Lancaster’s Method of Damping Identification Revisited

Identification of damping is an active area of research in structural dynamics. In one of the earliest works, Lancaster [1] proposed a method to identify the viscous damping matrix from measured natural frequencies and mode shapes. His method requires the modes to be normalized in a particular way, which in turn a priori needs the very same viscous damping matrix. A method, based on the poles and residues of the measured transfer functions, has been proposed to overcome this basic difficulty associated with Lancaster's method. This approach is then extended to a class of nonviscously damped systems where the damping forces depend on the past history of the velocities via convolution integrals over some kernel functions. Suitable numerical examples are given to illustrate the modified Lancaster's method developed here.

[1]  K. Foss.  COORDINATES WHICH UNCOUPLE THE EQUATIONS OF MOTION OF DAMPED LINEAR DYNAMIC SYSTEMS , 1956 .

[2]  P. Hughes,et al.  Modeling of linear viscoelastic space structures , 1993 .

[3]  Peter Lancaster.  Expressions for Damping Matrices in Linear Vibration Problems , 1961 .

[4]  A. Sestieri,et al.  Analysis Of Errors And Approximations In The Use Of Modal Co-Ordinates , 1994 .

[5]  D. J. Ewins,et al.  Modal Testing: Theory and Practice , 1984 .

[6]  T. K. Hasselman,et al.  Method for Constructing a Full Modal Damping Matrix from Experimental Measurements , 1972 .

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

[8]  Claus-Peter Fritzen,et al.  Identification of mass, damping, and stiffness matrices of mechanical systems , 1986 .

[9]  L. Peterson,et al.  Extraction of Normal Modes and Full Modal Damping from Complex Modal Parameters , 1997 .

[10]  Sondipon Adhikari,et al.  Dynamics of Nonviscously Damped Linear Systems , 2002 .

[11]  Etienne Balmes,et al.  New Results on the Identification of Normal Modes from Experimental Complex Modes , 1994 .

[12]  S. R. Ibrahim.  Dynamic Modeling of Structures from Measured Complex Modes , 1982 .

[13]  S. Adhikari,et al.  Identification of damping: Part 1, viscous damping , 2001 .

[14]  F. R. Vigneron.  A Natural Modes Model and Modal Identities for Damped Linear Structures , 1986 .

[15]  Sondipon Adhikari,et al.  Eigenrelations for Nonviscously Damped Systems , 2001 .

[16]  M. Biot.  Linear thermodynamics and the mechanics of solids , 1958 .

[17]  D. J. Mook,et al.  Mass, Stiffness, and Damping Matrix Identification: An Integrated Approach , 1992 .

[18]  David Newland.  On the modal analysis of non-conservative linear systems , 1987 .

[19]  D. Golla.  Dynamics of viscoelastic structures: a time-domain finite element formulation , 1985 .

[20]  Daniel J. Inman,et al.  A symmetric inverse vibration problem for nonproportional underdamped systems , 1997 .

[21]  D. Inman,et al.  Identification of a Nonproportional Damping Matrix from Incomplete Modal Information , 1991 .

[22]  J. Fabunmi,et al.  Damping Matrix Identification Using the Spectral Basis Technique , 1988 .

[23]  P. Caravani,et al.  Identification of Damping Coefficients in Multidimensional Linear Systems , 1974 .

[24]  I. Fawzy.  Orthogonality of generally normalized eigenvectors and eigenrows , 1977 .

[25]  John E. Mottershead,et al.  Theory for the estimation of structural vibration parameters from incomplete data , 1990 .

[26]  Jean-Guy Béliveau,et al.  Identification of Viscous Damping in Structures From Modal Information , 1976 .