Acoustic Green's Function Approximations

1998 ◽  
Vol 06 (04) ◽  
pp. 435-452 ◽  
Author(s):  
Robert P. Gilbert ◽  
Zhongyan Lin ◽  
Klaus Hackl
Keyword(s):  
Inverse Problem ◽  
Normal Mode ◽  
Eigenvalue Problems ◽  
Normal Modes ◽  
Modal Parameters ◽  
Mindlin Plate ◽  
Ocean Bottom ◽  
Hankel Transformation ◽  
Poroelastic Materials ◽  
Function Approximations

Normal-mode expansions for Green's functions are derived for ocean–bottom systems. The bottom is modeled by Kirchhoff and Reissner–Mindlin plate theories for elastic and poroelastic materials. The resulting eigenvalue problems for the modal parameters are investigated. Normal modes are calculated by Hankel transformation of the underlying equations. Finally, the relation to the inverse problem is outlined.

Experimental Study for Extraction of Normal Modes

1995 ◽  
Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Normal Modes ◽  
Measurement Data ◽  
Mode Shapes ◽  
Complex Frequency ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Incomplete System ◽  
Coupled Structures

Abstract A frequency-domain technique to extract the normal mode from the measurement data for highly coupled structures is developed. The relation between the complex frequency response functions and the normal frequency response functions is derived. An algorithm is developed to calculate the normal modes from the complex frequency response functions. In this algorithm, only the magnitude and phase data at the undamped natural frequencies are utilized to extract the normal mode shapes. In addition, the developed technique is independent of the damping types. It is only dependent on the model of analysis. Two experimental examples are employed to illustrate the applicability of the technique. The effects due to different measurement locations are addressed. The results indicate that this technique can successfully extract the normal modes from the noisy frequency response functions of a highly coupled incomplete system.

scholarly journals Computational notes on the electronic properties of carboxylic acid

2020 ◽  
Vol 9 (2) ◽  
pp. 1079-1082
Keyword(s):  
Acetic Acid ◽  
Carboxylic Acid ◽  
Electronic Properties ◽  
Carboxylic Acids ◽  
Normal Mode ◽  
Normal Modes ◽  
Carboxyl Groups ◽  
Vibrational Characteristics ◽  
Vibrational Features ◽  
Acetic Acids

The present work describing the electronic properties and vibrational characteristics of carboxylic acids. Acetic acid is chosen as model molecules then optimized at B3LYP/6-31g(d,p) level of theory. The vibrational frequencies were calculated at the same level of theory. Band assignments which were calculated as 18 normal modes were assigned as one compare the normal mode coordinates with original one. Band assignments were described indicating the directions of normal modes in terms the vibrating atoms of the acetic acids. It could be concluded that DFT could be a useful tool for elucidation both the structural and vibrational features of carboxylic acids and then further utilized for assignment of the structures contains carboxyl groups which are known as most reactive structures in chemistry, biology and environment.

scholarly journals Normal modes in thermal AdS via the Selberg zeta function

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Victoria Martin ◽  
Andrew Svesko
Keyword(s):  
Zeta Function ◽  
Heat Kernel ◽  
Normal Mode ◽  
Kernel Method ◽  
Normal Modes ◽  
Quasinormal Mode ◽  
Partition Functions ◽  
Selberg Zeta Function ◽  
Exact Agreement ◽  
Spin Fields

The heat kernel and quasinormal mode methods of computing 1-loop partition functions of spin ss fields on hyperbolic quotient spacetimes \mathbb{H}^{3}/\mathbb{Z}ℍ3/ℤ are related via the Selberg zeta function. We extend that analysis to thermal \text{AdS}_{2n+1}AdS2n+1 backgrounds, with quotient structure \mathbb{H}^{2n+1}/\mathbb{Z}ℍ2n+1/ℤ. Specifically, we demonstrate the zeros of the Selberg function encode the normal mode frequencies of spin fields upon removal of non-square-integrable modes. With this information we construct the 1-loop partition functions for symmetric transverse traceless tensors in terms of the Selberg zeta function and find exact agreement with the heat kernel method.

scholarly journals INFLUENCE OF A LIQUID ON THE NATURAL FREQUENCIES OF ALMOST CIRCULAR PLATES

