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.

A Numerical Method for Representing Retardation Functions With Complex Exponentials

2017 ◽  
Author(s):  
Fushun Liu ◽  
Lei Jin ◽  
Jiefeng Chen ◽  
Wei Li
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Added Mass ◽  
Memory Effects ◽  
Floating Structure ◽  
Frequency Dependent ◽  
Laplace Domain ◽  
The Time Domain ◽  
Frequency Domain Techniques

Numerical time- or frequency-domain techniques can be used to analyze motion responses of a floating structure in waves. Time-domain simulations of a linear transient or nonlinear system usually involve a convolution terms and are computationally demanding, and frequency-domain models are usually limited to steady-state responses. Recent research efforts have focused on improving model efficiency by approximating and replacing the convolution term in the time domain simulation. Contrary to existed techniques, this paper will utilize and extend a more novel method to the frequency response estimation of floating structures. This approach represents the convolution terms, which are associated with fluid memory effects, with a series of poles and corresponding residues in Laplace domain, based on the estimated frequency-dependent added mass and damping of the structure. The advantage of this approach is that the frequency-dependent motion equations in the time domain can then be transformed into Laplace domain without requiring Laplace-domain expressions of the added mass and damping. Two examples are employed to investigate the approach: The first is an analytical added mass and damping, which satisfies all the properties of convolution terms in time and frequency domains simultaneously. This demonstrates the accuracy of the new form of the retardation functions; secondly, a numerical six degrees of freedom model is employed to study its application to estimate the response of a floating structure. The key conclusions are: (1) the proposed pole-residue form can be used to consider the fluid memory effects; and (2) responses are in good agreement with traditional frequency-domain techniques.

ABCD Matrix: A Unique Tool for Linear Two-Wire Transmission Line Modelling

2003 ◽  
Vol 40 (3) ◽  
pp. 220-229 ◽  
Author(s):  
Pedro L. D. Peres ◽  
Carlos R. de Souza ◽  
Ivanil S. Bonatti
Keyword(s):  
Differential Equations ◽  
Transmission Line ◽  
Frequency Domain ◽  
Transmission Lines ◽  
Time Domain ◽  
Mathematical Concepts ◽  
Frequency Dependent ◽  
Abcd Matrix ◽  
The Time Domain

The aim of this note is to show that all the behaviour of a two-wire transmission line can be directly derived from the application of ABCD matrix mathematical concepts, avoiding the explicit use of differential equations. An important advantage of this approach is that the transmission line modelling arises naturally in the frequency domain. Therefore the consideration of frequency-dependent parameters can be carried out in a simple way compared with the time-domain. Some standard examples of transmission lines are analysed through the use of ABCD matrices and a case study of a balun network is presented.

DYNAMIC INFINITE ELEMENTS FOR SOIL-STRUCTURE INTERACTION ANALYSIS IN A LAYERED SOIL MEDIUM

2007 ◽  
Vol 07 (04) ◽  
pp. 693-713 ◽  
Author(s):  
C. B. YUN ◽  
S. H. CHANG ◽  
C. G. SEO ◽  
J. M. KIM
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Soil Structure ◽  
Interaction Analysis ◽  
Soil Structure Interaction ◽  
Shape Functions ◽  
Frequency Dependent ◽  
Structure Interaction ◽  
Infinite Elements ◽  
Stiffness Matrices

This paper presents the dynamic infinite element formulations that have been developed for soil-structure interaction analysis both in frequency domain and time domain by the present authors and our colleagues during the past 20 years. Axisymmetric, 2D and 3D layered half-space soil media were considered in the developments. The displacement shape functions of the infinite elements were established using approximate expressions of analytical solutions in frequency domain to represent the characteristics of multiple waves propagating into the unbounded outer domain of the media. The shape functions were determined in terms of the excitation frequency as well as the spatial and material characteristics of the far-field soil region. Thereby the element mass and stiffness matrices are frequency dependent. As for time domain analysis, the shape functions were further simplified to obtain closed-form frequency-dependent mass and stiffness matrices, which can analytically be transformed into time domain terms by the Fourier transform. The proposed infinite elements were verified using benchmark examples, which showed that the present formulations are very effective for the soil-structure interaction analysis either in frequency or in time domain. Example applications to actual soil-structure interaction problems are also given to demonstrate the capability and versatility of the present methodology.

