On a component mode synthesis method and its application to incompatible substructures

Abstract Component Mode Synthesis (CMS) methods are substructuring techniques frequently employed in structural dynamics. A given structure is subdivided into components or substructures which are analyzed independently for natural frequencies and for mode shapes. The substructure mode shapes are then assembled to give frequencies and mode shapes of the original structure. In this paper, we construct a substructure interface impedance operator and present a spectral analysis that demonstrates that the method of Craig and Bampton (CB) is the most ‘natural’ CMS method. Next, we consider the CB method for assembling heterogeneous substructures and recast it into a hybrid variational formulation. We develop finite element procedures for ‘gluing’ non-conforming and incompatible finite element substructure models, and discuss their computational aspects. The result is a Hybrid Craig-Bampton (HCB) method that is a finite element refinement of the ‘intermediate structure’ concept introduced by Hale and Meirovitch, and which can be used as an interface reduction method. It is illustrated with the eigen analysis of heterogeneous and homogeneous finite element models of a High Speed Civil Transport (HSCT) aircraft.

[1]  Charbel Farhat,et al.  A simple and efficient automatic fem domain decomposer , 1988 .

[2]  Henryk Flashner.  An orthogonal decomposition approach to modal synthesis , 1986 .

[3]  R. Craig,et al.  On the use of attachment modes in substructure coupling for dynamic analysis , 1977 .

[4]  Roy R. Craig,et al.  Structural Dynamics: An Introduction to Computer Methods , 1981 .

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

[6]  A. L. Hale,et al.  On the Substructure Synthesis Method , 1981 .

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

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

[9]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[10]  R. Guyan.  Reduction of stiffness and mass matrices , 1965 .

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

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

[13]  Roy R. Craig,et al.  Substructure coupling for dynamic analysis and testing , 1977 .

[14]  C. Farhat,et al.  A method of finite element tearing and interconnecting and its parallel solution algorithm , 1991 .

[15]  Charbel Farhat,et al.  Using a reduced number of Lagrange multipliers for assembling parallel incomplete field finite element approximations , 1992 .

[16]  B. Parlett.  The Symmetric Eigenvalue Problem , 1981 .

[17]  S. Rubin,et al.  An improved component-mode representation , 1974 .

[18]  Leonard Meirovitch,et al.  A general dynamic synthesis for structures with discrete substructures , 1980 .

[19]  J. Spanos,et al.  Selection of component modes for flexible multibody simulation , 1991 .

[20]  R. Hintz.  Analytical Methods in Component Modal Synthesis , 1975 .

[21]  Albert L. Klosterman.  On the experimental determination and use of modal representations of dynamic characteristics , 1971 .

[22]  Roy R. Craig,et al.  A review of substructure coupling methods for dynamic analysis , 1976 .

[23]  Roy R. Craig,et al.  Block-Krylov component synthesis method for structural model reduction , 1988 .

[24]  B. Parlett,et al.  The use of a refined error bound when updating eigenvalues of tridiagonals , 1985 .