scholarly journals Stress Waves in Composite Laminates Excited by Transverse Plane Shock Waves

1996 ◽  
Vol 3 (6) ◽  
pp. 419-433 ◽  
Author(s):  
G.R. Liu ◽  
K.Y. Lam ◽  
E.S. Chan
Keyword(s):  
Fourier Transform ◽  
Composite Laminates ◽  
Underwater Explosion ◽  
Stress Waves ◽  
Plane Shock ◽  
Wave Fields ◽  
Underwater Explosions ◽  
Reinforced Plastic ◽  
The Fourier Transform ◽  
The Time Domain

A simple 1-dimensional model is presented to investigate elastic stress waves in composite laminates excited by underwater explosion shocks. The focus is on the elastic dynamic stress fields in the composite laminate immediately after the action of the shock wave. In this model, the interaction between the laminate and the water is taken into account, and the effects of the laminate-water interaction on the stress wave fields in the laminate are investigated. In the formulation of the model, wave fields in the laminate and the water are the first obtained in the frequency domain and then transferred into the time domain using the Fourier transform techniques. A quadrature technique is used to deal with the Fourier transform integrals in which the integrands have very sharp peaks on the integral axis. Numerical examples for stress waves in a steel plate and a glass reinforced plastic sandwich laminate are presented. The technique and the results presented in this article may be used in the design of ship hull structures subjected to underwater explosions.

A Deep Neural Network Model for Learning Runtime Frequency Response Function Using Sensor Measurements

2021 ◽  
Author(s):  
Yongzhi Qu ◽  
Gregory W. Vogl ◽  
Zechao Wang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fourier Transform ◽  
Time Domain ◽  
Frequency Response Function ◽  
Frequency Component ◽  
Operating Conditions ◽  
Input Output ◽  
The Fourier Transform ◽  
The Time Domain

Abstract The frequency response function (FRF), defined as the ratio between the Fourier transform of the time-domain output and the Fourier transform of the time-domain input, is a common tool to analyze the relationships between inputs and outputs of a mechanical system. Learning the FRF for mechanical systems can facilitate system identification, condition-based health monitoring, and improve performance metrics, by providing an input-output model that describes the system dynamics. Existing FRF identification assumes there is a one-to-one mapping between each input frequency component and output frequency component. However, during dynamic operations, the FRF can present complex dependencies with frequency cross-correlations due to modulation effects, nonlinearities, and mechanical noise. Furthermore, existing FRFs assume linearity between input-output spectrums with varying mechanical loads, while in practice FRFs can depend on the operating conditions and show high nonlinearities. Outputs of existing neural networks are typically low-dimensional labels rather than real-time high-dimensional measurements. This paper proposes a vector regression method based on deep neural networks for the learning of runtime FRFs from measurement data under different operating conditions. More specifically, a neural network based on an encoder-decoder with a symmetric compression structure is proposed. The deep encoder-decoder network features simultaneous learning of the regression relationship between input and output embeddings, as well as a discriminative model for output spectrum classification under different operating conditions. The learning model is validated using experimental data from a high-pressure hydraulic test rig. The results show that the proposed model can learn the FRF between sensor measurements under different operating conditions with high accuracy and denoising capability. The learned FRF model provides an estimation for sensor measurements when a physical sensor is not feasible and can be used for operating condition recognition.

Discrete Time, Discrete Frequency

2021 ◽  
pp. 106-155
Author(s):  
Victor Lazzarini
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Discrete Time ◽  
Time Domain ◽  
Continuous Time ◽  
Time Varying ◽  
Discrete Frequency ◽  
The Fourier Transform ◽  
Definition Of ◽  
The Time Domain

This chapter is dedicated to exploring a form of the Fourier transform that can be applied to digital waveforms, the discrete Fourier transform (DFT). The theory is introduced and discussed as a modification to the continuous-time transform, alongside the concept of windowing in the time domain. The fast Fourier transform is explored as an efficient algorithm for the computation of the DFT. The operation of discrete-time convolution is presented as a straight application of the DFT in musical signal processing. The chapter closes with a detailed look at time-varying convolution, which extends the principles developed earlier. The conclusion expands the definition of spectrum once more.

Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. T117-T123 ◽  
Author(s):  
Chunlei Chu ◽  
Paul L. Stoffa
Keyword(s):  
Fourier Transform ◽  
Frequency Response ◽  
Time Domain ◽  
Wave Equations ◽  
Time Integration ◽  
Expansion Method ◽  
Rapid Expansion ◽  
The Fourier Transform ◽  
The Time Domain ◽  
Response Modeling

Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency.

Prediction of Ground Vibration from High Speed Trains Using a Vehicle–Track–Ground Coupling Model

2016 ◽  
Vol 16 (08) ◽  
pp. 1550051 ◽  
Author(s):  
H. L. Yao ◽  
Z. Hu ◽  
Z. Lu ◽  
Y. X. Zhan ◽  
J. Liu
Keyword(s):  
Fourier Transform ◽  
High Speed ◽  
Dynamic Stiffness ◽  
Ground Vibration ◽  
Coupling Model ◽  
Vehicle Speed ◽  
High Speed Trains ◽  
Rail Irregularity ◽  
The Fourier Transform ◽  
The Time Domain

The dynamically induced ground vibration from high speed trains (HSTs) is investigated using a semi-analytical vehicle–track–ground coupling model. A multi-body vehicle is adopted along with rail irregularity considered in the model. The soil is simulated as a saturated poroelastic half-space with two elastic layers. The coupling system is solved in the transformed domain by applying the Fourier transform, and the dynamic stiffness matrix method is used to deal with the layered soil. The time-domain solutions are obtained by the inverse fast Fourier transform (FFT). The effects of the vehicle speed, observation location, rail irregularity, subgrade-bed stiffness, and vehicle type on the ground vibration are investigated thoroughly. The results show that all these factors can significantly affect the dynamically induced ground vibration.

Temporal windowing and inverse transform of the wavefield in the Laplace-Fourier domain

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. R207-R222 ◽  
Author(s):  
Sangmin Kwak ◽  
Hyunggu Jun ◽  
Wansoo Ha ◽  
Changsoo Shin
Keyword(s):  
Fourier Transform ◽  
Time Window ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Fourier Domain ◽  
Gain Function ◽  
The Fourier Transform ◽  
The Time Domain ◽  
Derivatives Of ◽  
Complex Damping

Temporal windowing is a valuable process, which can help us to focus on a specific event in a seismogram. However, applying the time window is difficult outside the time domain. We suggest a windowing method which is applicable in the Laplace-Fourier domain. The window function we adopt is defined as a product of a gain function and an exponential damping function. The Fourier transform of a seismogram windowed by this function is equivalent to the partial derivative of the Laplace-Fourier domain wavefield with respect to the complex damping constant. Therefore, we can obtain a windowed seismogram using the partial derivatives of the Laplace-Fourier domain wavefield. We exploit the time-windowed wavefield, which is modeled directly in the Laplace-Fourier domain, to reconstruct subsurface velocity model by waveform inversion in the Laplace-Fourier domain. We present the windowed seismograms by introducing an inverse Laplace-Fourier transform technique and demonstrate the effect of temporal windowing in a synthetic Laplace-Fourier domain waveform inversion example.

scholarly journals Ivestigation of the Dynamic Stress State of Foam Media in Cosserat Elasticity

2020 ◽  
Vol 22 (3) ◽  
pp. 739-750
Author(s):  
Heorhiy Sulym ◽  
Olena Mikulich ◽  
Vasyl’ Shvabyuk
Keyword(s):  
Fourier Transform ◽  
Stress State ◽  
Dynamic Stress ◽  
Integral Equation Method ◽  
Stationary Problem ◽  
Cosserat Continuum ◽  
Boundary Integral ◽  
Two Dimensional ◽  
The Fourier Transform ◽  
The Time Domain

AbstractThe paper presents studies on the application of the boundary integral equation method for investigation of dynamic stress state of foam media with tunnel cavities in Cosserat continuum. For the solution of the non-stationary problem, the Fourier transform for time variable was used. The potential representations of Fourier transform displacements and microrotations are written. The fundamental functions of displacements and microrotations for the two-dimensional case of Cosserat continuum are built. Thus, the fundamental functions of displacement for the time-domain problem are derived as the functions of the two-dimensional isotropic continuum and the functions, which are responsible for the effect of shear-rotation deformations. The method of mechanical quadrature is applied for numerical calculations. Numerical example shows the comparison of distribution of dynamic stresses in the foam medium with the cavity under the action of impulse load accounting for the shear-rotation deformations effect and without accounting for this effect.

