Rayleigh Damping Coefficients Research Articles

Determining damping characteristics of railway-overhead-wire system for finite-element analysis

ABSTRACTIn order to investigate the damping characteristics of railway-overhead-wire systems, we propose herein an approach based on the continuous wavelet transform (CWT) and two existing formulas concerning Rayleigh damping coefficients (RDCs). In the proposed process, the displacement histories of a real catenary are first obtained by using a set of noncontact photogrammetric devices, following which an exclusive catenary damping ratio related to the first dominant modal component in the catenary response is identified through a complex Morlet CWT. Thereafter, iterative finite-element analysis is conducted to find the optimal RDCs, which involves using two related formulas and the similarity between the catenary displacements obtained by simulation and experimentation. The results of our study demonstrate that this combined approach is constructive, especially for structures with closely spaced modes, such as catenaries. For the case studied herein, the catenary modal damping ratio at 1.19 Hz is approximately 1%, and the mass and stiffness proportional Rayleigh damping coefficients are approximately 0.02845 and 0.00274, respectively.

Performance evaluation of CWH base isolated building during two major earthquakes in Christchurch

The seismic performance and parameter identification of the base isolated Christchurch Women’s Hospital (CWH) building are investigated using the recorded seismic accelerations during the two large earthquakes in Christchurch. A four degrees of freedom shear model is applied to characterize the dynamic behaviour of the CWH building during these earthquakes. A modified Gauss-Newton method is employed to identify the equivalent stiffness and Rayleigh damping coefficients of the building. The identification method is first validated using a simulated example structure and finally applied to the CWH building using recorded measurements from the Mw 6.0 and Mw 5.8 Christchurch earthquakes on December 23, 2011. The estimated response and recorded response for both earthquakes are compared with the cross correlation coefficients and the mean absolute percentage errors reported. The results indicate that the dynamic behaviour of the superstructure and base isolator was essentially within elastic range and the proposed shear linear model is sufficient for the prediction of the structural response of the CWH Hospital during these events.

Dynamic responses of a continuous beam railway bridge under moving high speed train with random track irregularity

This paper addresses the dynamic response of a continuous beam bridge with different levels of track irregularities under a single, moving high-speed train. The train is modeled as one-foot sprung masses. The bridge is described as an Euler-Bernoulli beam supported by several hinged supports. Rayleigh damping coefficients of the bridge are calculated by using the modal damping ratio. Random track irregularities are generated by power spectrum density functions. The interaction equation of motion is derived and then solved by using the Newmark-beta method combined with the Newton-Raphson method. The dynamic impact factors of a single-span simply supported bridge and a five-span continuous beam bridge under the same train are calculated and compared for verification. Additionally, a three-span continuous beam bridge with various damping ratios and track irregularities under a Korea Train Express (KTX) train is used as an example to investigate the dynamic impact factors at the midpoints of different bridge spans in both downward and upward directions, the deck rotations at the bridge supports, and the average maximum acceleration of the train bodies under different conditions.

Identification of modal damping ratios of four‐flue chimney of a thermoelectrical plant using pseudo‐inverse matrix method

AbstractSome computational issues related to the identification of modal parameters of structures are presented in this paper. Optimal estimation of modal parameters often requires the solution of an overdetermined linear system of equations. Hence the computation of a pseudo‐inverse matrix is involved. In this paper the numerical performance of different algorithms for Moore–Penrose pseudo‐inverse computation have been tested for modal analysis of a four‐flue chimney of a thermoelectrical plant. The computational scheme herein adopted for parameter identification is based on well‐known modal properties and has a fast rate of convergence to solution. The computation of the Rayleigh damping coefficients a and b is an important step in the area of the modal superposition technique. The proposed approach can accurately predict damping ratios and all the eigenvectors without evaluating mass and stiffness matrices. Copyright © 2007 John Wiley & Sons, Ltd.

Direct finite-element analysis of the frequency responseof a Y-Z lithium niobate SAW filter

A direct finite-element model is developed for the full-scaleanalysis of the electromechanical phenomena involved in surface acoustic wave (SAW) devices. The equationsof wave propagation in piezoelectric materials are discretized using theGalerkin method, in which an implicit algorithm of the Newmark family withunconditional stability is implemented. The Rayleigh damping coefficients areincluded in the elements near the boundary to reduce the influence of thereflection of waves. The performance of the model is demonstrated by theanalysis of the frequency response of a Y-Z lithium niobate filter withtwo uniform ports, with emphasis on the influence of the number of electrodes.The frequency response of the filter is obtained through the Fourier transformof the impulse response, which is solved directly from the finite-elementsimulation. It shows that the finite-element results are in good agreementwith the characteristic frequency response of the filter predicted by thesimple phase-matching argument. The ability of the method to evaluate theinfluence of the bulk waves at the high-frequency end of the filter passbandand the influence of the number of electrodes on insertion loss is noteworthy.We conclude that the direct finite-element analysis of SAW devices can be usedas an effective tool for the design of high-performance SAW devices. Somepractical computational challenges of finite-element modeling of SAW devicesare discussed.

On the role of Rayleigh damping

The computation of the Rayleigh damping coefficients α and β is an important consideration in the area of the modal superposition technique. In this paper, an experimental investigation carried out on square and rectangular plates with various boundary conditions to determine the damping ratios for a few modes of vibration is reported. Based on the experimental findings, the Rayleigh damping coefficients can be computed for subsequent use in the modal superposition technique.