Time-domain integration methods of exponentially damped linear systems

2018 ◽  
Vol 114 (4) ◽  
pp. 347-374 ◽  
Author(s):  
Meng-Fu Wang ◽  
Zhi-Hui Wang
Keyword(s):  
Linear Systems ◽  
Time Domain ◽  
Integration Methods ◽  
Domain Integration

Time-Domain Nonlinear SSI Analysis of Foundation Sliding Using Frequency-Dependent Foundation Impedance Derived From SASSI

2008 ◽  
Author(s):  
Mansour Tabatabaie ◽  
Thomas Ballard
Keyword(s):  
Frequency Domain ◽  
Linear Systems ◽  
Time Domain ◽  
Soil Structure ◽  
Wave Radiation ◽  
Far Field ◽  
Frequency Dependent ◽  
Nonlinear Springs ◽  
Mat Foundation ◽  
The Time Domain

Dynamic soil-structure interaction (SSI) analysis of nuclear power plants is often performed in frequency domain using programs such as SASSI [1]. This enables the analyst to properly a) address the effects of wave radiation in an unbounded soil media, b) incorporate strain-compatible soil shear modulus and damping properties and c) specify input motion in the free field using the de-convolution method and/or spatially variable ground motions. For structures that exhibit nonlinearities such as potential base sliding and/or uplift, the frequency-domain procedure is not applicable as it is limited to linear systems. For such problems, it is necessary to solve the problem in the time domain using the direct integration method in programs such as ADINA [2]. The authors recently introduced a sub-structuring technique called distributed parameter foundation impedance (DPFI) model that allows the structure to be partitioned from the total SSI system and analyzed in the time domain while the foundation soil is modeled using the frequency-domain procedure [3]. This procedure has been validated for linear systems. In this paper we have expanded the DPFI model to incorporate nonlinearities at the soil/structure interface by introducing nonlinear shear and normal springs arranged in series between the DPFI and structure model. This combination of the linear far-field impedance (DPFI) plus nonlinear near-field soil springs allows the foundation sliding and/or uplift behavior be analyzed in time domain while maintaining the frequency-dependent stiffness and radiation damping nature of the far-field foundation impedance. To check the accuracy of this procedure, a typical NPP foundation mat supported at the surface of a layered soil system and subjected to harmonic forced vibration was first analyzed in the frequency domain using SASSI to calculate the target linear response and derive a linear, far-field DPFI model. The target linear solution was then used to validate two linear time-domain ADINA models: Model 1 consisting of the mat foundation+DPFI derived from the linear SASSI model and Model 2 consisting of the total SSI system (mat foundation plus a soil block). After linear alignment, the nonlinear springs were added to both ADINA models and re-analyzed in time domain. Model 2 provided the target nonlinear solution while Model 1 provided the results using the DPFI+nonlinear springs. By increasing the amplitude of the vibration load, different levels of foundation sliding were simulated. Good agreement between the results of two models in terms of the displacement response of the mat and cyclic force-displacement behavior of the springs validates the accuracy of the procedure presented herein.

Generation of Synthetic Seismograms Using Linear Systems Theory

1971 ◽  
Vol 8 (11) ◽  
pp. 1409-1422 ◽  
Author(s):  
O. G. Jensen ◽  
R. M. Ellis
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Systems Theory ◽  
Linear Systems ◽  
Time Domain ◽  
Synthetic Seismograms ◽  
Elastic Wave Propagation ◽  
Arbitrary Angle ◽  
Teleseismic Events

The linear systems theory for elastic wave propagation in a multilayered crust has been extended to time domain solutions. Attenuation is specifically included. This direct time domain approach allows the computation of synthetic seismograms for P or SV waveforms incident at an arbitrary angle at the base of the crustal section. To demonstrate the utility of the technique, seismograms are computed for various conditions and comparisons made with teleseismic events recorded in central Alberta.

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