A NEURAL NETWORK FOR POSITION INVARIANT PATTERN RECOGNITION COMBINING SPIKING NEURONS WITH THE FOURIER-TRANSFORM

1996 ◽  
Vol 07 (06) ◽  
pp. 727-733 ◽  
Author(s):  
MICHAEL STOECKER ◽  
HERBERT J. REITBOECK
Keyword(s):  
Neural Network ◽  
Fourier Transform ◽  
Time Domain ◽  
Amplitude Spectrum ◽  
Dynamic Network ◽  
Spiking Neurons ◽  
Invariant Representation ◽  
Activity Distribution ◽  
The Fourier Transform ◽  
The Time Domain

We present an approach for position invariant recognition of individual objects in composite scenes, combining neural networks and algorithmic methods. A dynamic network of spiking neurons is used to generate object definition and figure/ground separation via temporal signal correlations. A shift invariant representation of the network spike activity distribution is subsequently realized via the amplitude spectrum of the Fourier-transform. Objects and their transformed representations are therefore linked in the time domain. The model segregates scenes and classifies individual patterns independent of their position in the input scene.

scholarly journals Frequency Domain System Identification With Instrumental Variable Based Subspace Algorithm

1997 ◽  
Author(s):  
Tomas McKelvey
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Instrumental Variable ◽  
Theoretical Discussion ◽  
Subspace Algorithm ◽  
Input And Output ◽  
Rank Constraint ◽  
The Fourier Transform ◽  
The Time Domain

Abstract In this paper we discuss how the time domain subspace based identification algorithms can be modified in order to be applicable when the primary measurements are given as samples of the Fourier transform of the input and output signals or alternatively samples of the transfer function. An instrumental variable (IV) based subspace algorithm is presented. We show that this method is consistent if a certain rank constraint is satisfied and the frequency domain noise is zero mean with bounded covariances. An example is presented which illuminates the theoretical discussion.

Calculation of the pulsed electromagnetic field of a plane annular magnetic current

Antennas ◽  
2021 ◽  
Author(s):  
I. P. Kovalyov ◽  
N. I. Kuzikova
Keyword(s):  
Magnetic Field ◽  
Fourier Transform ◽  
Electric Field ◽  
Wave Front ◽  
Time Domain ◽  
Vector Potential ◽  
Magnetic Current ◽  
The Fourier Transform ◽  
The Time Domain ◽  
The Magnetic Field

The work calculates the radiation fields of a plane ring magnetic current in the time domain. Two functions are considered that describe the dependence of the magnetic current on time: the delta function and the unit drop. All calculations are performed in the time domain without using the Fourier transform. First, the time-dependent vector potential is calculated. When writing expressions for the vector potential, the annular magnetic current is represented by the difference between two circular magnetic currents. Then, the magnetic field created by the ring magnetic current is found through the vector potential. Only one φ-th component of the magnetic field is nonzero. Further, from Maxwell's equations through the magnetic field, the components of the electric field of the annular magnetic current are calculated. On the basis of the formulas obtained, various special cases showing the dependence of the emitted field on time and spatial coordinates are considered. The time dependence of the electric field on the ring axis is calculated. It is shown that the Fourier transform of this field leads to a formula known from the literature in the frequency domain for calculating the field on the axis of the ring. The graphs are given showing that near the wave front, the transverse components of the electric and magnetic fields differ only by a factor equal to the wave resistance of the medium (120π for the air medium). The images of the electric field at different times are shown. In the given pictures of the fields, one can observe the movement of the radiation field near the wave front and the formation of a static field in the vicinity of the ring. The analytical expressions obtained in this work can be used to calculate antennas and other structures excited by a coaxial line. They can be used to solve integral equations in the time domain.

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