A Numerical Investigation of the Characteristics of Seismic Signals Induced by Rockfalls

This study proposes a numerical coupling approach to simulate seismic signals of rockfalls and conducts a parametric analysis to explore the characteristics of the seismic signals generated by rockfalls. To validate the approach, three field rockfall tests were selected for comparison. The rockfall velocity, duration, seismic frequency, Husid plot, Arias intensity, and spectrogram of the seismic signals were compared. We found that friction between rocks and the ground affects rock falling behavior. In addition, the local damping and Rayleigh damping assignments in the numerical model have strong effects on the simulation results. The volume of the falling rock and the falling speed of the rock affect the Arias intensity. The coupling approach proposed could be extended and can potentially be used as a useful tool in rockfall hazard estimations.

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.

Determining the Rayleigh damping parameters of flexible pavements for finite element modeling

The dynamic analysis has been successfully used to predict the pavement response based on the finite element modeling, during which the stiffness and mass matrices have been established well, whereas the method to determine the damping matrix based on Rayleigh damping is still under development. This article presents a novel method to determine the two parameters of the Rayleigh damping for dynamic modeling in pavement engineering. Based on the idealized shear beam model, a more reasonable method to calculate natural frequencies of different layers is proposed, by which the global damping matrix of the road pavement can be assembled. The least squares method is simplified and used to calculate the frequency-independent damping. The best-fit Rayleigh damping is obtained by only determining the natural frequencies of the two modal. Finite element model and in-situ field test subjected by the same falling weight deflectometer pulse loads are performed to validate the accuracy of this method. Good agreements are noted between simulation and field in-situ results demonstrating that this method can provide a more accurate approach for future finite element modeling and back-calculation.

Critical remarks on Rayleigh damping model considering the explicit scheme for the dynamic response analysis of high rise buildings

This paper numerically investigates the validity of Rayleigh damping model considering explicit operator to assess the dynamic response of high rise buildings under seismic loads. Considering transverse and longitudinal seismic waves, the bending moment, shear force, axial force, and and inter story drift are evaluated for a Core wall and a frame system of 46 story each. It is found that considering the explicit scheme, the dynamic responses are amplified significantly especially for axial forces. The reported amplification can be attributed to the ignorance of stiffness proportional Rayleigh damping coefficient which is associated with the stability issue of the implemented explicit operator. The paper indicates that Rayleigh damping model does not provide the required/expected damping for the higher modes of higher frequencies hence, it is not appropriate to be used along with the explicit operator especially for buildings of wide range of frequencies. It is worth pointing out that for classical dynamic analysis which follows the implicit scheme, Rayleigh damping seems to well consider the higher modes of high frequencies with higher damping ratio in comparison to the initial mode shapes. Consequently, the literature explicit scheme should be revised to accurately consider a proper damping for the higher modes which is crucial to assess the total response of structures of long periods and wide range of frequencies such as high rise buildings among others.

Optimal Method for Determination of Rayleigh Damping Co-efficients for Different Materials using Modal Analysis

Rayleigh damping co-efficients are the essential parameters to determine the damping matrix of a system in dynamic analysis. For the systems with multiple degrees of freedom, it is difficult to arrive for suitable Rayleigh damping co-efficients. This paper represents a simple and effective method for the determination of Rayleigh co-efficients α and β for the system with multiple degrees of freedom. An unrealistic constant damping ratio for all modes is assumed to get rational value of α and β, which leads the determination of progressively varying damping ratio for all modes. By comparing the damping ratio arrived from assumed α and β with assumed unrealistic damping ratio, the suitable and most precise values are determined. This method is implemented for different materials with different boundary conditions by considering different significant modes and the effect of above parameters on α and β values are also discussed.