Problem of Uniqueness of Non-Linear Joint Parameter Identification by Force-State Mapping Without Knowing the Joint Model

2005 ◽  
Author(s):  
J. H. Wang ◽  
H. Y. Huang
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Important Method ◽  
Joint Force ◽  
Non Linear ◽  
Uniqueness Of The Solution ◽  
Data Points ◽  
The Time Domain ◽  
Frequency Domain Approach ◽  
The Mathematical Model

The technique of Force-State Mapping is an important method to identify the parameters of non-linear joints. There are two approaches with the concept of Force-State Mapping, i.e., the time domain and frequency domain approaches. The advantages of the frequency domain approach compared to time domain approach are (1) the number of data points for identification can be drastically reduced; (2) it is possible to select arbitrarily the data in frequency domain for identification. In this work, an example is given to show that the above conclusion (i.e., the advantages of the frequency domain approach) is false. The result identified by the frequency domain approach is data and model dependent. One obtains different parameters when different data or model are used for identification. The reason for the non-uniqueness of the solution is that the joint force can’t be determined completely by a few discrete data in the frequency domain provided that the mathematical model of the joint is not exactly known in advance.

NON LINEAR ANALYSIS OF SHIP MOTIONS AND LOADS IN LARGE AMPLITUDE WAVES

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
G Mortola ◽  
A Incecik ◽  
O Turan ◽  
S.E. Hirdaris
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Large Amplitude ◽  
Linear Time ◽  
Ship Motions ◽  
Wave Loads ◽  
Time Step ◽  
Strip Theory ◽  
Non Linear ◽  
The Time Domain

A non linear time domain formulation for ship motions and wave loads is presented and applied to the S175 containership. The paper describes the mathematical formulations and assumptions, with particular attention to the calculation of the hydrodynamic force in the time domain. In this formulation all the forces involved are non linear and time dependent. Hydrodynamic forces are calculated in the frequency domain and related to the time domain solution for each time step. Restoring and exciting forces are evaluated directly in time domain in a way of the hull wetted surface. The results are compared with linear strip theory and linear three dimensional Green function frequency domain seakeeping methodologies with the intent of validation. The comparison shows a satisfactory agreement in the range of small amplitude motions. A first approach to large amplitude motion analysis displays the importance of incorporating the non linear behaviour of motions and loads in the solution of the seakeeping problem.

Comparison of Time and Frequency Domain Simulations of an Offshore Floating Wind Turbine

2011 ◽  
Author(s):  
Maxime Philippe ◽  
Aure´lien Babarit ◽  
Pierre Ferrant
Keyword(s):  
Wind Turbine ◽  
Frequency Domain ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Domain Model ◽  
Floating Platform ◽  
Floating Wind Turbine ◽  
Non Linear ◽  
Offshore Floating Wind Turbine ◽  
The Time Domain

Time domain simulations of an offshore floating wind turbine have been performed. Hydrodynamic impulse responses of the floating platform are calculated with linear hydrodynamic simulation tool ACHIL3D. A user defined module for the wind turbine design code FAST has been developed to calculate hydrodynamic and mooring loads on the structure. Resolution of the movements of the system is done with FAST. Simulation results in time domain are compared with frequency domain results. In the frequency domain model, the whole system is linearized. In the time domain model, the wind turbine model is not linearized. A good agreement between time and frequency domain calculations is observed, even for the pitch motion. Furthermore we observe a non linearity in the response of sway, roll and yaw degrees of freedom around 0.3 rad.s-1. The effect of viscous damping on the movements of the floating wind turbine system has been studied with the time domain model, and a non linear hydrostatic and Froude-Krylov load model has been developed. Effects of these non linear terms are shown.

Optimal Fractional-Order Damping

2003 ◽  
Author(s):  
Tom T. Hartley ◽  
Carl F. Lorenzo
Keyword(s):  
Response Time ◽  
Frequency Domain ◽  
Fractional Order ◽  
Time Domain ◽  
Magnitude Response ◽  
Squared Error ◽  
Single Term ◽  
Hankel Norm ◽  
The Time Domain ◽  
Frequency Domain Approach

In this note, we consider the single term optimal fractional-order damper for an otherwise undamped oscillator. First, we find the single term damper that minimizes the time domain integral of the squared step error (2-norm) and the integral of the time-weighted squared error (Hilbert-Schmidt-Hankel-norm). Next we consider a more intuitive frequency domain approach that insures the maximally flat magnitude response. Time- and frequency-domain plots are given for comparison with the integer-order solutions.

Application of Frequency Domain Methods for Response Based Analysis of Flexible Risers

2017 ◽  
Author(s):  
C. Armstrong ◽  
Y. Drobyshevski ◽  
C. Chin
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Composite Structures ◽  
Full Time ◽  
Threshold Limit ◽  
Frequency Domain Methods ◽  
Non Linear ◽  
Flexible Risers ◽  
The Time Domain ◽  
Extreme Responses

Response Based Analysis (RBA) is an advanced method for the prediction of long term distributions of critical responses in offshore floating systems. For complex non-linear systems such as flexible risers, RBA requires time domain simulations that form the core data to which probabilistic models are applied. Because RBA requires significantly larger amounts of data than traditional short term analysis approaches, running the required number of simulations in the time domain can quickly become unfeasible if the system’s physics being modelled are exceedingly complex. In addition, flexible risers are complex composite structures with highly dynamic, non-linear responses which further limit the feasibility of application of the RBA process to these systems. As an alternative, frequency domain solvers, such as that used in the OrcaFlex software, are potential substitutes for portions of datasets due to their processing times being significantly faster than time domain solvers. A comparison of extreme responses generated by frequency and time domain solvers was performed over the duration of two storms. An upper threshold limit for the frequency domain’s accuracy was found by comparing the differences of the two solver’s responses as the storm progressed; where the differences became too large the threshold limit was set. For environmental conditions smaller than this threshold, the frequency domain solver may provide a quicker method for predicting the riser responses. Conditions that exceed this threshold require full time domain analysis for accurate responses to be generated. Limitations of the frequency domain solvers include their reduced ability to deal with non-linear mechanics such as bending/curvature responses. As a result, curvature component results from the frequency domain are limited in their direct usability, especially when exposed to more extreme metocean conditions and locations along the riser that are subject to larger curvature (generally where risers are connected to structures with greater stiffness). Although these limitations exist, the frequency domain solver may still provide reasonable insight into metocean conditions that potentially cause extreme responses. A method is proposed for the use of both frequency and time domain simulations in the flexible riser flowline RBA process. Screening, filtering and ‘stitching’ methods utilizing the speed of the frequency domain solver are presented in order to compensate for the time domain’s extensive computation times. The proposed method of stitching, when applied to an example storm history, required 39% of the processing time when using only the time domain solver.

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.

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.

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