STRUCTURAL
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PROCEEDINGS OF THE 7TH INTERNATIONAL CONFERENCE EDITED BY: N. S. FERGUSON H. F. WOLFE M. A. FERMAN S. A. RIZZI
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27 July 2000
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Seventh International Conference on Recent Advances in Structural Dynamics 6. AUTHOR(S) Conference Committee
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13. ABSTRACT (Maximum 200 words) The Final Proceedings for Seventh International Conference on Recent Advances in Structural Dynamics, 24 July 2000 - 27 July 2000 Aeronautics and Flutter; Analytical Developments; Numerical Methods; Finite Element Methods; Nonlinear Vibration; Experimental techniques; Rotating Machines; Control; System Identification; Acoustic Fatigue and Thermal Effects; Power Flow Approaches and Impact Dynamics
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1048 16. PRICE CODE
EOARD, Aerodynamics, Fatigue, Aeroelasticity 17. SECURITY CLASSIFICATION OF REPORT UNCLASSIFIED NSN 7540-01-280-5500
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STRUCTURAL DYNAMICS:
RECENT ADVANCES
Proceedings of the 7th International Conference Volume II Proceedings of the Seventh International Conference on Recent Advances in Structural Dynamics, held at the Institute of Sound and Vibration Research, University of Southampton, England, from 24th to 27th July, 2000, co-sponsored by the US Airforce European Office of Aerospace Research and Development, the Air Force Research Laboratory, Wright Patterson Air Force Base, Parks College of Engineering and Aviation, St. Louis University, and the Structural Acoustics Branch at NASA Langley Research Center. Edited by N.S. FERGUSON Institute of Sound and Vibration Research, University of Southampton, Southampton, UK. H.F. WOLFE Air Force Research Laboratory Wright Patterson Air Force Base, Ohio, USA. M.A. FERMAN Parks College of Engineering and Aviation St Louis University, St Louis, USA and S.A. RIZZI NASA Langley Research Center Hampton, Virginia, USA
> The Institute of Sound and Vibration Research, University of Southampton, UK. ISBN no. 0854327215
hQFöO-ll'JrtS-
PREFACE
The International Conference series on Recent Advances in Structural Dynamics enters its third decade of existence since its inception in 1980. This is the seventh conference to be held at the Institute of Sound and Vibration Research(ISVR) and it is through the continued support and sponsorship, in time and resources, of the ISVR, the Air Force Research Laboratory(Wright Patterson Air Force Base), Parks College of Engineering and Aviation(St Louis University) and NASA Langley Research Center that we have succeeded in organising the event. On this occasion there are two new co-organisers, Prof. M.A. Ferman and Dr S.A. Rizzi, who have been excellent replacements for Prof. C. Mei, who previously contributed so much. The new coorganisers have been instrumental in the organisation of new sessions, one namely Aerodynamics and Flutter, and have also continued the long standing tradition, topics and interests of the Structural Dynamics community, such as Acoustic Fatigue. The conference has maintained its high standards by continuing to review submitted papers and thanks are directed towards the authors, Invited Speakers, paper reviewers and session chairmen for their contribution and support. Likewise the conference has a strong international participation, allowing for good technical discussion, dissemination and interchange of ideas. It is also anticipated that the published proceedings will provide a good source of material for future research activities and be a true record of the papers presented. The arrangement of the papers, in two volumes, is to accompany the programme of presentations and likewise the papers are grouped into the most appropriate sessions. The organisers would like to thank the following for their contribution to the success of the conference: the United States Air Force European Office of Aerospace Research and Development. Personally I would like to acknowledge and thank all of the other conference organisers of the event: Dr. H.F. Wolfe Prof. M.A. Ferman Dr. S.A. Rizzi
Air Force Research Laboratory, Wright Patterson Air Force Base, USA Parks College of Engineering and Aviation, St Louis University, USA Structural Acoustics Branch, NASA Langley Research Center, USA
Last, but not least, also tremendous thanks to Mrs. M.Z. Strickland, Conference Secretary and general assistant for all things technical and administrative.
