This work addresses the direct eigenanalysis of the problem that results from the linearization of the dynamics of constrained systems about arbitrary, problem-dependent steady solutions. The procedure is outlined; the expected properties of the eigensolution are illustrated; implementation issues, related to the application of the procedure to an existing multi-body formulation, are addressed. The soundness of the proposed approach is illustrated by a simple, yet exhaustive example, and by the analysis of a relatively detailed model of a flexible helicopter rotor blade.
SchildersW. H. A.van der VorstH. A.RommesJ.Model order reduction: theory, research aspects and applications (Berlin, Heidelberg: Springer2008)
2.
CraigR. R.BamptonM. C. C.‘Coupling of substructures for dynamic analysis’AIAA J.67 (1968): 1313–1319
3.
SchiehlenW.‘Multibody system dynamics: Roots and perspectives’Multibody Syst. Dyn.12 (1997): 149-188 DOI: 10.1023/A: 1009745432698
4.
ShabanaA. A.‘Flexible multibody dynamics: Review of past and recent developments’Multibody Syst. Dyn.12 (1997): 189-222 DOI: 10.1023/A: 1009773505418
5.
GéradinM.CardonaA.Flexible multibody dynamics: a finite element approach (Chichester: John Wiley and Sons2001)
6.
Da LioM.LotR.Analisi modale di sistemi multibody descritti in coordinate naturali (in Italian)In Proceedings of the XIV Congresso Nazionale AIMETA,Como, Italy, 6–9 October 1999.
7.
CossalterV.LotR.MaggioF.‘The modal analysis of a motorcycle in straight running and on a curve’Meccanica391 (2004): 1-16 DOI: 10.1023/A: 1026269926222
8.
WallrappO.‘Standardization of flexible body modeling in multibody system codes, part I: Definition of standard input data’Mech. Struct. Mach.223 (1994): 283–304
9.
KoutsovasilisP.BeitelschmidtM.‘Comparison of model reduction techniques for large mechanical systems - a study on an elastic rod’Multibody Syst. Dyn.20 (2008): 111-128 DOI: 10.1007/s11044-008-9116-4
10.
BoschiV.De SalvoR.MasaratiP.QuarantaG.SannibaleV.‘Seismic attenuation system synthesis by reduced order models from multibody analysis’In Proceedings of the Multibody Dynamics 2007, ECCOMAS Thematic Conference, Milano, 25–28 June 2007
11.
EscalonaJ. L.ChamorroR.‘Stability analysis of vehicles on circular motions using multibody dynamics’Nonlinear Dyn.53 (2008): 237-250 DOI: 10.1007/s11071-007-9311-5
12.
NikraveshP. E.‘Newtonian-based methodologies in multi-body dynamics’Proc. IMechE, Part K: J. Multi-body Dynamics 222 K4 (2008): 277-288 DOI: 10.1243/14644193JMBD152
13.
BrenanK. E.CampbellS. L.PetzoldL. R.Numerical solution of initial-value problems in differential-algebraic equations (New York: North-Holland1989)
StewartG. W.‘On the sensitivity of the eigenvalue problem Ax = λBx’SIAM J. Numer. Anal.9 (4) (1972): 669-686 DOI: 10.1137/0709056
18.
MolerC. B.StewartG. W.‘An algorithm for generalized matrix eigenvalue problems’SIAM J. Numer. Anal.10 (2) (1973): 241-256 DOI: 10.1137/0710024
19.
LehoucqB.SorensenD. C.VuP.‘ARPACK: An implementation of the implicitly re-started arnoldi iteration that computes some of the eigenvalues and eigenvectors of a large sparse matrix’Available from netlib@ornl.gov under the directory scalapack.
20.
WilkiezKeats W.MirickP. H.LangstonC. W.‘Rotating shake test and modal analysis of a model helicopter rotor blade’ ARL technical report 1389, TM 4760, NASA, June 1997
21.
JohnsonW.Helicopter theory (Princeton, New Jersey: Princeton University Press1980)
22.
BielawaR. L.Rotary wing structural dynamics and aeroelasticity (Washington, DC: AIAA1992)
