scholarly journals Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 705
Author(s):  
Yongxian Wang ◽  
Houwang Tu ◽  
Wei Liu ◽  
Wenbin Xiao ◽  
Qiang Lan
Keyword(s):  
Spectral Methods ◽  
Normal Modes ◽  
Collocation Methods ◽  
Single Frequency ◽  
Dense Matrix ◽  
Eigenvalues And Eigenvectors ◽  
Time Data ◽  
Simple Processing ◽  
Atmospheric Acoustics ◽  
Galerkin Spectral Method

The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a time-independent single-frequency sound source. Its solution consists of a set of discrete modes radiating into the upper atmosphere, usually related to the continuous spectrum. In this article, we present two spectral methods, the Chebyshev-Tau and Chebyshev-Collocation methods, to solve for the atmospheric acoustic normal modes, and corresponding programs are developed. The two spectral methods successfully transform the problem of searching for the modal wavenumbers in the complex plane into a simple dense matrix eigenvalue problem by projecting the governing equation onto a set of orthogonal bases, which can be easily solved through linear algebra methods. After the eigenvalues and eigenvectors are obtained, the horizontal wavenumbers and their corresponding modes can be obtained with simple processing. Numerical experiments were examined for both downwind and upwind conditions to verify the effectiveness of the methods. The running time data indicated that both spectral methods proposed in this article are faster than the Legendre-Galerkin spectral method proposed previously.

Monitoring the Variability of the Stratospheric Aerosol Layer over Tomsk in 2016–2018 Based on Lidar Data

2021 ◽  
pp. 61-72
Author(s):  
V. N. Marichev ◽  
◽  
D. A. Bochkovskiia ◽  
Keyword(s):  
Volcanic Eruptions ◽  
Temperature Inversion ◽  
Cold Season ◽  
Stratospheric Aerosol ◽  
Single Frequency ◽  
Winter Period ◽  
Lidar Data ◽  
Aerosol Layer ◽  
Time Data ◽  
Academy Of Sciences

The results of observations of the features of intraannual variability for the vertical structure of background aerosol in the stratosphere over Western Siberia in 2016–2018 are presented and analyzed. Experimental data were obtained at the lidar complex of Zuev Institute of Atmospheric Optics (Siberian Branch, Russian Academy of Sciences) with a receiving mirror diameter of 1 m. The objective of the study is to investigate the dynamics of background stratospheric aerosol, since during this period there were no volcanic eruptions leading to the transport of eruptive aerosol into the stratosphere. The results of the study confirm a stable intraannual cycle of maximum aerosol filling of the stratosphere in winter, a decrease in spring to the minimum, practical absence in summer, and an increase in autumn. At the same time, the variability of stratification and aerosol filling is observed for different years. It was found that aerosol is concentrated in the layer up to 30 km all year round, except for the winter period. It is shown that the vertical aerosol stratification is largely determined by the thermal regime of the tropo- sphere–stratosphere boundary layer. The absence of a pronounced temperature inversion at the tropopause contributes to an increase in the stratosphere–troposphere exchange and, as a result, to the aerosol transport to the stratosphere. This situation is typical of the cold season. For the first time, data on the quantitative content of stratospheric aerosol (its mass concentration) were obtained from single- frequency lidar data.

Operational modal analysis of a nonlinear oscillation system under a harmonic excitation

2020 ◽  
pp. 095440622097755
Author(s):  
Xuchu Jiang ◽  
Feng Jiang ◽  
Biao Zhang
Keyword(s):  
Modal Analysis ◽  
Nonlinear Oscillation ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Harmonic Excitation ◽  
Forced Response ◽  
Operational Modal Analysis ◽  
Single Frequency ◽  
Modal Parameters ◽  
Oscillation System

Operational modal analysis (OMA) is a procedure that allows the modal parameters of a structure to be extracted from the measured response to an unknown excitation generated during operation. Nonlinearity is inevitably and frequently encountered in OMA. The problem: The traditional OMA method based on linear modal theory cannot be applied to a nonlinear oscillation system. The solution: This paper aims to propose a nonlinear OMA method for nonlinear oscillation systems. The new OMA method is based on the following: (1) a self-excitation phenomenon is caused by nonlinear components; (2) the nonlinear normal modes (NNMs) of the system appear under a single-frequency harmonic excitation; and (3) using forced response data, the symbolic regression method (SR) can be used to automatically search for the NNMs of the system, whose modal parameters are implicit in the expression structure expressing each NNM. The simulation result of a three-degree-of-freedom (3-DOF) nonlinear system verifies the correctness of the proposed OMA method. Then, a disc-rod rotor model is considered, and the proposed OMA method’s capability is further evaluated.

