. Four prevalent categories of time delay are considered. For laminated beams with relatively high adhesive stiffness, a constant delay feedback is considered for systems made up of individual beams with same elasticity, and neutral delay otherwise. In systems where delay is significantly due to adhesive softening, distributed delay is considered. Lastly, in structures where the mechanism of dissipating energy is nonlinear, a corresponding nonlinear delay effect is investigated. The mechanism of stabilization mainly relies on the intrinsic structural damping, unlike in previous works where researchers introduced additional dampings such as boundary feedback and material damping. The objective of this work is to establish the asymptotic behavior of a vibrating Timoshenko laminated beam using structural or utmost a single frictional damping in presence of different forms of time delay. The energy method for partial differential equations is the main tool used to establish wellposedness results and asymptotic behavior. The existence and uniqueness of the solution is proved using the linear semi group theory, whereas for energy decay properties, the multiplier technique involving constructing a suitable Lyapunov functional equivalent to the energy is utilized. With appropriate assumptions on the delay weight and wave speeds, it is established that the energy of the system at least decays exponentially due to structural damping. Furthermore, a single additional frictional damping guarantees polynomial decay despite the presence of constant or distributed delay feedback. For nonlinear structural damping, with help of some convexity arguments, general decay result is achieved. In summary, depending on the damping mechanism(s), exponential, polynomial, or general decay results of a laminated beam system subject to different forms of delay feedback are established.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Mpungu, Kassimu
author_facet	Mpungu, Kassimu
author_sort	Mpungu, Kassimu
title	Stability analysis of laminated beam systems with delay using lyapunov functional
title_short	Stability analysis of laminated beam systems with delay using lyapunov functional
title_full	Stability analysis of laminated beam systems with delay using lyapunov functional
title_fullStr	Stability analysis of laminated beam systems with delay using lyapunov functional
title_full_unstemmed	Stability analysis of laminated beam systems with delay using lyapunov functional
title_sort	stability analysis of laminated beam systems with delay using lyapunov functional
granting_institution	Universiti Teknologi Malaysia
granting_department	Faculty of Science - Mathematics
publishDate	2022
url	http://eprints.utm.my/id/eprint/101563/1/KassimuMpunguPFS2022.pdf.pdf
_version_	1776100727825891328

Stability analysis of laminated beam systems with delay using lyapunov functional

Similar Items