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Nonlinear Dispersive Elastic Waves in Solids : = Exact, Approximate, and Numerical Solutions.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Nonlinear Dispersive Elastic Waves in Solids :/
Reminder of title:	Exact, Approximate, and Numerical Solutions.
Author:	Khajehtourian, Romik.
Description:	1 online resource (117 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Contained By:	Dissertation Abstracts International79-02B(E).
Subject:	Aerospace engineering. -
Online resource:	click for full text (PQDT)
ISBN:	9780355232110

Nonlinear Dispersive Elastic Waves in Solids : = Exact, Approximate, and Numerical Solutions.
Khajehtourian, Romik.

Nonlinear Dispersive Elastic Waves in Solids :Exact, Approximate, and Numerical Solutions. - 1 online resource (117 pages)

Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355232110Subjects--Topical Terms:

686400
Aerospace engineering.
Index Terms--Genre/Form:

554714
Electronic books.

Nonlinear Dispersive Elastic Waves in Solids : = Exact, Approximate, and Numerical Solutions.
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100 1 $a Khajehtourian, Romik. $3 1179004
245 1 0 $a Nonlinear Dispersive Elastic Waves in Solids : $b Exact, Approximate, and Numerical Solutions.
264 0 $c 2017
300 $a 1 online resource (117 pages)
336 $a text $b txt $2 rdacontent
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500 $a Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
500 $a Adviser: Mahmoud I. Hussein.
502 $a Thesis (Ph.D.) $c University of Colorado at Boulder $d 2017.
504 $a Includes bibliographical references
520 $a Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium.
520 $a The first part of the dissertation examines the propagation of a large-amplitude elastic wave in a one-dimensional homogeneous medium with a focus on the effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the thickness is small compared to the wavelength, an exact, closed-form formulation is presented for the treatment of two types of nonlinearity in the strain-displacement gradient relation: Green-Lagrange and Hencky. The derived relation is then verified by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-breaking dispersion (by Fourier transformation). A high-order perturbation analysis is also conducted yielding an explicit analytical space-time solution, which is shown to be spectrally accurate. The results establish a perfect match between theory and simulation and reveal that regardless of the strength of the nonlinearity, the dispersion relation fully embodies all information pertaining to the nonlinear harmonic generation mechanism that unfolds as an arbitrary-profiled wave evolves in the medium.
520 $a In the second part of the dissertation, the analysis is extended to a continuous periodic thin rod exhibiting multiple phases or embedded local resonators. The extended method, which is based on a standard transfer-matrix formulation augmented with a nonlinear enrichment at the constitutive material level, yields an approximate band structure that is accurate to an amplitude that is roughly one eighth of the unit cell length. This approach represents a new paradigm for examining the balance between periodicity and nonlinearity in shaping the nature of wave motion.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Aerospace engineering. $3 686400
650 4 $a Mechanics. $3 527684
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0538
690 $a 0346
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Colorado at Boulder. $b Aerospace Engineering. $3 1179005
773 0 $t Dissertation Abstracts International $g 79-02B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10617841 $z click for full text (PQDT)