A Legendre-Galerkin spectral method for constructing atmospheric acoustic normal modes

2018 ◽  
Vol 143 (6) ◽  
pp. 3595-3601 ◽  
Author(s):  
Richard B. Evans ◽  
Xiao Di ◽  
Kenneth E. Gilbert
Keyword(s):  
Spectral Method ◽  
Normal Modes ◽  
Galerkin Spectral Method

Second-Order Fourier Synthesis of Broadband Acoustic Signals Using Normal Modes

1997 ◽  
Vol 05 (04) ◽  
pp. 355-370 ◽  
Author(s):  
E. K. Skarsoulis
Keyword(s):  
Time Domain ◽  
Normal Modes ◽  
Acoustic Signals ◽  
Second Order ◽  
Single Frequency ◽  
Closed Form Expression ◽  
Fourier Synthesis ◽  
Eigenvalues And Eigenfunctions ◽  
Intermediate Order ◽  
The Time Domain

A scheme for approximate normal-mode calculation of broadband acoustic signals in the time domain is proposed based on a second-order Taylor expansion of eigenvalues and eigenfunctions with respect to frequency. For the case of a Gaussian impulse source a closed-form expression is derived for the pressure in the time domain. Using perturbation theory, analytical expressions are obtained for the involved first and second frequency-derivatives of eigenvalues and eigenfunctions. The proposed approximation significantly accelerates arrival-pattern calculations, since the eigenvalues, the eigenfunctions and their frequency-derivatives need to be calculated at a single frequency, the central frequency of the source. Furthermore, it offers a satisfactory degree of accuracy for the lower and intermediate order modes. This is due to the fact that essential wave-theoretic mechanisms such as dispersion and frequency dependence of mode amplitudes are contained in the representation up to a sufficient order. Numerical results demonstrate the efficiency of the method.

scholarly journals The Convergence of the Legendre–Galerkin Spectral Method for Constructing Atmospheric Acoustic Normal Modes

2020 ◽  
Vol 28 (03) ◽  
pp. 2050002
Author(s):  
Richard B. Evans
Keyword(s):  
Legendre Polynomials ◽  
Normal Modes ◽  
Sobolev Norm ◽  
Linear Operators ◽  
Basis Sets ◽  
Spectral Approximation ◽  
Spectral Approximations ◽  
Potential Applications ◽  
Galerkin Spectral Method ◽  
Theoretical Results

The asymptotic rate of convergence of the Legendre–Galerkin spectral approximation to an atmospheric acoustic eigenvalue problem is established, as the dimension of the approximating subspace approaches infinity. Convergence is in the [Formula: see text] Sobolev norm and is based on the existing theory [F. Chatelin, Spectral Approximations of Linear Operators (SIAM, 2011)]. The assumption is made that the eigenvalues are simple. Numerical results that help interpret the theory are presented. Eigenvalues corresponding to acoustic modes with smaller [Formula: see text] norms are especially accurately approximated, even with lower dimensioned basis sets of Legendre polynomials. The deficiencies in the potential applications of the theoretical results are noted in connection with the numerical examples.

Analysis of eigenvalues and eigenvectors of polymer particles: random normal modes

2001 ◽  
Vol 11 (3) ◽  
pp. 191-196 ◽  
Author(s):  
K. Fukui ◽  
B.G. Sumpter ◽  
D.W. Noid ◽  
C. Yang ◽  
R.E. Tuzun
Keyword(s):  
Normal Modes ◽  
Polymer Particles ◽  
Eigenvalues And Eigenvectors

WHAT ABOUT ADIABATIC NORMAL MODES?

2001 ◽  
Vol 09 (01) ◽  
pp. 287-309 ◽  
Author(s):  
A. TOLSTOY
Keyword(s):  
Normal Mode ◽  
Normal Modes ◽  
Single Frequency ◽  
Test Case ◽  
Test Cases ◽  
Flat Bottom ◽  
Energy Conserving ◽  
Water Test ◽  
Independent Behavior ◽  
Benchmark Solutions

