Space-time-wave number-frequency Z(x,t,k,f) analysis of SAW generation on fluid filled cylindrical shells

Ultrasonics ◽  
2004 ◽  
Vol 42 (1-9) ◽  
pp. 383-389 ◽  
Author(s):  
Loı̈c Martinez ◽  
Bruno Morvan ◽  
Jean Louis Izbicki
Keyword(s):  
Cylindrical Shells ◽  
Space Time ◽  
Wave Number ◽  
Number Frequency

Turbulence functions useful for probes (space–time correlation) and for scattering (wave-number–frequency spectrum) analysis

1968 ◽  
Vol 46 (23) ◽  
pp. 2683-2702 ◽  
Author(s):  
I. P. Shkarofsky
Keyword(s):  
Characteristic Size ◽  
Time Correlation ◽  
Exponential Model ◽  
Time Correlation Function ◽  
Maximum Energy ◽  
Confluent Hypergeometric Function ◽  
Space Time ◽  
Wave Number ◽  
Taylor’S Hypothesis ◽  
Number Frequency

The wave-number–frequency dependent spectral function, S(k, ω), and the space–time correlation function, C(r, t), are considered in a turbulent flowing plasma. The decay mechanisms are associated with either velocity fluctuations about the mean convection velocity or diffusion effects or attachment, or combinations of these, including the Brownian motion model. The ψ(k, ω) function, which is the ratio of S(k, ω) to its frequency-integrated value, depends on the mechanism and exhibits a profile which can be Gaussian, Lorentzian, a Z function, a Hermite polynomial modification of the Gaussian, or a confluent hypergeometric function. Anisotropic forms are also considered.The function C(r, t), obtained by convolving ψ (r, t) with C(r), the space autocorrelation function, is next considered. Adopting a Gaussian or an exponential model (which may be anisotropic) for C(r), we illustrate C(r, t) forms, which can readily be manipulated. Furthermore, letting r = 0, we derive two conditions for the applicability of Taylor's hypothesis. The assumption of frozen flow is not necessary, only that the root-mean-square Lagrangian displacement in a given time, associated with the decay, be much smaller than both the flow distance and the characteristic size of blobs having maximum energy.

Origins of features in wave number-frequency spectra of space-time images of the ocean

2012 ◽  
Vol 117 (C6) ◽  
pp. n/a-n/a ◽  
Author(s):  
William J. Plant ◽  
Gordon Farquharson
Keyword(s):  
Space Time ◽  
Wave Number ◽  
Frequency Spectra ◽  
Number Frequency

ANALYSIS OF TIME-DOMAIN ACOUSTIC WAVEFIELDS IN HORIZONTALLY CONTINUOUSLY LAYERED CONFIGURATIONS BASED ON THE MODIFIED CAGNIARD METHOD

1993 ◽  
Vol 01 (02) ◽  
pp. 185-196
Author(s):  
MARTIN D. VERWEIJ ◽  
ADRIANUS T. DE HOOP
Keyword(s):  
Time Domain ◽  
Neumann Series ◽  
Frequency Domain Analysis ◽  
Time Instant ◽  
Space Time ◽  
Wave Number ◽  
Wave Propagation Problem ◽  
Acoustic Equations ◽  
Number Frequency ◽  
The Individual

A combination of the Neumann series and the modified Cagniard method is used to derive a theoretically exact space-time domain solution for the 3-D acoustic wave propagation problem in horizontally continuously layered media. Firstly, integral transformations (among which is a one-sided temporal Laplace transformation) are applied to the space-time domain basic acoustic equations. Secondly, a system of transform domain integral equations is derived, which is solved using a convergent Neumann series. Finally, the individual terms of this series are transformed back to the space-time .domain using the modified Cagniard method. The space-time domain series turns out to be convergent for every continuously layered configuration and at any time instant. In contrast to the standard angular wave number-frequency domain analysis, in the present analysis, difficulties due to turning points, etc., are avoided.

