Identification of non-proportional viscous damping matrix of beams by finite element model updating

Abstract

A methodology has been proposed to estimate non-proportional viscous damping matrix of beams from measured complex eigendata using finite element model updating technique. Representation of damping through a proportional damping matrix ignoring the complexity of eigenvectors may not be appropriate when external damping devices are employed. The current literature of determination of non-proportional damping matrix demands measurement of a large number of complex modes which is extremely difficult in practice. A gradient based finite element model updating algorithm implementing inverse eigensensitivity method has been presented through a series of numerically simulated cantilever beams. The method can accurately predict the non-proportional damping matrix even if the measured eigenvectors are polluted with random noise. The novelty of the current method is that it can sustain a high level of modal and coordinate sparsity in measurement. The method assumes prior determination or updating of the mass and stiffness matrices.

Identification of damping and complex modes in structural vibrations

“…It is notable from Figure 9 to 13 that the damping and stiffness matrices obtained from experimental data are not strictly symmetric, although the proposed expressions (16) and (17) for the stiffness and damping matrix, respectively, are based on the assumptions of a conservative system. There could be multiple reasons which cause the experimentally identified damping and stiffness matrices to become non-symmetric.…”

“…Thus, a full set of eigenvalues and eigenvectors are required to reproduce the exact damping matrix. Modal incompleteness is discussed in relation to modal damping identification methods in [15][16][17], while the influence of modal incompleteness on the specific expression in (16) has not yet been investigated. The derived expression (16) is now integrated in an output-only system identification technique, as summarized in Table 1.…”

“…The performance of the existing damping identification methods has been demonstrated by numerical simulations with simultaneous knowledge about structural excitation and response and with the presence of noisy data records and modal incompleteness [15][16][17]. However, the estimation of structural damping has also been investigated experimentally [18], with a given equation of motion and known excitation and response records.…”

“…The lumped mass m = m f + m c = 2.2 kg is the sum of the floor mass m f and the effective mass of the columns m c . The stiffness matrix in Figure 9 (b) is estimated by the expression in(17), which yields the stiffness matrix in(18) with great numerical accuracy.…”

Model Updating for Systems with General Proportional Damping Using Complex FRFs

“…Lin [31] proposed the improved model-updating method based on the function-weighted sensitivity method. Mondal and Chakraborty [32] identified nonproportional viscous damping matrix by matching the imaginary parts of complex mode shapes. In that method, the mass and stiffness have to be accurately obtained firstly.…”