2014 ◽  
Vol 06 (05) ◽  
pp. 1450052 ◽  
Author(s):  
MANUEL GASCÓN-PÉREZ ◽  
PABLO GARCÍA-FOGEDA
Keyword(s):  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Normal Modes ◽  
Virtual Mass ◽  
Circular Plates ◽  
Hankel Transformation ◽  
Fluid System ◽  
Surrounding Fluid ◽  
Good Agreement

In this work, the influence of the surrounding fluid on the dynamic characteristics of almost circular plates is investigated. First the natural frequencies and normal modes for the plates in vacuum are calculated by a perturbation procedure. The method is applied for the case of elliptical plates with a low value of eccentricity. The results are compared with other available methods for this type of plates with good agreement. Next, the effect of the fluid is considered. The normal modes of the plate in vacuum are used as a base to express the vibration mode of the coupled plate-fluid system. By applying the Hankel transformation the nondimensional added virtual mass 2 increment (NAVMI) are calculated for elliptical plates. Results of the NAVMI factors and the effect of the fluid on the natural frequencies are given and it is shown that when the eccentricity of the plate is reduced to zero (circular plate) the known results of the natural frequencies for circular plates surrounded by liquid are recovered.

Identification of a Significantly Non-Proportionally Damped Structure Using Force Appropriation

1995 ◽  
Author(s):  
P. S. Holmes ◽  
J. R. Wright ◽  
J. E. Cooper
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Normal Mode ◽  
Normal Modes ◽  
Dynamic Tests ◽  
High Quality ◽  
Element Analysis ◽  
Standard Curve ◽  
Complex Modes ◽  
Phase Resonance

Abstract Dynamic tests were carried out on an aluminium plate with significant non-proportional damping applied via two oil filled dampers. Normal mode force appropriation (phase resonance) methods were used to measure the undamped normal modes of the plate and the results compared with corresponding complex modes obtained using a standard curve fitting (phase separation) approach. It is demonstrated that, as long as suitable excitation positions are chosen, high quality undamped normal modes can be identified while the curve fitted modes are highly complex. A Finite Element analysis of the plate was used to show how the results of normal mode force appropriation are directly comparable, particularly when damping is non-proportional.

scholarly journals Use of ice-sheet normal modes for initialization and modelling small changes

1997 ◽  
Vol 25 ◽  
pp. 85-95 ◽  
Author(s):  
Richard C. A. Hindmarsh
Keyword(s):  
Normal Mode ◽  
Time Constant ◽  
Normal Modes ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Short Term ◽  
Scale Theory ◽  
Digital Elevation ◽  
Linearized Model ◽  
Term Response

Linearizations about two horizontal-dimensional ice sheets are proposed as methods of generating normal mode initializations for ice-sheet models and for computing the short-term response. Linearized models can be generated directly from balance-flux calculations without the need for tuning the rate factor.A linearized model is compared with the Eismint Benchmark, and the normal modes for two coarse Antarctic digital elevation models are computed and compared. Volumetric relaxation spectra are presented. The slowest mode has a time constant comparable to that computed from scale theory.

scholarly journals Normal Mode Analysis as a Routine Part of a Structural Investigation

Molecules ◽  
2019 ◽  
Vol 24 (18) ◽  
pp. 3293 ◽  
Author(s):  
Jacob A. Bauer ◽  
Jelena Pavlović ◽  
Vladena Bauerová-Hlinková
Keyword(s):  
Normal Mode ◽  
Structural Study ◽  
Computer Technology ◽  
Structural Investigation ◽  
Normal Mode Analysis ◽  
Computational Cost ◽  
Normal Modes ◽  
Mode Analysis ◽  
Computationally Expensive ◽  
The Web

Normal mode analysis (NMA) is a technique that can be used to describe the flexible states accessible to a protein about an equilibrium position. These states have been shown repeatedly to have functional significance. NMA is probably the least computationally expensive method for studying the dynamics of macromolecules, and advances in computer technology and algorithms for calculating normal modes over the last 20 years have made it nearly trivial for all but the largest systems. Despite this, it is still uncommon for NMA to be used as a component of the analysis of a structural study. In this review, we will describe NMA, outline its advantages and limitations, explain what can and cannot be learned from it, and address some criticisms and concerns that have been voiced about it. We will then review the most commonly used techniques for reducing the computational cost of this method and identify the web services making use of these methods. We will illustrate several of their possible uses with recent examples from the literature. We conclude by recommending that NMA become one of the standard tools employed in any structural study.

