Error Caused by Damping Formulating in Multiple Support Excitation Problems

The effect of multiple support excitation is an important issue in studying large-span structures. Researchers have shown that the damping related terms in the equation of motion can induce errors in the analysis. Wrongly modelling the damping matrix can induce false damping forces between the structure and the reference coordinates. In multiple support excitation problems, this error is increased when absolute coordinates are used. In this paper, this part of the error is defined as virtual damping error. The error caused by using Rayleigh damping instead of Modal damping is called damping truncation error. This study focuses on the virtual damping error and the damping truncation error that exist in the modeling methods widely used in multiple support excitation problems, namely, large mass method (LMM), relative motion method (RMM), and absolute displacement method (ADM). A new Rayleigh damping formula is proposed for LMM to prevent virtual damping error. A form of equation of motion derived from the converged LMM was proposed in the authors’ previous work. This equation of motion is proved in this paper to be equivalent to RMM when modal damping and the new Rayleigh damping formula are used. RMM is proved free from the virtual damping error. The influence of multiple support excitation effect on the damping formulating errors is studied by spectral analysis. One simplified spring-mass model and two bridge models are used for numerical simulation. The results from the numerical simulation testify to the conclusions from the spectral analysis.

Seismic Analysis of Hybrid System Bridge of Multi-Span Continuous Girder and Arches

The Chengdong Hanjiang Bridge in Ankang City is a multi-span continuous beam-arch combination system bridge of (75+2×125+160+2×125+75) m, and its site is located in the earthquake zone. Calculation model based on Midas / Civil finite element software process analysis method is applied to seismic response analysis using power. At the same time, in order to influence the travelling wave effect and the seismic isolation system on the internal force of the bridge structure, corresponding finite element models were established and calculated with time history analysis. The finite element model under non-uniform excitation uses the “Large Mass Method” (LMM) for analysis and calculation under different wave velocity multi-point excitations. The results show that after considering the traveling wave effect, the displacement and bending moment of the control section of each hole increase, and the internal force of the fixed pier increases. When the wave velocity is 600m/s, the traveling wave effect strengthens the seismic response of the structure the most. With the increase of the wave velocity, the seismic response of the structure gradually approaches the seismic response under uniform excitation. After the friction pendulum seismic isolation support is used, it is fixed. The bending moment of Pier No.32 has been reduced by 80%, the stiffness of the whole bridge is more balanced, the forces of each pier are relatively close, and the isolation effect is good.

Research on the Traveling Wave Effect of a Rigid-Continuous Girder Bridge with High Piers Based on Multi-Support Excitation

This paper, aiming at rigid-continuous girder bridge with high piers, uses the large mass method (LMM) to analyze the seismic response of such special structure under a series of different phase differences by considering both rigid foundation and elastic foundation models. In addition, this paper discusses the influence rules for extreme response of different parts of structure due to traveling wave effect. The result shows that traveling wave effect greatly affects the rigid-continuous girder bridge with high piers. When considering the traveling wave effect, the internal force of bridge piers presents increasing trend, and the displacement of pier top reduces with increasing phase differences. The internal force and extreme displacement response of bridge structure present cyclical variations with phase differences, and that cycle is consistent with the characteristic period of bridge.

Analysis of Traveling Wave Effect on Half-Through CFST Arch Bridge by Large Mass Method

For long span arch bridges, the traveling wave effect is an important aspect on seismic response of structure which cannot ignore. The Big Mass Method was used to analyze the seismic response of a half-through CFST arch bridge under both uniform and non-uniform excitations. The results showed that the traveling wave effect caused by non-uniform excitation led to more obvious seismic response in both internal forces and displacements. The skewback section was most dangerous. The waveform of internal forces caused by non-uniform excitation was quite similar to that caused by uniform excitation, but the amplitude of the latter is bigger than the former. It can conclude that the traveling wave effect would cause the unsynchronized vibration to the structure elements which led to the lager responses.

Seismic Response Analysis of Long Span Cable-Stayed Bridge under Non-Uniform Excitation

In this paper, non-uniform dynamic analysis of a cable-stayed bridge is carried out using the large mass method. The Ed Yangtze River highway bridge, constructed in Hubei province, is chosen as a numerical example. In the non-uniform dynamic analysis, various wave velocities are used for the travelling ground motion. Displacements and internal forces solutions obtained for the spatially varying ground motions are compared with those of the uniform excitation. It is observed that the velocity of the ground motion greatly influences the response of the bridge and the variability of the ground motions should be included in the time-history analysis of cable-stayed bridges.

Empirical Mode Decomposition Application for Structural Seismic Responses

Large mass method is used to calculate structural seismic responses of long-span bridges. Due to the inherent characteristics of large mass method, the larger scale of long span bridge, different geological conditions, seismic input time delay of different foot stall, the displacement curve of seismic responses will be drifted and distorted from the normal. In this paper, Empirical Mode Decomposition（EMD) based on the large mass method is proposed to remove pseudo component and drift displacement. Then displacement response curve is reconstructed using the remaining components, the drift and distortion of structural seismic responses is successfully removed by this method.

Study of the Analysis Methods of Wave-Passage Effect Based on ABAQUS

Wave-passage effect of the seismic is the main reason of multi-support excitations, and there are always two analysis methods which are large mass method and acceleration method to study on the multi-support excitations, this paper take one kind of trussed structure as an example, use the two methods to consider the wave-passage effect of seismic, compare the difference between the results from using the two methods, and also compare the difference between single-support and multi-support excitations. This paper draw a conclusion that it is a precise way to using ABAQUS to analysis the wave-passage effect of the seismic; wave-passage effect of the seismic has an great influence on the reaction of long-span spatial structures, it must be considered in the similar projects; and the large method and acceleration method both have their advantages and disadvantages, so we should give concrete analysis to concrete problems.

Improved Large Mass Method for Structural Base Excitation Analysis

To verify the precision and possible applicability of the large mass method (LMM) widely used in multiple-supported structures subjected to non-uniform base excitations, numerical simulations of a two-degrees-of-freedom (2-DOF) finite element model using the Rayleigh damping assumption are performed respectively according to the LMM and the relative motion method (RMM). Through comparisons with the RMM, the error origins and the applicability of the LMM are discussed. Then the improved LMM is presented herein based on the modification of ground motions considering the influences of Rayleigh damping coefficient α. It indicates that the LMM is not applicable to multi-support excitation analysis in the case of Rayleigh damping, which can cause significant errors. And the errors depend on the damping coefficient α. It’s also proved that the improved LMM is able to yield results that are identical to those of the RMM.

Concepts and Application of the Large Mass Method in Vibration Analysis of SSME Engine Structures

The large mass method is used to obtain the total dynamic response of structures using excitations prescribed at base points. This paper presents the concepts and application of the method derived and used in the analysis of Space Shuttle Main Engine (SSME) structures. The theory and limitations that make the method work are discussed first. The effect on the system responses, including the addition of nonelastic (rigid body and large mass) modes due to the presence of the large masses, is then covered. The resonance concept leads to the establishment of criteria to define the analytic limit of the excitation frequency. The significance of the pseudostatic component and the relationship with the nonelastic modes are investigated in a simple system. The study shows that the frequency ratios, system properties, and the similarity between excitations are key factors to make the pseudostatic term more prominent. Examples with sinusoidal excitation are used to demonstrate the concepts. The method is finally applied in the SSME structures with excitations compiled from engine test data. Results are compared to further demonstrate the concepts and define the future needs for improved test data.