N.S. Ferguson
Seventh International Conference on Recent Advances in Structural Dynamics Volume II Contents Page No. INVITED PAPERS K.KTAMMA, R.KANAPADY, X.ZHOU and D.SHA Recent Advances in Computational Structural Dynamics Algorithms
731
ACOUSTIC FATIGUE RUDRESCU Nonlinear Vibrations of thermally Buckled Panels
757
J-M.DHA1NAUT, BIN DUAN, C.MEI, S.M.SPOTTSWOOD andHF.WOLFE Non-Linear response of composite panels to random excitations at elevated temperatures
769
S.M.SPOTISWOOD,HF.WOLFE and D.L.BROWN The effects of record length on determining the cumulative damage of a ceramic matrix composite beam
785
P.ROJNNINGHAM/D.M. A.MILLAR and R.G.WHTTE High intensity acoustic testing of doubly curved composite honeycomb sandwich panels 801 N.W.M.BISHOP,N.DAVIS, A.CASERIO and S.KERR Fatigue Analysis of an F16 Navigation Pod
815
S.A.RIZZI andAAMURAVYOV Comparison of non-linear random response using equivalent linearization and numerical simulation
833
J.LEE Effects of temperature dependent physical properties on the responses of thermally buckled plates
847
FE and APPLICATIONS
K.DEDOUCH, J.HORACEK and J.SVEC Frequency modal analysis of supraglottal vocal tract
863
G.CATANIA Combined influence of cutouts and initial stresses on the free vibration response of general, double curvature shell structures
875
S.E.HIRDARIS S.E.and A.W.LEES On the identification of natural frequencies of thick portal frames
887
CREMILLAT, G.R.TOMUNSON and R LEWIN A new multiple-layer finite element shell incorporating very thin damping layers: application to a multilayered cylindrical shell
901
D.K.L.TSANG, S.O.OYADIJI and A.Y.T.LEUNG Predicting the dynamic stress intensity factor for a circumferential crack in a hollow cylinder using fractal finite element method
913
SYSTEM IDENTIFICATION S.D.GARVEY, M.I. FRISWELL and J.E.T. PENNY A Geometric-Algebraic Approach to Identifying Second Order Continuous Systems
925
A.RTVOLA Comparison between second and higher order spectral analysis in detecting structural damages
937
N.JAKSIC, M.BOLTEZAR and A.KUHELJ Parameter identification of a single degree of freedom dynamical system based on phase space variables
951
K.WORDEN, G.W.MANSON and CREMILLAT Damage Localisation Using Novelty Indices
965
HOON SOHN, M.L.FUGATE and CRFARRAR Damage Diagnosis Using Statistical Process Control
979
C.K.MECHEFSKE, Y.WU and B.K.RUTT MRI Gradient Coil Cylinder Sound Field Simulation and Measurement 995 Z.CHEN, C.K.MECHEFSKE Application of the Prony Method in Machine Condition Monitoring
1003
K.T.FEROZ, S.O.OYADIJI, J.R.WRIGHT and A.Y.T.LEUNG Finite element analysis of rubber mounts under shock loading
1015
HUANG YU, TANG YIQUN, YE WEIMIN and CHEN ZHUCHANG A dynamic calculation model of Shanghai saturated soft soil 1027 C.J.GJONES, D.J.THOMPSON and M.G.R.TOWARD The dynamic stiffness of the ballast layer in railway track
1037
INVITED PAPERS
Recent Advances in Computational Structural Dynamics Algorithms K. K. Tamma? R. KanapadyJ X. Zhou} and D. Sha§ Dept. of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455 U. S. A Abstract Recent advances describing a generalized unified framework for the generic design of time discretized operators for structural dynamics applications is described. Emanating from a generalized time weighted philosophy for performing the time discretization process, the burden of weight carried by the so-called and resulting discrete numerically assigned [DNA] algorithmic markers serves as a prelude to providing a basis for the classification, characterization and design of computational algorithms for structural dynamic computations. An overview of recent advances encompassing time discretized operators which we have recently classified as Type 1, 2 and 3 is briefly highlighted and subsequently, for illustration, emphasis is primarily placed on applicability of Type3 classification to general non-linear/linear problems, practical issues, and implementation aspects. 1 Introduction For the solution of the semi-discretized system of equations of structural dynamic problems, the so-called time integration algorithms are widely used. Especially for non-linear structural dynamic problems, time integration algorithms are the major tools, which leads to the primary motivation for a precise understanding of computational algorithms for time dependent problems. Due to the cumbersome issues associated with nonlinear situations, most of the time integration algorithms are customarily developed starting from the linear semi-discretized system or modal equations. The extension of time integration algorithms to non-linear problems is then conducted. In contrast, we focus our attention here on recent advances in the design and application of computational algorithms under the umbrella of a generalized unified framework for the simulation of structural dynamics problems. Emanating from and explained via a generalized time weighted residual philosophy, Tamma et al. [1, 2] have recently described the resulting time discretized operators for the semi-discretized single field or two field equations of motion of structural dynamic problems as pertaining to three major classifications, namely, Type 1 classification, Type 2 classification, and Type 3 classification (see [1, 2] for details). Type 1 classification are an outcome of selecting the weighted time fields (which are matrix representations) as the homogeneous solution of the linear semi-discretized system of equations with or without the notion of 'Professor, to receive correspondence,
[email protected] tDoctoral student,
[email protected] 'Doctoral student,
[email protected] ^Visiting Professor, Dalian University of Technology, P. R. China,
[email protected]
731
