Abstract
In this paper, we propose a model updating method for systems with nonviscous proportional damping. In comparison to the traditional viscous damping model, the introduction of nonviscous damping will not only reduce the vibration of the system but also change the resonance frequencies. Therefore, most of the existing updating methods cannot be directly applied to systems with nonviscous damping. In many works, for simplicity, the Rayleigh damping model has been applied in the model updating procedure. However, the assumption of Rayleigh damping may result in large errors of damping for higher modes. To capture the variation of modal damping ratio with frequency in a more general way, the diagonal elements of the modal damping matrix and relaxation parameter are updated to characterize the damping energy dissipation of the structure by the proposed method. Spatial and modal incompleteness are both discussed for the updating procedure. Numerical simulations and experimental examples are adopted to validate the effectiveness of the proposed method. The results show that the systems with general proportional damping can be predicted more accurately by the proposed updating method.
Highlights
Damping is a significant factor which describes the energy dissipation from vibration
As the derivation of modal data may lead to extra errors, especially for the imaginary parts of the mode-shapes, to overcome the drawback, this paper will focus on the model updating based on complex frequency response functions (FRFs). e main contributions of this paper is to derive the sensitivity of the dynamic stiffness matrix with respect to the physical and damping parameters for systems with nonviscous proportional damping, which can been seen in Section 2.2 and 2.3
Without the assumption of Rayleigh or Cauchy damping models, the arbitrary variation of modal damping ratios with respect to frequency can be captured within the interested frequency range. e proposed method is validated by numerical and experimental examples. e results show that the dynamic response can be predicted accurately by the updated analytical model
Summary
Damping is a significant factor which describes the energy dissipation from vibration. As the derivation of modal data may lead to extra errors, especially for the imaginary parts of the mode-shapes, to overcome the drawback, this paper will focus on the model updating based on complex FRFs. e main contributions of this paper is to derive the sensitivity of the dynamic stiffness matrix with respect to the physical and damping parameters for systems with nonviscous proportional damping, which can been seen in Section 2.2 and 2.3. To characterize the damping energy dissipation of the structure, in addition to the material and geometry parameters, the diagonal elements of the modal damping matrix and the relaxation parameters are chosen as the updating parameters In this way, without the assumption of Rayleigh or Cauchy damping models, the arbitrary variation of modal damping ratios with respect to frequency can be captured within the interested frequency range. Without the assumption of Rayleigh or Cauchy damping models, the arbitrary variation of modal damping ratios with respect to frequency can be captured within the interested frequency range. e proposed method is validated by numerical and experimental examples. e results show that the dynamic response can be predicted accurately by the updated analytical model
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