Numerical study of an intrinsic component mode synthesis method

Abstract Component mode synthesis belongs to the class of Galerkin methods and it enables us to compute the normal modes of linearly elastic structures which can be divided into several substructures whose lowest eigenfrequencies and corresponding normal modes are known. Energy transfer between substructures is achieved thanks to the introduction in the Ritz procedure of mode shapes defined on the whole structure, usually called ‘static modes’ or ‘constraint modes’. A new fixed interface method is presented in a continuous framework: it is based on a non-conventional choice of constraint modes tied to the normal modes of the Poincare-Steklov operator associated with the interface between the substructures. Error bounds are given in the case of three-dimensional elasticity. An efficient domain decomposition algorithm is presented in detail as well as various tests.

[1]  J. H. Wang,et al.  A substructure modal synthesis method with high computation efficiency , 1990 .

[2]  R. L. Goldman,et al.  Vibration analysis by dynamic partitioning. , 1969 .

[3]  F. Léné,et al.  Numerical analysis of junctions between plates , 1989 .

[4]  Angus E. Taylor.  Introduction to functional analysis , 1959 .

[5]  M. El-Raheb,et al.  Vibration of a liquid with a free surface in a spinning spherical tank , 1981 .

[6]  J. Pasciak,et al.  An iterative method for elliptic problems on regions partitioned into substructures , 1986 .

[7]  Philippe G. Ciarlet,et al.  Plates and Junctions in Elastic Multi-Structures: An Asymptotic Analysis , 1991 .

[8]  R. Craig.  A review of time-domain and frequency-domain component mode synthesis method , 1985 .

[9]  F. Bourquin.  Synthese modale et analyse numerique des multistructures elastiques , 1991 .

[10]  Leonard Meirovitch,et al.  A general substructure synthesis method for the dynamic simulation of complex structures , 1980 .

[11]  F. Bourquin.  Analysis and comparison of several component mode synthesis methods on one-dimensional domains , 1990 .

[12]  W. Hurty.  Dynamic Analysis of Structural Systems Using Component Modes , 1965 .

[13]  Ivo Babuška,et al.  Error estimates for the combinedh andp versions of the finite element method , 1981 .

[14]  Dominique Leguillon,et al.  Computation of singular solutions in elliptic problems and elasticity , 1987 .

[15]  R. Macneal.  A hybrid method of component mode synthesis , 1971 .

[16]  Philippe G. Ciarlet,et al.  Junctions between three-dimensional and two-dimensional linearly elastic structures , 1989 .

[17]  A. Preumont.  Vibrations des structures, interactions avec les fluides, sources d'excitations aleatoires , 1989 .

[18]  F. Bourquin,et al.  Component mode synthesis and eigenvalues of second order operators : discretization and algorithm , 1992 .

[19]  Leonard Meirovitch,et al.  Computational Methods in Structural Dynamics , 1980 .

[20]  Synthèse modale : théorie et extensions , 1985 .

[21]  S. Rubin.  Improved Component-Mode Representation for Structural Dynamic Analysis , 1975 .

[22]  P. Grisvard,et al.  Singularités en elasticité , 1989 .

[23]  P. Lascaux,et al.  Analyse numérique matricielle appliquée a l'art de l'ingénieur , 1987 .

[24]  Modélisation d'une plaque pliée , 1987 .

[25]  M. Aufranc.  Sur quelques problemes de jonctions dans les multi-structures elastiques , 1990 .

[26]  V. A. Kondrat'ev,et al.  Boundary problems for elliptic equations in domains with conical or angular points , 1967 .

[27]  H. Dret,et al.  Modeling of a folded plate , 1990 .

[28]  R. Ohayon,et al.  Substructure variational analysis of the vibrations of coupled fluid–structure systems. Finite element results , 1979 .

[29]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[30]  P. Tallec,et al.  Domain decomposition methods for large linearly elliptic three-dimensional problems , 1991 .

[31]  Roger Valid.  La mécanique des milieux continus et le calcul des structures , 1977 .

[32]  P. G. Ciarlet,et al.  Modeling and justification of eigenvalue problems for junctions between elastic structures , 1989 .

[33]  Junctions between three-dimensional and two-dimensional nonlinearly elastic structures , 1991 .

[34]  G. M. L. Gladwell,et al.  Branch mode analysis of vibrating systems , 1964 .

[35]  Remarks on dynamic substructuring , 1989 .