Frequency-domain ray series for viscoelastic waves with a non-symmetric stiffness matrix

We present an imaging scheme for mapping cross‐hole electrical conductivity using nonlinear traveltime tomography. Data used are peak arrival time estimates based on an approximate wavefield transform of the synthetic frequency‐domain electromagnetic (EM) field. Direct transformation of frequency‐domain EM fields to wavefields is known to be an ill‐posed problem because the kernel of integral transform is highly damped. In this study, instead of solving such an unstable problem, we approximate the wavefield in the transformed domain via a ray series expansion. If reflected and refracted energy is weak compared to that of direct wave, picking of the peak arrival time may be reduced to estimating the coefficients of the leading term in the ray series expansion. This simplification is valid when the conductivity contrast between background medium and the target anomalous body is small. The first three terms in the expansion are identical to the closed‐form solution for the vertical magnetic field caused by a vertical magnetic dipole source in a homogeneous whole‐space. An adaptive simulated annealing scheme is used to estimate the coefficients of ray series. For a whole‐space, exact traveltime can be extracted using only four frequency samples in our approach, whereas the direct numerical wavefield transform needed at least ten frequencies to construct a reasonable waveform. Nonlinear traveltime tomography using thusly‐extracted peak arrivals from synthetic data shows a reasonable image of the conductivity structure between boreholes.

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A wavelet-based model of one-dimensional periodic structure for wave-propagation analysis

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2009.0369 ◽

2009 ◽

Vol 466 (2113) ◽

pp. 263-281 ◽

Cited By ~ 3

Author(s):

Parikshit Sonekar ◽

Mira Mitra

Keyword(s):

Wave Propagation ◽

Frequency Domain ◽

Periodic Structure ◽

Stiffness Matrix ◽

Dynamic Stiffness ◽

Fe Model ◽

Loading Conditions ◽

Dynamic Stiffness Matrix ◽

One Dimensional ◽

Propagation Analysis

In this paper, a wavelet-based method is developed for wave-propagation analysis of a generic multi-coupled one-dimensional periodic structure (PS). The formulation is based on the periodicity condition and uses the dynamic stiffness matrix of the periodic cell obtained from finite-element (FE) or other numerical methods. Here, unlike its conventional definition, the dynamic stiffness matrix is obtained in the wavelet domain through a Daubechies wavelet transform. The proposed numerical scheme enables both time- and frequency-domain analysis of PSs under arbitrary loading conditions. This is in contrast to the existing Fourier-transform-based analysis that is restricted to frequency-domain study. Here, the dispersion characteristics of PSs, especially the band-gap features, are studied. In addition, the method is implemented to simulate time-domain wave response under impulse loading conditions. The two examples considered are periodically simply supported beam and periodic frame structures. In all cases, the responses obtained using the present periodic formulation are compared with the response simulated using the FE model without the periodicity assumption, and they show an exact match. This validates the accuracy of the periodic assumption to obtain the time- and frequency-domain wave responses up to a high-frequency range. Apart from this, the proposed method drastically reduces the computational cost and can be implemented for homogenization of PSs.

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Performance Simulation for the Supporting Structure of Aero-Engine Rotor in Wide Frequency Domain

International Journal of Vehicle Structures and Systems ◽

10.4273/ijvss.11.5.14 ◽

2019 ◽

Vol 11 (5) ◽

Author(s):

Baoxu Li

Keyword(s):

Finite Element ◽

Frequency Domain ◽

Dynamic Characteristics ◽

Stiffness Matrix ◽

Structural Model ◽

Test Method ◽

Supporting Structure ◽

Aero Engine ◽

Rotor Support ◽

Engine Rotor

The inertia load of aero-engine indeterminate rotor support is calculated by the finite element method coupled with plane stress element and Fourier ring element. Without considering the dynamic characteristics of rotor’s supporting structure, the test results are error-prone and inefficient. A new method for testing the supporting structure performance of aero-engine rotor in wide frequency domain is proposed. On this basis, the structural model of the casing-support and the structural model of aero-engine rotor are constructed by substructure modelling method. Combining the two sub-models, the semi-physical simulation model of the vibration of the engine rotor’s supporting structure is obtained. By superimposing the additional dynamic stiffness matrix of the casing-supporting structure at the designated DOF position in the overall stiffness matrix of the finite element model of the rotor structure, the overall stiffness matrix of the aero-engine rotor supporting structure is obtained. The effective stiffness matrix can be used to calculate the structural dynamic characteristics of aero-engine rotor supporting structure. Experiments show that the average error of the proposed method is 0.0023 and the number of units is 7.98 e4. The calculation time and storage space are reduced by 310 minutes and 166 GB respectively compared with the performance test method of rotor support based on finite element analysis, which shows that the proposed method is more efficient and accurate.

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Low-frequency electromagnetic fields in applied geophysics: Waves or diffusion?

