introduc0on# - m. ruzzene - school of aerospace engineering · 2011-10-10 · –...

M. Ruzzene – Introduc0on

Introduc0on

Massimo Ruzzene D. Guggenheim School of Aerospace Engineering G. Woodruff School of Mechanical Engineering

Georgia Ins0tute of Technology Atlanta, GA

5/3/11 1

Wave Propaga+on in Linear and Nonlinear Periodic Media: Analysis and Applica+ons

June 21-‐25, 2010

Francesco Romeo Dipar0mento di Ingegneria StruHurale e Geotecnica

Universita’ La Sapienza Roma


About me…

I. Degrees •  1999 Ph.D. in Mechanical Engineering, Politecnico di Torino, Torino, Italy. •  1995 Laurea in Mechanical Engineering, Politecnico di Torino, Torino, Italy.

II. Employment •  2009-‐Present Associate Professor, Georgia Ins0tute of Technology, School of

Mechanical Engineering, Atlanta GA. •  2007-‐Present Associate Professor, Georgia Ins0tute of Technology, School of

Aerospace Engineering, Atlanta GA. •  2002-‐2007 Assistant Professor, Georgia Ins0tute of Technology, School of

Aerospace Engineering, Atlanta GA. •  1999-‐2002 Assistant Professor, Department of Mechanical Engineering, The

Catholic University of America, Washington DC.

MASSIMO RUZZENE SCHOOL OF AEROSPACE ENGINEERING

Georgia InsDtute of Technology Atlanta, GA


About me… Aosta

Torino

Udine

Washington DC

Atlanta GA

M. Ruzzene – Introduc0on 5/3/11 M. Ruzzene

Introduc0on to

Periodic Structures (with a structural engineering bias…)


Defini0on

•  A periodic structure consists of a number of iden0cal structural components (periodic elements, unit cell) which are joined together end-‐to-‐end and/or side-‐by-‐side to form the whole structure

•  Atomic la[ces of pure crystals: –  “Lumped-‐mass systems” interconnected by inter-‐atomic forces

•  Structural systems: mass and elas0city are distributed, and they define a periodic structure when their distribu0on is periodic over the structural domain


Periodic structures

Honeybee Cells

Iron-‐carbon f.c.c. La[ce Crystal

Subunits in a La[ced Protein

Truss Architecture in a Steel Construc0on

Fiber-‐Reinforced Composite

Honeycomb Structure


Engineering structures

•  Review of the state-‐of-‐the art:



•  Engineering structures which are or have been treated as periodic include: – Mul0 storey buildings –  Elevated guideways for high speed transporta0on vehicles {Maglev}

– Mul0 span bridges – Mul0 blade turbines and rotary compressors –  Chemical pipelines –  S0ffened plates and shells in aerospace and ship structures –  The space sta0on and space trusses in general –  Layered composite structures


Trusses


A quick historical background

•  Brillouin(*) traces the history of the subject back to Newton: –  the systems considered were lumped masses joined by massless springs

•  Rayleigh (1887) is the first that considers con0nuous periodic structures: –  String with a periodic density varia0on undergoing harmonic vibra0ons –  Found expression of the phase veloci0es and the propaga0on and aHenua0on

constants

•  Between 1900 and 1960 mathema0cal techniques were developed for analyzing increasingly complicated: –  crystal la[ce structures –  periodic electrical circuits and –  con0nuous transmission lines

(*) L. BRILLOUIN “Wave Propaga0on in Periodic Structures” Dover, New York – 1946.


A quick historical background •  These techniques have been invaluable in subsequent studies of con0nuous

periodic engineering structures

•  Cremer and Leilich used some of them in 1953 to study harmonic flexural wave mo0on along a one dimensional periodic beam either with simple supports or with point masses at regular Intervals:

–  Simple supports : monocoupled periodic system (basic periodic element is coupled to its neighbors through one degree of freedom)

–  At any frequency there exist a single mode of wave propaga0on and one pair of equal and opposite propaga0on constants

