Multi-scaled analysis of the damped dynamics of an elastic rod with an essentially nonlinear end attachment

Panagopoulos, P; Georgiades, F; Tsakirtzis, S; Vakakis, AF; Bergman, LA

dc.contributor.author	Panagopoulos, P	en
dc.contributor.author	Georgiades, F	en
dc.contributor.author	Tsakirtzis, S	en
dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Bergman, LA	en
dc.date.accessioned	2014-03-01T01:26:43Z
dc.date.available	2014-03-01T01:26:43Z
dc.date.issued	2007	en
dc.identifier.issn	0020-7683	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18198
dc.subject	Essential nonlinearity	en
dc.subject	Multi-scaled analysis	en
dc.subject	Nonlinear damped transitions	en
dc.subject.classification	Mechanics	en
dc.subject.other	Essential nonlinearity	en
dc.subject.other	Frequency-energy plot (FEP)	en
dc.subject.other	Multi-scaled analysis	en
dc.subject.other	Nonlinear damped transitions	en
dc.subject.other	Damping	en
dc.subject.other	Dynamical systems	en
dc.subject.other	Hamiltonians	en
dc.subject.other	Hilbert spaces	en
dc.subject.other	Stiffness	en
dc.subject.other	Viscosity	en
dc.subject.other	Wavelet transforms	en
dc.subject.other	Nonlinear systems	en
dc.title	Multi-scaled analysis of the damped dynamics of an elastic rod with an essentially nonlinear end attachment	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijsolstr.2007.02.025	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijsolstr.2007.02.025	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	We study multi-frequency transitions in the transient dynamics of a viscously damped dispersive finite rod with an essentially nonlinear end attachment. The attachment consists of a small mass connected to the rod by means of an essentially nonlinear stiffness in parallel to a viscous damper. First, the periodic orbits of the underlying harniltonian system with no damping are computed, and depicted in a frequency-energy plot (FEP). This representation enables one to clearly distinguish between the different types of periodic motions, forming back bone curves and subharmonic tongues. Then the damped dynamics of the system is computed; the rod and attachment responses are initially analyzed by the numerical Morlet wavelet transform (WT), and then by the empirical mode decomposition (EMD) or Hilbert-Huang transform (HTT), whereby, the time series are decomposed in terms of intrinsic mode functions (IMFs) at different characteristic time scales (or, equivalently, frequency scales). Comparisons of the evolutions of the instantaneous frequencies of the IMFs to the WT spectra of the time series enables one to identify the dominant IMFs of the signals, as well as, the time scales at which the dominant dynamics evolve at different time windows of the responses; hence, it is possible to reconstruct complex transient responses as superposition of the dominant IMFs involving different time scales of the dynamical response. Moreover, by superimposing the WT spectra and the instantaneous frequencies of the IMFs to the FEPs of the underlying hamiltonian system, one is able to clearly identify the multi-scaled transitions that occur in the transient damped dynamics, and to interpret them as 'jumps' between different branches of periodic orbits of the underlying hamiltonian system. As a result, this work develops a physics-based, multi-scaled framework and provides the necessary computational tools for multi-scaled analysis of complex multi-frequency transitions of essentially nonlinear dynamical systems. (c) 2007 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Solids and Structures	en
dc.identifier.doi	10.1016/j.ijsolstr.2007.02.025	en
dc.identifier.isi	ISI:000249214700027	en
dc.identifier.volume	44	en
dc.identifier.issue	18-19	en
dc.identifier.spage	6256	en
dc.identifier.epage	6278	en