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.

scholarly journals Constraining 1-D inner core attenuation through measurements of strongly coupled normal mode pairs

2020 ◽  
Vol 223 (1) ◽  
pp. 612-621 ◽  
Author(s):  
S Talavera-Soza ◽  
A Deuss
Keyword(s):  
Normal Mode ◽  
Inner Core ◽  
Strong Dependence ◽  
Normal Modes ◽  
Cross Coupling ◽  
Body Waves ◽  
Spectral Amplitude ◽  
Cylindrical Anisotropy ◽  
Strongly Coupled ◽  
Mode Pair

SUMMARY We measured inner core normal mode pair 10S2–11S2, which cross-couples strongly for 1-D structure and is sensitive to shear wave velocity, and find that our measurements agree with a strongly attenuating inner core. In the past, this mode pair has been used to try to resolve the debate on whether the inner core is strongly or weakly attenuating. Its large spectral amplitude in observed data, possible through the apparent low attenuation of 10S2, has been explained as evidence of a weakly attenuating inner core. However, this contradicted body waves and other normal modes studies, which resulted in this pair of modes being excluded from inner core modelling. Modes 10S2 and 11S2 are difficult to measure and interpret because they depend strongly on the underlying 1-D model used. This strong dependence makes these modes change both their oscillation characteristics and attenuation values under a small 1-D perturbation to the inner core model. Here, we include this effect by allowing the pair of modes to cross-couple or resonate through 1-D structure and treat them as one hybrid mode. We find that, unlike previously thought, the source of 10S2 visibility is its strong cross-coupling to 11S2 for both 1-D elastic and anelastic structure. We also observe that the required 1-D perturbation is much smaller than the 2 per cent vs perturbation previously suggested, because we simultaneously measure 3-D structure in addition to 1-D structure. Only a 0.5 per cent increase in inner core vs or a 0.5 per cent decrease in inner core radius is required to explain 10S2–11S2 observations and a weakly attenuating inner core is not needed. In addition, the 3-D structure measurements of mode 10S2 and its cross-coupling to 11S2 show the typical strong zonal splitting pattern attributed to inner core cylindrical anisotropy, allowing us to add further constrains to deeper regions of the inner core.

scholarly journals Spectral Analysis of Multidimensional Stochastic Geophysical Models with an Application to Decadal ENSO Variability

2011 ◽  
Vol 68 (1) ◽  
pp. 13-25 ◽  
Author(s):  
Richard Kleeman
Keyword(s):  
Normal Mode ◽  
Linear Models ◽  
Decadal Variability ◽  
Normal Modes ◽  
Spectral Character ◽  
Stochastic Forcing ◽  
Spectral Matrix ◽  
Enso Variability ◽  
Cross Spectrum ◽  
The Cross

Abstract Simple linear models with additive stochastic forcing have been rather successful in explaining the observed spectrum of important climate variables. Motivated by this, the authors analyze the spectral character of such a general stochastic system of finite dimension. The spectral matrix is derived in the case that the spectrum is a linear combination of dynamical variables and their stochastic forcings. It is found that the most convenient basis for analysis is provided by the normal modes. In general the spectrum consists of two pieces. The first “diagonal” piece is a symmetric Lorentzian curve centered on the normal mode frequencies with breadth and strength determined by the normal mode dissipation. The second cross-spectrum piece derives usually from the coherency of the stochastic forcing of two different normal modes. The cross-spectrum is smaller in magnitude than the corresponding two diagonal pieces. This relative magnitude is controlled by the Wiener coherency, which is equal to the magnitude of the correlation of the stochastic forcings of different normal modes. This new analysis framework is studied in detail for the ENSO case for which a two-dimensional stochastically forced oscillator has been previously suggested as a minimal model. It is found that the observed spectrum is rather easily reproduced given appropriate dissipation. Further, it is found that the cross-spectrum results in a phase-dependent enhancement or suppression of frequencies smaller than the dominant ENSO frequency. This therefore provides a new mechanism for decadal ENSO variability. Since the cross-spectrum is phase dependent, the decadal variability generated has a distinctive spatial character. The significance of the cross-spectrum depends on the Wiener coherency, which in turn depends on the statistics of the stochastic forcing.

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