scholarly journals Error Caused by Damping Formulating in Multiple Support Excitation Problems

2020 ◽  
Vol 10 (22) ◽  
pp. 8180
Author(s):  
Han Qin ◽  
Luyu Li
Keyword(s):  
Numerical Simulation ◽  
Spectral Analysis ◽  
Truncation Error ◽  
Equation Of Motion ◽  
Rayleigh Damping ◽  
Modal Damping ◽  
Multiple Support ◽  
Support Excitation ◽  
Large Mass Method ◽  
Bridge Models

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.

Improved Large Mass Method for Structural Base Excitation Analysis

2010 ◽  
Vol 29-32 ◽  
pp. 1588-1593 ◽  
Author(s):  
Guo Liang Zhou ◽  
Xiao Jun Li
Keyword(s):  
Degrees Of Freedom ◽  
Ground Motions ◽  
Element Model ◽  
Large Mass ◽  
Damping Coefficient ◽  
Base Excitation ◽  
Rayleigh Damping ◽  
Support Excitation ◽  
Large Mass Method ◽  
Structural Base

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.

scholarly journals Approach for Selection of Rayleigh Damping Parameters Used for Time History Analysis

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
R. E. Spears ◽  
S. R. Jensen
Keyword(s):  
Seismic Analysis ◽  
Time History ◽  
System Response ◽  
Piping System ◽  
Nuclear Facilities ◽  
Rayleigh Damping ◽  
Modal Damping ◽  
American Society ◽  
Selection Of ◽  
Civil Engineers

Nonlinearities, whether geometric or material, need to be addressed in seismic analysis. One good analysis method that can address these nonlinearities is direct time integration with Rayleigh damping. Modal damping is the damping typically specified in seismic analysis Codes and Standards (ASCE 4-98, 1998, “Seismic Analysis of Safety-Related Nuclear Structures and Commentary,” American Society of Civil Engineers, Reston, Virginia and ASCE/SEI 43-05, 2005, “Seismic Design Criteria for Structures, Systems, and Components in Nuclear Facilities,” American Society of Civil Engineers, Reston, Virginia.). Modal damping is constant for all frequencies where Rayleigh damping varies with frequency. An approach is proposed here for selection of Rayleigh damping coefficients to be used in seismic analyses that is consistent with given modal damping. The approach uses the difference between the modal damping response and the Rayleigh damping response along with effective mass properties of the model being evaluated to match overall system response levels. This paper provides a simple example problem to demonstrate the approach. It also provides results for a finite element model representing an existing piping system. Displacement, acceleration, and stress results are compared from model runs using modal damping and model runs using Rayleigh damping with coefficients selected using the proposed method.

A Semi-Discrete Approach for the Numerical Simulation of Freestanding Blocks

2016 ◽  
pp. 416-439
Author(s):  
Fernando Peña
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Numerical Modeling ◽  
Discrete Model ◽  
Mathematical Formulation ◽  
Equation Of Motion ◽  
Rigid Bodies ◽  
The Body ◽  
Discrete Approach ◽  
Rocking Motion

This chapter addresses the numerical modeling of freestanding rigid blocks by means of a semi-discrete approach. The pure rocking motion of single rigid bodies can be easily studied with the differential equation of motion, which can be solved by numerical integration or by linearization. However, when we deal with sliding and jumping motion of rigid bodies, the mathematical formulation becomes quite complex. In order to overcome this complexity, a Semi-Discrete Model (SMD) is proposed for the study of rocking motion of rigid bodies, in which the rigid body is considered as a mass element supported by springs and dashpots, in the spirit of deformable contacts between rigid blocks. The SMD can detect separation and sliding of the body; however, initial base contacts do not change, keeping a relative continuity between the body and its base. Extensive numerical simulations have been carried out in order to validate the proposed approach.

scholarly journals Influence of Multiple-Support Excitation on Seismic Response of Reinforced Concrete Arch Bridges

2019 ◽  
Vol 10 (1) ◽  
pp. 17 ◽  
Author(s):  
Marta Savor Novak ◽  
Damir Lazarevic ◽  
Josip Atalic ◽  
Mario Uros
Keyword(s):  
Reinforced Concrete ◽  
Spatial Variation ◽  
Seismic Response ◽  
Ground Motion ◽  
Seismic Analysis ◽  
Numerical Study ◽  
Relative Significance ◽  
Multiple Support ◽  
Arch Bridges ◽  
Support Excitation

Although post-earthquake observations identified spatial variation of ground motion (i.e., multiple-support excitation) as a frequent cause of the unfavorable response of long-span bridges, this phenomenon is often not taken into account in seismic design to simplify the calculation procedure. This study investigates the influence of multiple-support excitation accounting for coherency loss and wave-passage effects on the seismic response of reinforced concrete deck arch bridges of long spans founded on rock sites. Parametric numerical study was conducted using the time-history method, the response spectrum method, and a simplified procedure according to the European seismic standards. Results showed that multiple-support excitation had a detrimental influence on response of almost all analyzed bridges regardless of considered arch span. Both considered spatial variation effects, acting separately or simultaneously, proved to be very important, with their relative significance depending on the response values and arch locations analyzed and seismic records used. Therefore, it is suggested that all spatially variable ground-motion effects are taken into account in seismic analysis of similar bridges.