In this paper we closely examine the performance of several propagation models, i.e., KRAKEN (coupled and adiabatic) and PE (energy-conserving), applied to a number of the SWAM'99 range-dependent shallow water test cases (FLAT, DOWN, and UP). We begin by considering range-independent behavior (including the ORCA model) in: the CAL case of Workshop'97 (Vancouver, '97),9 the first segment of FLATa, and the Benchmark Wedge test case3 but with a flat bottom of 200 m depth. We next examine the proper Benchmark Wedge behavior for the sloping bottom for our PE (conserving and nonconserving) and for our normal mode model (KRAKEN, adiabatic and coupled). These preliminary tests confirm that the models are behaving properly under known conditions and that the input parameters have been appropriately set. Thus, when we study the models' behavior on the new SWAM'99 cases we will have some confidence that they are being applied properly. It is nontrivial to run these models even when one is familiar with them. The SWAM'99 test cases which are examined here are run only to 10 km range (five-step segments) and at a single frequency of 25 Hz. No elasticity is considered. We find that all the models generally agree, but there are quantitive differences. Since there are no proper benchmark solutions for these SWAM'99 test cases, it is difficult to determine to what extent any of them are in error. However, for the purposes of Matched Field Processing, particularly the tomographic geoacoustic inversion using adibatic normal modes (KRAKEN), it is likely that the simple adiabatic normal mode KRAKEN model is sufficiently accurate under most circumstances, i.e., unless there is a loss or gain of a critical mode.

scholarly journals A method of power system simulation model reduction for transmission grid frequency response analysis

2020 ◽  
Vol 209 ◽  
pp. 07010
Author(s):  
Valery Solodovnikov ◽  
Vladimir Tulsky ◽  
Roman Shamonov
Keyword(s):  
Power System ◽  
Simulation Model ◽  
System Simulation ◽  
Load Flow ◽  
Single Frequency ◽  
Response Analysis ◽  
Great Effort ◽  
Power System Simulation ◽  
Time Data ◽  
Harmonic Power

Application of the frequency scan method for the determination of resonant conditions in a transmission power grid requires great effort since the harmonic power system simulation model needs to be developed. This process is rather complicated since the original model used for fundamental frequency load-flow analysis is built with respect to certain assumptions and, thus, intolerable errors are introduced when frequency-domain properties of the power system are investigated. To strike a balance between inputs needed for the development of such model (time, data amounts) and accuracy of the results, it is proposed to employ a method which makes it possible to represent dead-end, double-ended and tapped 110-220 kV substations as a single frequency-dependent equivalent so that the harmonic power system model is reduced. Such an element essentially is a series R-L or R-L-C shunt, parameters of which vary with frequency. The algorithm for the evaluation of its parameters is proposed and the test case for a real 110 kV grid area is discussed. Results of the method application show that it can be used in practice.

IGS RTS for real-time global ionospheric total electron content modeling: Method and Applications

2020 ◽  
Author(s):  
Ningbo Wang ◽  
Zishen Li ◽  
Liang Wang
Keyword(s):  
Real Time ◽  
Sampling Rate ◽  
Global Scale ◽  
Global Network ◽  
Single Frequency ◽  
Space Representation ◽  
Electron Content ◽  
Time Data ◽  
Total Electron ◽  
Real Time Mode

<p>To enable GNSS applications with low or no time latency, real-time services (RTS) of the International GNSS Services (IGS) has been launched since 2013. The IGS RTS provides real-time data streams with latencies of less than few seconds, containing multi-frequency and multi-constellation GNSS measurements from a global network of high-quality GNSS receivers, which provides the opportunity to reconstruct global ionospheric models in real-time mode. For the computation of real-time global ionospheric maps (RT-GIM), a 2-day predicted global ionospheric model is introduced along with real-time slant ionospheric delays extracted from real-time IGS global stations. GPS and GLONASS L1+L2, BeiDou B1+B2 and Galileo E1+E5a signals with a sampling rate of 1 Hz are used to extract slant TEC (STEC) estimates. Spherical harmonic expansion up to degree and order 15 is employed for global vertical TEC (VTEC) modeling by combining the observed and predicted ionospheric data in real-time mode. Real-time ionospheric State Space Representation (SSR) corrections are then distributed in RTCM 1264 message (123.56.176.228:2101/CAS05) aside from the generation of RT-GIM in IONEX v1.0 format (available at ftp://ftp.gipp.org.cn/product/ionex/). The quality of CAS RT-GIMs is assessed during an 18-month period starting from August 2017, by comparison with GPS differential slant TECs at the selected IGS stations over continental areas, Jason-3 VTECs over the oceans and IGS combined final GIMs on a global scale, respectively. Results show that CAS’s RT-GIM products exhibit a relative error of 13.9%, which is only approximately 1-2% worse than the final ones during the test period. Additionally, the application of RT-GIM on the single-frequency precise point positioning (PPP) of smartphones is also presented.</p>

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