Geophysics ◽

10.1190/1.2208275 ◽

2006 ◽

Vol 71 (4) ◽

pp. W29-W40 ◽

Cited By ~ 40

Author(s):

Lars O. Løseth ◽

Hans M. Pedersen ◽

Bjørn Ursin ◽

Lasse Amundsen ◽

Svein Ellingsrud

Keyword(s):

Frequency Domain ◽

Low Frequency ◽

Wave Theory ◽

Signal Propagation ◽

Dipole Source ◽

Conductive Materials ◽

Em Field ◽

Domain Description ◽

Ray Series ◽

Low Frequency Waves

Low-frequency electromagnetic (EM) signal propagation in geophysical applications is sometimes referred to as diffusion and sometimes as waves. In the following we discuss the mathematical and physical approaches behind the use of the different terms. The basic theory of EM wave propagation is reviewed. From a frequency-domain description we show that all of the well-known mathematical tools of wave theory, including an asymptotic ray-series description, can be applied for both nondispersive waves in nonconductive materials and low-frequency waves in conductive materials. We consider the EM field from an electric dipole source and show that a common frequency-domain description yields both the undistorted pulses in nonconductive materials and the strongly distorted pulses in conductive materials. We also show that the diffusion-equation approximation of low-frequency EM fields in conductive materials gives the correct mathematical description, and this equation has wave solutions. Having considered both a wave-picture approach and a diffusion approach to the problem, we discuss the possible confusion that the use of these terms might lead to.

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Dynamic Analysis of an Array of Connected Floating Breakwaters

Journal of Marine Science and Engineering ◽

10.3390/jmse7090298 ◽

2019 ◽

Vol 7 (9) ◽

pp. 298 ◽

Cited By ~ 1

Author(s):

Ćatipović ◽

Ćorak ◽

Alujević ◽

Parunov

Keyword(s):

Dynamic Analysis ◽

Frequency Domain ◽

Stiffness Matrix ◽

Three Dimensional ◽

Equation Of Motion ◽

Three Dimensions ◽

Body Formulation ◽

Multi Body ◽

Floating Breakwaters

In this paper, a model for dynamic analysis of array of floating breakwaters is developed and tested. Special attention is given to modeling connections between neighboring elements of the array. A linear three-dimensional floating multi-body formulation is used as a foundation for the presented model. An additional stiffness matrix is derived which introduces the influence of the connections onto motion of the array. The stiffness matrix is used to couple motions in vertical and horizontal planes i.e. the connections are modeled in three-dimensions. The equation of motion is solved in the frequency domain. The newly developed model is tested on an array of three connected breakwaters. The motion and the performance of the breakwater array are investigated under different significant heights and directions of the incoming waves.

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Frequency domain-based analysis of floor vibrations using the dynamic stiffness matrix method

Journal of Vibration and Control ◽

10.1177/1077546318795931 ◽

2018 ◽

Vol 25 (4) ◽

pp. 763-776 ◽

Cited By ~ 4

Author(s):

Tong Guo ◽

Zhiliang Cao ◽

Zhiqiang Zhang ◽

Aiqun Li

Keyword(s):

Finite Element ◽

Frequency Domain ◽

Stiffness Matrix ◽

Road Traffic ◽

Dynamic Stiffness ◽

Design Stage ◽

Element Analysis ◽

Frequency Spectra ◽

Dynamic Stiffness Matrix ◽

Floor Vibrations

Buildings may experience excessive floor vibrations due to inner excitations such as walking people and running machines, or ground motion caused by the road traffic. Therefore, it is often necessary to evaluate the vibration level at the design stage. In this paper, a frequency domain-based model for predicting vertical vibrations of a building floor is provided, where the floor is simplified as a rectangular plate stiffened by beams in two orthogonal directions, while vertical motion and rotation of the slab–column joints are viewed as the unknown degrees of freedom. The dynamic stiffness matrix of the whole structure is obtained from those of the floor and column elements. To validate the proposed solution, a five-story building was analyzed, and frequency spectra were compared with those from the finite element method. Besides, a prototype building was analyzed and validated based on field measured data. It is found that the proposed solution could predict vibration responses with satisfactory accuracy, and is more computationally efficient than finite element analysis.

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Representation theorem for viscoelastic waves with a non-symmetric stiffness matrix

Studia Geophysica et Geodaetica ◽

10.1007/s11200-020-0158-2 ◽

2021 ◽

Author(s):

Luděk Klimeš

Keyword(s):

Representation Theorem ◽

Stiffness Matrix ◽

Viscoelastic Waves

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An accurate frequency-domain model of water interaction with cylinders of arbitrary shape during earthquakes

Advances in Bridge Engineering ◽

10.1186/s43251-020-00026-3 ◽

2021 ◽

Vol 2 (1) ◽

Author(s):

Mi Zhao ◽

Xiaojing Wang ◽

Piguang Wang ◽

Chao Zhang ◽

Xiuli Du

Keyword(s):

Frequency Domain ◽

Seismic Response ◽

Stiffness Matrix ◽

Continued Fraction ◽

Numerical Solutions ◽

Dynamic Stiffness ◽

Arbitrary Cross Section ◽

Domain Model ◽

Weighted Residual Method ◽

Dynamic Stiffness Matrix

AbstractAn accurate frequency domain model is proposed to analyze the seismic response of uniform vertical cylinders with arbitrary cross section surrounded by water. According to the boundary conditions and using the variables separation method, the vertical modes of the hydrodynamic pressure are firstly obtained. Secondly, the three-dimensional wave equation can be simplified to a two-dimensional Helmholtz equation. Introducing the scaled boundary coordinate, a scaled boundary finite element (SBFE) equation which is a linear non-homogeneous second-order ordinary equation is derived by weighted residual method. The dynamic-stiffness matrix equation for the problem is furtherly derived. The continued fraction is acted as the solution of the dynamic-stiffness matrix for cylinder dynamic interaction of cylinder with infinite water. The coefficient matrices of the continued fraction are derived recursively from the SBFE equation of dynamic-stiffness. The accuracy of the present method is verified by comparing the hydrodynamic force on circular, elliptical and rectangle cylinders with the analytical or numerical solutions. Finally, the proposed model is used to analyze the natural frequency and seismic response of cylinders.

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