Research on Damping Engagement Methodology in Dynamic Analysis of Isolated Structure

Damping has a significant influence on the calculation of structural seismic response. In this paper, we compare the commonly used viscous damping (Rayleigh damping (RD) and Caughey damping (CD)) in combination with the isolated structure test. To avoid the arbitrariness of choosing two reference vibration frequencies in constructing RD, all the combinations of the first several vibration frequencies were calculated. Because the material characteristics of the isolation layer and the superstructure are significantly different and the deformation of the isolation layer is large, we construct nonproportional damping according to these two kinds of damping and make a comparative analysis. Analyzing experimental data, we can obtain the optimal frequency combination of RD and nonproportional damping during dynamic analysis of the isolated structure, the priority order of choosing damping models. For the calculation of RD, the 1st modal frequency of the structure should be included, and the 2nd and 3rd modal frequencies of the nonisolated structure are proposed to calculate the nonproportional damping based on Rayleigh damping (NP-RD) for the three-story frame structure in this paper. RD and nonproportional damping based on Caughey damping (NP-CD) are firstly recommended to be used in the calculation of the isolated structure, followed by NP-RD and then CD.

Extended Modal Reduction for On-Board Rotor With Multifrequency Parametric Excitation

A new reduction method is proposed to investigate the behavior stability of rotor-bearing systems subject to a multifrequency rotational motion of their base. Combining the modal analysis and the construction of specific dynamic Ritz vectors, this method is able to deal with complex rotordynamics characteristics such as nonproportional damping, nonself-adjoint matrices, or time-varying parametric coefficients. This paper focuses first on assessing the accuracy and efficiency of the reduction method by computing time history and spectral responses of full and reduced models due to multifrequency base excitations. Its main potential is then highlighted in the parametric stability analysis through Floquet theory. The proposed numerical examples are composed with academic and industrial rotors, both modeled with one-dimensional Timoshenko beam finite element and supported by hydrodynamic journal bearings.

Model Reduction Methods for Rotor Dynamic Analysis: A Survey and Review

The focus of this literature survey and review is model reduction methods and their application to rotor dynamic systems. Rotor dynamic systems require careful consideration in their dynamic models as they include unsymmetric stiffness, localized nonproportional damping, and frequency-dependent gyroscopic effects. The literature reviewed originates from both controls and mechanical systems analysis and has been previously applied to rotor systems. This survey discusses the previous literature reviews on model reduction, reduction methods applied to rotor systems, the current state of these reduction methods in rotor dynamics, and the ability of the literature to reduce the complexities of large order rotor dynamic systems but allow accurate solutions.

Rayleigh Quotient and Dissipative Systems

Rayleigh quotients in the context of linear, nonconservative vibrating systems with viscous and nonviscous dissipative forces are studied in this paper. Of particular interest is the stationarity property of Rayleigh-like quotients for dissipative systems. Stationarity properties are examined based on the perturbation theory. It is shown that Rayleigh quotients with stationary properties exist for systems with proportional viscous and nonviscous damping forces. It is also shown that the stationarity property of Rayleigh quotients in the case of nonproportional damping (viscous and nonviscous) is conditional upon the diagonal dominance of the modal damping matrix.