Structural Dynamics Fundamentals and Advanced Applications, Volume I: Volume I

916 Pages·2020·37.715 MB·English

by  Alvar M. Kabe, Brian H. Sako

Structural Dynamics
Fundamentals and
Advanced Applications
Volume I
Alvar M. Kabe
Brian H. Sako
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Thefirstauthordedicates thisworktohischildren,Nickole, Caroline,
and Erik, and their mother, Erika, for without them it would not have
been possible. The second author dedicates his work to his wife, Lee
Anne, and his daughter, Erin, for their endless patience,
encouragement, and support.
Both authors also express sinceregratitude to theircolleagues at The
AerospaceCorporationfortheprivilegeofworkingwiththemonsome
of the most challenging engineering problems in aerospace.
About the authors
Dr. Alvar M. Kabe is the Principal Director of the Structural Mechanics
Subdivision of The Aerospace Corporation. His prior experience includes
Director of the Structural Dynamics Department and Manager of the Flight
Loads Section at The Aerospace Corporation. Dr. Kabe has made funda-
mental contributions to the state of the art of launch vehicle and spacecraft
structural dynamics. He introduced the concept of multishaker correlated
random excitation to better isolate modes for measurement in mode survey
tests,andtheconceptofusingthesuperpositionofscaledfrequencyresponse
functions to isolate modes for identification. He then introduced the concept
of using structural connectivity information as additional constraints when
optimally adjusting dynamic models to better match test data; this work
has been cited over 260 times in other publications. Dr. Kabe developed
theatmosphericflightturbulence/gustandtime-domainbuffetloadsanalysis
methodologies used on several operational launch vehicle programs, and
he pioneered the concept of using structural dynamic models to compute
atmospheric flight static-aeroelastic loads.
Dr.Kabeledthedevelopmentofacontinuallyevolvingintegrateddynamics
analysissystemthathasbeenusedforovertwodecadestocomputeloadson
over a dozen launch vehicle systems and their payloads. Thework included
independentlydevelopingand implementing analysismethodologies, devel-
oping loads and stress analysis models, computing loads, and establishing
structural margins. This also included independent day-of-launch placards
analyses and independent go/no-go launch recommendations.
Dr. Kabe has led, co-chaired, or participated on numerous high level
reviews and assessment teams that have had significant impact. He was a
member of the Defense Science Board’s Aviation Safety Task Force, and
he co-chaired four US Air Force Titan IV Independent Readiness Reviews.
He led the Space Shuttle Radar Topography Mission assessment, and he
co-chaired NASA’s Mars Sample Return project review. In addition,
Dr. Kabe is on the NASA Engineering Safety Center Structural Dynamics
Technical Discipline Team as a subject-matter expert.
Dr.Kabehaspublished23technicalpapersandwrittenover150corporate
technical reports. He has taught undergraduate and graduate structural
dynamics classes, presented invited seminars at major universities, and
the Keynote at an AIAA Structural Dynamics Specialist conference.
xi
xii About the authors
Dr.Kabehasreceivednumerousawardsandover40lettersofcommenda-
tion. The awards include the Trustees Distinguished Achievement Award,
TheAerospaceCorporation’shighestaward,TheAerospaceCorporation’s
President’s Award, Division and Group Achievement Awards, and
nine Program Recognition Awards. Dr. Kabe is a Registered Professional
Engineer in the state of California; his BS, MS, and PhD degrees are from
UCLA.
Dr. Brian H. Sakois aDistinguished Scientistinthe Structural Mechanics
Subdivision of The Aerospace Corporation. Prior to this position, Dr. Sako
was an Engineering Specialist, a Senior Engineering Specialist, and an
Aerospace Fellow. Dr. Sako has made significant contributions to the fields
of structural dynamics, numerical analysis, and time series data analysis.
Hisdevelopmentofthefilteringapproachusedtoseparatethemorerapidly
varying wind features from more slowly varying components is used on
several launch vehicle programs to develop turbulence forcing functions
for atmospheric flight loads analysis. Dr. Sako also developed an approach
to remove tones from wind tunnel buffet test data; the approach was used,
forexample,onNASA’sSpaceLaunchSystemprogram.Hisdevelopments
have also made significant contributions to the assessment of the internal
dynamic properties of rocket engines, pogo stability of launch vehicles,
and the development of forcing functions for loads analysis.
Dr. Sako developed state-of-the-art time series analysis and mode param-
eter identification tools that are currently used to analyze data and identify
structural dynamic parameters on numerous operational systems. The time
series data analysis tool is used to assess flight and ground vibration test
data.Themodeparameteridentificationtoolisusedtoextractmodeparam-
eters from launch vehicle and satellite mode survey test data, as well as
flight data. Dr. Sako’s developments are used routinely to assess data
from operational launch and space systems.
Dr. Sako has published 25 technical papers and written 100 corporate
technical reports. He has taught graduate classes in numerical analysis,
engineering mathematics, and signal processing. Dr. Sako has earned
numerous awards and letters of commendation, including The Aerospace
Corporation’s President’s Award, Division and Group Achievement
Awards, and several Program Recognition Awards. Dr. Sako’s BA and
MAdegreesarefromtheUniversityofHawaii,andhisPhDisfromUCLA.
About the authors xiii
Dr.Kabe’strainingandexpertiseareinstructuraldynamicsandDr.Sako’s
areinappliedmathematics.Theyhaveworkedtogetherforthreedecadeson
the most complex structural dynamics systems in existence, and their
complimentary expertise and experience have led to the development of
first-of-a-kindmethodologiesandsolutionstocomplexstructuraldynamics
problems. Dr. Kabe’s and Dr. Sako’s experience and contributions encom-