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

scholarly journals Time and Frequency Domain Dynamic Analysis of Offshore Mooring

2021 ◽  
Vol 9 (7) ◽  
pp. 781
Author(s):  
Shi He ◽  
Aijun Wang
Keyword(s):  
Dynamic Analysis ◽  
Frequency Domain ◽  
Time Domain ◽  
Linearization Method ◽  
Euler Method ◽  
Single Component ◽  
Hydrodynamic Drag ◽  
Lumped Mass ◽  
Mooring Lines ◽  
The Time Domain

The numerical procedures for dynamic analysis of mooring lines in the time domain and frequency domain were developed in this work. The lumped mass method was used to model the mooring lines. In the time domain dynamic analysis, the modified Euler method was used to solve the motion equation of mooring lines. The dynamic analyses of mooring lines under horizontal, vertical, and combined harmonic excitations were carried out. The cases of single-component and multicomponent mooring lines under these excitations were studied, respectively. The case considering the seabed contact was also included. The program was validated by comparing with the results from commercial software, Orcaflex. For the frequency domain dynamic analysis, an improved frame invariant stochastic linearization method was applied to the nonlinear hydrodynamic drag term. The cases of single-component and multicomponent mooring lines were studied. The comparison of results shows that frequency domain results agree well with nonlinear time domain results.

A Multiple Harmonic Open-Loop Controller for Hydro/Aerodynamic Force Measurements in Rotating Machinery Using Magnetic Bearings

2002 ◽  
Vol 124 (4) ◽  
pp. 827-834 ◽  
Author(s):  
D. O. Baun ◽  
E. H. Maslen ◽  
C. R. Knospe ◽  
R. D. Flack
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Open Loop ◽  
Rotating Machinery ◽  
Operating Conditions ◽  
Rotor Vibration ◽  
Aerodynamic Forces ◽  
Analog Input ◽  
Input And Output ◽  
The Time Domain

Inherent in the construction of many experimental apparatus designed to measure the hydro/aerodynamic forces of rotating machinery are features that contribute undesirable parasitic forces to the measured or test forces. Typically, these parasitic forces are due to seals, drive couplings, and hydraulic and/or inertial unbalance. To obtain accurate and sensitive measurement of the hydro/aerodynamic forces in these situations, it is necessary to subtract the parasitic forces from the test forces. In general, both the test forces and the parasitic forces will be dependent on the system operating conditions including the specific motion of the rotor. Therefore, to properly remove the parasitic forces the vibration orbits and operating conditions must be the same in tests for determining the hydro/aerodynamic forces and tests for determining the parasitic forces. This, in turn, necessitates a means by which the test rotor’s motion can be accurately controlled to an arbitrarily defined trajectory. Here in, an interrupt-driven multiple harmonic open-loop controller was developed and implemented on a laboratory centrifugal pump rotor supported in magnetic bearings (active load cells) for this purpose. This allowed the simultaneous control of subharmonic, synchronous, and superharmonic rotor vibration frequencies with each frequency independently forced to some user defined orbital path. The open-loop controller was implemented on a standard PC using commercially available analog input and output cards. All analog input and output functions, transformation of the position signals from the time domain to the frequency domain, and transformation of the open-loop control signals from the frequency domain to the time domain were performed in an interrupt service routine. Rotor vibration was attenuated to the noise floor, vibration amplitude ≈0.2 μm, or forced to a user specified orbital trajectory. Between the whirl frequencies of 14 and 2 times running speed, the orbit semi-major and semi-minor axis magnitudes were controlled to within 0.5% of the requested axis magnitudes. The ellipse angles and amplitude phase angles of the imposed orbits were within 0.3 deg and 1.0 deg, respectively, of their requested counterparts.

Sign in / Sign up

Export Citation Format

Share Document