Shaking table test and numerical simulation of an isolated cylindrical latticed shell under multiple-support excitations

2019 ◽  
Vol 18 (3) ◽  
pp. 611-630 ◽  
Author(s):  
Xue Suduo ◽  
Shan Mingyue ◽  
Li Xiongyan ◽  
Liang Shuanzhu ◽  
Huang Fuyun ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Shaking Table Test ◽  
Shaking Table ◽  
Multiple Support

Modal Damping Estimation: An Alternative for Hilbert Spectral Analysis

2019 ◽  
Author(s):  
Mohammadreza Hatami ◽  
Mohammadreza Maddipour Farrokhifard ◽  
Vaithianathan Mani Venkatasubramanian
Keyword(s):  
Spectral Analysis ◽  
Modal Damping ◽  
Damping Estimation

Effects of Bounce on Particle Transport, Deposition and Removal in Turbulent Channel Flow

2002 ◽  
Author(s):  
Ali Reza Mazaheri ◽  
Goodarz Ahmadi ◽  
Haifeng Zhang
Keyword(s):  
Numerical Simulation ◽  
Channel Flow ◽  
Particle Transport ◽  
Fluid Velocity ◽  
Turbulent Channel Flow ◽  
Equation Of Motion ◽  
Particle Bounce ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral ◽  
Fluid Velocity Field

Effects of bounce on particle transport, deposition and removal in turbulent channel flow are studied. The pseudo-spectral method is used to generate the instantaneous turbulent fluid velocity field by Direct Numerical Simulation (DNS) procedure. The particle equation of motion includes all the relevant hydrodynamic forces. In addition, simulation accounts for particle adhesion, resuspension and rebound processes. For particle bounce from the surface, the critical velocity is evaluated and is used in the analysis. Effects of bounce during particle-wall collisions on the deposition rate are also studied.

Comparison of seismic responses of a reticulated dome under stochastic uniform and spatially correlated and coherent multiple-support excitation for a scenario seismic event

2020 ◽  
Vol 35 (4) ◽  
pp. 113-125
Author(s):  
YG Li ◽  
TJ Liu ◽  
F Fan ◽  
HP Hong
Keyword(s):  
Spatial Correlation ◽  
Seismic Event ◽  
Amplitude Spectrum ◽  
Spatial Coherence ◽  
Single Layer ◽  
Seismic Load ◽  
Seismic Responses ◽  
Spatially Correlated ◽  
Multiple Support ◽  
Support Excitation

Structures with multiple supports can be sensitive to spatial coherence and spatial correlation. Since the historical recordings are insufficient for selecting records that match predefined inter-support distances of a structure, desired seismic magnitude (or intensity) and site to seismic source distance for structural analysis, such records need to be simulated. In this study, we use a procedure that is extended based on the stochastic point-source method to simulate records for scenario events. The application of the simulated records to a single-layer reticulated dome with multiple supports is presented. The application is aimed at investigating the differences between the responses subjected to spatially uniform excitation and to spatially correlated and coherent multiple-support excitation for a scenario seismic event, assessing the relative importance of the spatial coherence and spatial correlation on the responses, and evaluating the effect of the uncertainty in the spatially correlated and coherent records for a scenario event on the statistics of the seismic responses. The analysis results indicate that the spatial correlation of the Fourier amplitude spectrum has a predominant influence on the linear/nonlinear responses, and the consideration of spatially correlated and coherent excitation at multiple supports is very important. The consideration of uniform excitation severely underestimates the seismic load effects as compared to those obtained under spatially correlated and coherent multiple-support excitation.

Spectral analysis of turbulent effects on resistivity and the tearing instability

1988 ◽  
Vol 40 (3) ◽  
pp. 517-533 ◽  
Author(s):  
D. Deeds ◽  
G. van Hoven
Keyword(s):  
Numerical Simulation ◽  
Spectral Analysis ◽  
Energy Balance ◽  
Anomalous Resistivity ◽  
Tearing Mode ◽  
Simulation Code ◽  
System A ◽  
Tearing Instability ◽  
True Resistivity ◽  
Magnetic Tearing

Biskamp and Welter (1983) have defined an anomalous resistivity due to shortwavelength turbulence. They reported that this resistivity can be of either sign, and that negative anomalous resistivity in particular can affect the growth of the tearing instability. We use a spectral numerical-simulation code and ancillary diagnostics to analyse the behaviour of resistive magnetic tearing in the presence of turbulence of the sort postulated by Biskamp and Welter. We find that, in general, the ‘anomalous resistivity’ tends to return quickly towards zero even when artificially supported away from zero, and that its effect on tearing-mode behaviour is not consistent with its interpretation as a resistivity. We investigate analytically the behaviour reported by Biskamp and Welter, and the behaviour we observe. We also argue that, while not meaningful as a true resistivity, the ‘anomalous-resistivity’ parameter is a useful diagnostic showing the energy balance of the System – a property we refer to as Alfvénicity – illustrating, for example, the onset of nonlinearity in the tearing process.

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