transforming the semi-discretized system of equations into modal basis. The Type 1 classifications lead to explicit time integral representations of the exact solution of the linear semi-discretized system of equations of the structural dynamic problems. Here, the approximations for the dependent field variables are not pertinent. The Type 2 classification of time discretized operators are a result of introducing further approximations to the theoretical weighted time fields pertaining to Type 1 which still preserve the matrix representation for the weighted time fields and without considering the notion of transforming modal basis merely for convenience in the theoretical design developments. Again, for time discretized operators of Type 2 classification, approximations for the dependent field variables are not pertinent. In contrast, Type 3 classification of time discretized operators are a result of further introducing approximations to the theoretical weighted time fields, thereby leading to a degenerated vector or a degenerated scalar representation which does not preserve the original theoretical representations. As a consequence, the approximations for the dependent field variables is now necessary for designing the time integrators and the associated updates. This Type 3 classification leads to a wide variety of generalized integration operators in time which not only provide new avenues [3] but also recover the existing and so-called time integration algorithms (both dissipative and non-dissipative) we are mostly familiar with. Characterization as employed here, pertains to that which not only permits the classification of the time discretized operators to be undertaken but also provides the underlying theoretical basis towards their subsequent theoretical design via discrete numerically assigned [DNA] algorithmic markers which essentially comprise of: (i)weighted time fields utilized for enacting the time discretization process, and (ii) the corresponding conditions invoked (if any) and dictated by these weighted time fields for approximating the dependent field variable(s) in the design of time integrators and the associated updates. 2 Semi-Discretized Equations of Motion 2.1 Single-Field Form Firstly, we consider the semi-discretized system of equations of linear structural dynamic problems after space discretization (say in a finite element sense) of the single field form of representation resulting in Mü(t) + Cü(t) + Ku(t) = f(t),
u(0) = u0,ü(0) = ü0
(1)
where M is the mass matrix, C is the damping matrix, and K is the stiffness matrix. Under the framework of a time weighted residual approach with an arbitrary weighted time field, W(t), we have the representation after integrating by parts twice /
(wTM - WTC + WTK) udt
J ° r.t = - WTMu |£( +WTMu |f +WTCu C + / WTM Jo
732
(2)
2.2 Two-Field Form Alternatively, equation (1) can be cast into a two field representation by letting ü = v and ü = v, resulting in d + Ad = F
(3)
where A=
0
-I
d=
F=
0
Again considering the weighted residual satisfaction with an arbitrary weighted time field W(t), after integrating by parts once, leads to
WTd|At+/" [(wTA-WT)d-WTFJdt = 0
(4)
3 Time Discretized Operators of Type 1 Classification 3.1 Single Field Form Consider the weighted time fields W as the solution of the adjoint operator in Eq. 2, and substituting the obtained theoretical weighted time field W = W Exact{t) into equation (2) and transforming the resulting equation into modal basis by using the eigenvector matrix X obtained form
KX = Mxn2
(5)
The resulting exact time integral representations (equivalent to the Duhamel representations) are explicit in nature and are obtained as ( ft(*n+l) \
=
V ft(*n+l) /
\ 9i(fn) )
+L
(6)
where the details are given in [2]. An approximate integral operator is readily constructed by approximating the load term. The applicability of such Type 1 representations to linear/nonlinear problems is addressed in Refs. [1, 4]. Alternatively, without considering transformation to modal basis, although a theoretical representation can be derived, no practically useful time discretized representations result. 3.2 Two Field Form Next consider the weighted time fields, W, as the solution of the adjoint operator in Eq. 3, and substituting the fundamental solution, into equation (4), we have the closed form time integral representation of the equation (3) as /■At
exp[AAt]dn+1 = dn + /
Jo
733
exp[At']F(i' + t„)dtf
(7)
A key idea towards the generic theoretical design and development of a new generation of a generalized family of time discretized operators pertaining to Type 2 classification is that the matrix A is first decomposed into a symmetric and unsymmetric part as A = Afl + /JAn + (l-/?)An
(8)
where AD = a
M-'C 0 0 M-'C
An =
-aM-'C -I M-'K (l-ajM^C
(9)
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Figure 2: ü +100u(l + 10u2) = 0. GInOSlS22,«i=i/2,»2=V2 and SS22 0X = 1/2,02 = 1/2 with (a)ü„ = M„, (b)ün = \{un + un+i) and (c)un = un+1 due to [16].
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(c) Deformed shape of the cylindrical panel crown-line
(e) incremental a-form
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(f) incremental «-form
(g) incremental d-form
Figure 4: Cylindrical panel subjected to blast loading: geometry, boundary conditions and large, elastic, elasto-plastic dynamic response employing predictor multi-corrector [GInO] representations.
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d„+1=dn+1 +A2p+1%AdiPji+1At"-1 Till convergence ,,„ ' < e Design updates at end of time step ■ j+i
d£»i = «#> + (d„+1 -dn - A^WÄAt A2pWp-ld^At"-1)/(A2p+lWpAt"-1) 1
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