Direct identification and expansion of damping matrix for experimental–analytical hybrid modeling

Abstract The theory of direct experimental identification of damping matrix based on the dynamic stiffness matrix (DSM) method is further developed in this work. Based on the relationship between the DSMs of the smaller experimental model and larger analytical model, the mathematical relationship between the damping matrices of the two models is established. Examining the relationship, two methods are developed that can be used to expand the experimental damping matrix to the size of the analytical model. Validity of the expansion methods is demonstrated with numerical examples. The expanded damping matrix is intended to be combined with analytically formulated stiffness and mass matrices to build an experimental–analytical hybrid model. To find the frequency range, in which such a hybrid modeling is valid, a simple but effective method is developed.

[1]  Pietro Salvini,et al.  Direct updating of non conservative finite element models using measured input-output , 1992 .

[2]  Shirley J. Dyke,et al.  System equivalent reduction expansion process , 2008 .

[3]  Paul Sas,et al.  Application of a FRF Based Model Updating Technique for the Validation of Finite Element Models of Components of the Automotive Industry , 1995 .

[4]  Paul Sas,et al.  UPDATING OF DYNAMIC FINITE ELEMENT MODELS BASED ON EXPERIMENTAL RECEPTANCES AND THE REDUCED ANALYTICAL DYNAMIC STIFFNESS MATRIX , 1995 .

[5]  Sondipon Adhikari,et al.  Towards identification of a general model of damping , 2000 .

[6]  Mark Richardson,et al.  Mass, Stiffness, and Damping Matrix Estimates from Structural Measurements , 1987 .

[7]  Edward J. Berger,et al.  Friction modeling for dynamic system simulation , 2002 .

[8]  M. Dalenbring,et al.  DAMPING FUNCTION ESTIMATION BASED ON MEASURED VIBRATION FREQUENCY RESPONSES AND FINITE-ELEMENT DISPLACEMENT MODES , 1999 .

[9]  Z. Qu,et al.  Iterative methods for dynamic condensation of structural matrices , 2000 .

[10]  A. Berman,et al.  System identification of structural dynamic models Theoretical and practical bounds , 1984 .

[11]  D. Henwood,et al.  Approximating the hysteretic damping matrix by a viscous matrix for modelling in the time domain , 2002 .

[12]  Jay Kim,et al.  Identification of Damping Matrices from Measured Frequency Response Functions , 2001 .

[13]  Daniel J. Inman,et al.  Damping matrix identification and experimental verification , 1999, Smart Structures.

[14]  A. Berman.  Validity of Improved Mathematical Models, A. Commentary , 1998 .

[15]  Reduced model concepts , 2000 .

[16]  Ming-Shaung Ju,et al.  Estimation of Mass, Stiffness and Damping Matrices from Frequency Response Functions , 1996 .

[17]  Joon-Hyun Lee,et al.  DEVELOPMENT AND VALIDATION OF A NEW EXPERIMENTAL METHOD TO IDENTIFY DAMPING MATRICES OF A DYNAMIC SYSTEM , 2001 .

[18]  R. Christensen.  Theory of viscoelasticity : an introduction , 1971 .

[19]  Rune Brincker,et al.  Identification of Light Damping in Structures , 1990 .

[20]  David I. G. Jones.  Handbook of Viscoelastic Vibration Damping , 2001 .

[21]  Jeffery Edward Hylok,et al.  EXPERIMENTAL IDENTIFICATION OF DISTRIBUTED DAMPING MATRICES USING THE DYNAMIC STIFFNESS MATRIX , 2002 .

[22]  Gokhan O. Ozgen,et al.  Further Developments in the Dynamic Stiffness Matrix (DSM) Based Direct Damping Identification Method , 2005 .

[23]  Gokhan O. Ozgen,et al.  Applications of the Dynamic Stiffness Matrix (DSM) Based Direct Damping Identification Method , 2005 .

[24]  Alex Berman.  Inherently Incomplete Finite Element Model and Its Effects on Model Updating , 2000 .

[25]  John E. Mottershead,et al.  Finite Element Model Updating in Structural Dynamics , 1995 .

[26]  John L. Junkins,et al.  Identification method for lightly damped structures , 1988 .

[27]  Daniel J. Inman,et al.  An Iterative Approach to Viscous Damping Matrix Identification , 1997 .