–  These are given by

L. CREMER and H.O. LEILICH 1953 Archiv der Elektrischen Ubertragung 7,61 Zur Theorie der BiegekeHenleiter.



Propaga0on and aHenua0on zones alternate along frequency range



•  In 1964 Heckl inves0gated a two-‐dimensional rectangular grillage of beams which had both flexural and torsional s0ffness: –  Considered the mul0ple reflec0on and transmission processes as flexural waves in one

beam element impinge on the junc0ons with adjacent beams –  Established an equa0on for the propaga0on constants in terms of the reflec0on and

transmission coefficients which relate to a single wave in just one

•  Ungar examined the steady state harmonic responses and propaga0on constants of a one dimensional periodic beam made periodic by the aHachment of arbitrary but iden0cal non dissipa0ve impedances at regular intervals: –  found the propaga0on constants and response of the beam when excited

harmonically between the impedances

M. HECKL 1964 Journal of the Acous0cal Society of America 36, 1335-‐1343, “Inves0ga0ons on the vibra0ons of grillages and other simple beam structures. E. E. UNGAR 1966 Journal of the Acous+cal Society of America 39, 887-‐894 Steady state responses of one-‐dimensional periodic flexural systems


General property

INCIDENT

Structural periodicity (disconDnuiDes) represent sources of impedance mismatch:

TRANSMITTED REFLECTED

Interac0on between incident and reflected waves produces construc0ve/destruc0ve interference;

Impedance mismatch zones introduced PERIODICALLY along the structure generate frequency bands where waves DO NOT

PROPAGATE:

PASS/STOP FREQUENCY BANDS


Other applica0ons

Surface Acous0c Wave (SAW) devices: Band-‐pass delay line: excita0on is spa0ally periodic

From: Auld, B.A., Acous+c Fields and Waves in Solids. Krieger Publ. Co., 1990.


Other applica0ons

•  Surface Acous0c Wave (SAW) devices:

–  Resonator: energy is trapped in the standing wave region within the stop band of the periodic gra0ng

From: Auld, B.A., Acous+c Fields and Waves in Solids. Krieger Publ. Co., 1990.


Phononic materials

•  Strong similarity and parallels in the propaga0on of elas0c (EL) waves and electromagne0c (EM) waves in media with strong periodic modula0on in their EL and EM proper0es:

•  Periodic elas0c and dielectric composites are denoted as CLASSICAL BAND GAP MATERIALS:

–  Characterized by frequency regions (band gaps) where there is no propaga0on of waves

•  Much of the literature considers terminology and methodologies introduced in la[ce mechanics of crystals;

•  These materials are known as:

–  PHOTONIC Crystals (EM waves) –  PHONONIC Crystals (EL waves)

•  Both are intensively inves0gated and used to manipulate LIGHT and SOUND&VIBRATIONS


Phononic materials


22

Acous0c metamaterials

Focusing of sound: Flat acous0c lenses


23

Applica0ons

hHp://www.iv.co.kr/tech/sub3.htm

Tsukerman, I. TMAG, 41(7):2005

Ø  Signal processing •  SAW filters and resonators

Ø  Wave guiding Ø  Vibra0on isola0on

•  Mirrors •  Vibra0on isolators

Ø  Nega0ve refrac0on •  Ultrasonic super lenses

Phononic Devices and Meta-‐Materials for


COURSE OVERVIEW

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Lecturers

•  M. Ruzzene (Georgia Ins0tute of Technology): –  Basic analysis tools, structural la[ces, smart periodic structures, periodic sensors

•  A. Movchan (University of Liverpool):

–  Analy0cal and Numerical Models of Waves in Structured Media

•  P. Deymier (University of Arizona): –  Analysis and design of phononic crystals and acous0c metamaterials.Theore0cal and

numerical tools for Phononic crystal (Plane wave expansion method, FDTD, FE).

•  J. Jensen (Technical University of Denmark) –  Topology op0miza0on, photonic bandgap structures, transient problems, nonlineari0es.

•  A. Vakakis (University of Illinois Urbana-‐Champaign) –  Analy0cal techniques for nonlinear periodic systems, strongly nonlinear periodic

granular media.

•  F. Romeo (Sapienza -‐ Università di Roma): –  Analy0cal and numerical aspects of transfer matrices, maps approach for con0nuous

and discrete nonlinear periodic models.

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Schedule

5/3/11 26

introduc0on# - m. ruzzene - school of aerospace engineering · 2011-10-10 · –...

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