Vibrations of rotating cylindrical shells with functionally graded material using wave propagation approach

2018 ◽  
Vol 232 (23) ◽  
pp. 4342-4356 ◽  
Author(s):  
Muzammal Hussain ◽  
M Nawaz Naeem ◽  
Aamir Shahzad ◽  
Mao-Gang He ◽  
Siddra Habib
Keyword(s):  
Wave Propagation ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Wave Number ◽  
Type I ◽  
Rotating Speed ◽  
Simply Supported ◽  
Fundamental Frequencies

Fundamental natural frequencies of rotating functionally graded cylindrical shells have been calculated through the improved wave propagation approach using three different volume fraction laws. The governing shell equations are obtained from Love’s shell approximations using improved rotating terms and the new equations are obtained in standard eigenvalue problem with wave propagation approach and volume fraction laws. The effects of circumferential wave number, rotating speed, length-to-radius, and thickness-to-radius ratios have been computed with various combinations of axial wave numbers and volume fraction law exponent on the fundamental natural frequencies of nonrotating and rotating functionally graded cylindrical shells using wave propagation approach and volume fraction laws with simply supported edge. In this work, variation of material properties of functionally graded materials is controlled by three volume fraction laws. This process creates a variation in the results of shell frequency. MATLAB programming has been used to determine shell frequencies for traveling mode (backward and forward) rotating motions. New estimations show that the rotating forward and backward simply supported fundamental natural frequencies increases with an increase in circumferential wave number, for Type I and Type II of functionally graded cylindrical shells. The presented results of backward and forward simply supported fundamental natural frequencies corresponding to Law I are higher than Laws II and III for Type I and reverse effects are found for Type II, depending on rotating speed. Our investigations show that the decreasing and increasing behaviors are noted for rotating simply supported fundamental natural frequencies with increasing length-to-radius and thickness-to-radius ratios, respectively. It is found that the fundamental frequencies of the forward waves decrease with the increase in the rotating speed, and the fundamental frequencies of the backward waves increase with the increase in the rotating speed. This investigation has been made with three different volume fraction laws of polynomial (Law I), exponential (Law II), and trigonometric (Law III). The presented numerical results of nonrotating isotropic and rotating functionally graded simply supported are in fair agreement with parts of other earlier numerical results.

An hp-version adaptive finite element algorithm for eigensolutions of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yongliang Wang ◽  
Jianhui Wang
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Higher Order ◽  
Wave Number ◽  
Adaptive Finite Element ◽  
Content Type ◽  
Circular Cylindrical Shells ◽  
Geometrical Factors ◽  
Circumferential Wave

PurposeThis study presents a novel hp-version adaptive finite element method (FEM) to investigate the high-precision eigensolutions of the free vibration of moderately thick circular cylindrical shells, involving the issues of variable geometrical factors, such as the thickness, circumferential wave number, radius and length.Design/methodology/approachAn hp-version adaptive finite element (FE) algorithm is proposed for determining the eigensolutions of the free vibration of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation. This algorithm first develops the established h-version mesh refinement method for detecting the non-uniform distributed optimised meshes, where the error estimation and element subdivision approaches based on the superconvergent patch recovery displacement method are introduced to obtain high-precision solutions. The errors in the vibration mode solutions in the global space domain are homogenised and approximately the same. Subsequently, on the refined meshes, the algorithm uses higher-order shape functions for the interpolation of trial displacement functions to reduce the errors quickly, until the solution meets a pre-specified error tolerance condition. In this algorithm, the non-uniform mesh generation and higher-order interpolation of shape functions are suitable for addressing the problem of complex frequencies and modes caused by variable structural geometries.FindingsNumerical results are presented for moderately thick circular cylindrical shells with different geometrical factors (circumferential wave number, thickness-to-radius ratio, thickness-to-length ratio) to demonstrate the effectiveness, accuracy and reliability of the proposed method. The hp-version refinement uses fewer optimised meshes than h-version mesh refinement, and only one-step interpolation of the higher-order shape function yields the eigensolutions satisfying the accuracy requirement.Originality/valueThe proposed combination of methodologies provides a complete hp-version adaptive FEM for analysing the free vibration of moderately thick circular cylindrical shells. This algorithm can be extended to general eigenproblems and geometric forms of structures to solve for the frequency and mode quickly and efficiently.

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