pass numerous past and currently operational launch and space systems.
Preface
The two-volume work, Structural DynamicsdFundamentals and
Advanced Applications, is a comprehensive work that encompasses the
fundamentals of structural dynamics and vibration analysis, as well as
advanced applications used on extremely large and complex systems.
Becauseofthescopeofthework,thematerial isdivided intotwovolumes.
Volume I covers fundamentals, and Volume II covers advanced applica-
tions. The derivations are complete and rigorous, and the topics covered
are those needed to become a learned member of the structural dynamics
community and solve the complex problems encountered.
Volume I covers all the material needed for a first course in structural
dynamics, including a thorough discussion of Newton’s laws, single-
degree-of-freedom systems, damping, transfer and frequency response
functions, transient vibration analysis (frequency and time domain),
multi-degree-of-freedom systems, forced vibration of single- and multi-
degree-of-freedom systems, numerical methods for solving for the re-
sponses of single- and multi-degree-of-freedom systems, and symmetric
and nonsymmetric eigenvalue problems. This volume also includes a thor-
ough discussion ofreal andcomplexmodes, andthe conditions that leadto
each.Solutionstosystemswithgyroscopiceffectsduetospinningrotors,as
well as aeroelastic instability in simple systems, are covered as part of the
discussion on complexmodes. In addition, stochastic methods are covered,
including derivation of solutions for the response of single- and multi-
degree-of-freedom systems excited by random forces or base motion.
Volume II includes all material needed for graduate-level courses in
structuraldynamics.Thisincludesd’Alembert’sprinciple,Hamilton’sprin-
ciple,andLagrange’sequations,allofwhicharederivedfromfundamental
principles. Development of large complex structural dynamic models is
thoroughly covered with derivations and detailed discussion of component
modesynthesisandfluid/structureinteraction;anintroductiontoapplicable
finite element methods is also included. Material needed to solve complex
problems,suchastheresponseoflaunchvehiclesandtheirpayloadstotur-
bulence/gust, buffet, and static-aeroelastic loading encountered during at-
mospheric flight, is addressed from fundamental principles to the final
equations and response calculations. The formulations of the equations of
xv
xvi Preface
motion include aeroelasticity, and the response calculations include statis-
tical analysis of the response quantities.
Volume II also includes a thorough discussion of mode survey testing,
modeparameteridentification,andmodeladjustmenttoimproveagreement
with test data. Detailed data processing needed for the analysis of time
signals, such as digitization, filtering, and transform computation, is also
included with thorough derivations and proofs. Since the field of structural
dynamicsneedstodealwithvariabilityinpracticallyallaspects,acompre-
hensive discussion of probability and statistics is included, with detailed
derivations and proofs related to the statistics of time series data, small
sample statistics, and the combination of responses whose statistical
distributions are different. Volume II concludes with an extensive chapter
on continuous systems, which not only includes the classical derivations
and solutions for strings, membranes, beams, and plates but also the
derivationandclosedformsolutionsforrotatingdisksandsloshingoffluids
in rectangular and cylindrical tanks.
ThetwovolumesofStructuralDynamicsdFundamentalsandAdvanced
Applications were written with both the practicing engineer and students
just learning structural dynamics in mind. The derivations are rigorous
and comprehensive, thus making understanding the material easier; this
also allows more material to be covered in less time. To facilitate learning,
detailedsolutionstonearly300problemsareincluded.Thisallowsstudents
to work the problems and immediately check their solutions; and for
practicing engineers these problems serve as additional examples to those
provided within the chapters. As a final note, the material covered in the
two volumes can be divided into two primary categories: material that is
fundamental to learning and understanding structural dynamics; and
material that is being used to solveextremely complex structural dynamics
problems by the leading practitioners in the field.
CHAPTER
1
Structural dynamics
1. Introduction
The subject matter of this work is structural dynamics and the Laws of
Nature that describe the vibratory behavior of structures. In our endeavor,
we will use the language of mathematics to describe these laws and to
make engineering predictions of the dynamic behavior of structures. Since
weareinterestedinengineeringapplicationswherespeedsareconsiderably
less than the speed of light, the Law of Universal Gravitation and the Laws
of motion as developed by Sir Isaac Newton, and published in 1686 in
Philosophiae Naturalis Principia Mathematica (Newton, 1946), and
commonly referred to as The Principia, will be our interest. The Principia
isoneofthegreatestworksofscience,ifnotthegreatest;andthedefinitions
and laws Newton enunciated in The Principia impact our lives daily. New-
ton’s laws are used in practically every aspect of mechanical engineering,
including the disciplines of orbital mechanics, flight mechanics, fluid
dynamics, soil mechanics, environmental sciences, structures, civil engi-
neering, and structural dynamics, the subject matter of this work.
1.1 Newton’s laws of motion
Sir Isaac Newton’s three Laws of motion, as translated in 1729 from Latin
into English by Andrew Motte (Newton, 1946), are
(1) Everybodycontinues initsstateofrest,orofuniformmotioninaright
line,unlessitiscompelledtochangethatstatebyforcesimpressedupon
it.
(2) Thechangeofmotionisproportionaltothemotiveforceimpressedand
ismadeinthedirectionoftherightlineinwhichthatforceisimpressed.
1
StructuralDynamics.https://doi.org/10.1016/B978-0-12-821614-9.00001-X
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