A Semi-Analytical and Semi-Numerical Method for Acoustics Radiation Characteristics of Rotational Shells

2014 ◽  
Vol 936 ◽  
pp. 2071-2074
Author(s):  
Jing Lu
Keyword(s):  
Numerical Method ◽  
Analytical Method ◽  
Sound Pressure ◽  
Superposition Principle ◽  
Radiation Characteristics ◽  
Rotational Shell ◽  
Control Equation

A semi-analytical and semi-numerical method is presented for analyzing the acoustics radiation characteristics of a rotational shell. Combining the dynamics control equation and the sound pressure expression, the vibro-acoustics equation of the rotational shell is formulated firstly. Then, a semi-analytical method is developed based on the superposition principle. The comparisons with the document show that the proposed method is accurate and efficient.

Possible application of approximate models for calculation of selectivity of consecutive reactions under the effect of mass transfer

1982 ◽  
Vol 47 (5) ◽  
pp. 1301-1309 ◽  
Author(s):  
František Kaštánek ◽  
Marie Fialová
Keyword(s):  
Mass Transfer ◽  
Numerical Method ◽  
Analytical Method ◽  
Approximate Analytical Method ◽  
Approximate Models ◽  
Consecutive Reactions ◽  
The Difference

The possibility of use of approximate models for calculation of selectivity of consecutive reactions is critically analysed. Simple empirical criteria are proposed which enable safer application of approximate analytical reactions. A more universal modification has been formulated by use of which the difference of selectivity calculated by the exact numerical method and by the approximate analytical method is at maximum 12%.

scholarly journals Associated equations and their corresponding resonance curve

1999 ◽  
Vol 21 (3) ◽  
pp. 147-155
Author(s):  
Nguyen Van Dinh
Keyword(s):  
Numerical Method ◽  
Analytical Method ◽  
Nonlinear Oscillations ◽  
Resonance Curve ◽  
Practical Case ◽  
High Harmonics

In the theory of nonlinear oscillations, in order to identify the resonance curve we usually try to eliminate the diphase Ѳ in the equations of stationary oscillations. We obtain thus a certain frequency-amplitude relationship. In simple cases when the mentioned equations contain only and linearly the first harmonics (sin Ѳ, cos Ѳ) the elimination of Ѳ is elementary, by using the trigono-metrical identity sin2 Ѳ+ cos2 Ѳ = 1. In general, high harmonics (sin2 Ѳ, cos2 Ѳ, etc.) are present. Consequently the expressions of sin Ѳ, cos Ѳ are cumbersome or do not exist and the analytical elimination of Ѳ is quite inconvenient or impossible. For this reason, to identify the resonance curve of complicated systems, we use the numerical method. Below, intending to develop the analytical method, we shall propose a procedure enabling us to transform the "original" complicated equations of stationary oscillations into the so-called associated ones, only and linearly containing sin Ѳ, cos Ѳ. The equivalence of the original and associated equations will be treated and the associated resonance 'curve-that is determined by the associated equations-will be analyzed The discussion will be restricted to a simple practical case in which, beside sin Ѳ and cos Ѳ, only sin2 Ѳ and cos2 Ѳ are present. Nevertheless, the method proposed and the results obtained can be generalized.

Random Collocation Method (RCM)

2010 ◽  
Author(s):  
Hiroshi Isshiki
Keyword(s):  
Numerical Method ◽  
Collocation Method ◽  
Analytical Method ◽  
Traditional Method ◽  
Analytical Approach ◽  
Numerical Procedure ◽  
Computational Method ◽  
Weak Point ◽  
The Past ◽  
Innovative Idea

Recently, young people’s concern on theory is becoming very poor. If there is a numerical procedure that is friendlier with theory, the distance between theory and calculation would be decreased much, and the interaction between them would become more active. When the geometry of the domain is simple, the traditional analytical method using function expansion is very convenient in many numerical problems. In many problems, it has given very useful solutions for various problems. However, its effectiveness is usually limited to simple geometries of the domain. In the past, a fusion of the analytical approach and computational one has not been pursued sufficiently. If it becomes possible, it may give a different paradigm for obtaining the numerical solution. In the present paper, an innovative idea named Random Collocation Method (RCM) is discussed on how to overcome the weak point of the traditional method by combining it with computational method. It is the purpose of the present paper to develop the simplest numerical method and to make the distance between the theory and numerical method as small as possible.

scholarly journals Effects of pipe casing structure on acoustic emission characteristics of underwater pyrotechnic combustion

2019 ◽  
Vol 39 (1) ◽  
pp. 149-157
Author(s):  
Jie Li ◽  
Jun Du ◽  
Xian Chen ◽  
Yanli Wang
Keyword(s):  
Sound Pressure Level ◽  
Sound Pressure ◽  
Acoustic Radiation ◽  
Structural Characteristics ◽  
Bubble Formation ◽  
Pressure Level ◽  
Radiation Characteristics ◽  
Acoustic Testing ◽  
Gas Volume ◽  
Broadband Sound

In order to investigate the acoustic radiation characteristics of underwater, a pipe casing was introduced and the effects of its main structural characteristics on underwater combustion acoustic radiation were studied by acoustic testing. The results show that the addition of the pipe casing significantly increased the sound pressure level of underwater pyrotechnic combustion, especially the peak of sound pressure level that was increased by 15.9 dB from 155.5 to 171.4 dB at the frequency of 125 and 100 Hz. But the addition of the pipe casing had little effect on the frequency. These results indicated that adding a pipe casing is effective for improving sound pressure level in underwater pyrotechnic combustion. An increase in nozzle diameter from 10 to 12.5 mm resulted in an increase of gas volume, so the peak of sound pressure level and broadband sound pressure level is higher. Changing the pipe casing direction to vertical downward will make the bubble formation period shorter, which will generate more bubbles and strong wake; the interaction between bubbles and wake results in a higher intensity of turbulence, which accounts for the coalescence and breakup of bubbles in the fluid. Besides, changing the diameter of pipe casing can be used to lower the frequency of underwater noise.

scholarly journals Solving fractional circuits with sinusoidal sources by using the gcdAlpha method

2018 ◽  
Vol 19 ◽  
pp. 01008
Author(s):  
Marcin Sowa
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Fractional Differential Equations ◽  
Analytical Method ◽  
Fractional Differential

This paper concerns a study being part of a larger project aiming at solutions of problems with fractional time derivatives. The presented study concerns gcdAlpha – a semi-analytical method for solving fractional differential equations. The basis of the method is recalled along with the general form of problems it was designed to solve. Sources represented by sinusoidal time functions are considered and the general formulae for gcdAlpha are presented for this case. An exemplary circuit problem (containing fractional elements and a sinusoidal source) has been brought forward and solved. The results are compared with ones obtained through a solver basing on the numerical method called SubIval.

Motion Analyses of D-Type Driving Mechanism

2013 ◽  
Vol 816-817 ◽  
pp. 786-789
Author(s):  
Shi Yi Li ◽  
Wen Pu Shi
Keyword(s):  
Numerical Method ◽  
Analytical Method ◽  
Linear Velocity ◽  
Driving Mechanism ◽  
Connecting Rod ◽  
Numerical Example ◽  
Angular Velocities ◽  
The Given

Geometric analyses and mechanical analytical method are used to study a kind of D-type driving mechanism. The theoretical formulae of computing angular velocities of the connecting rod and the rocker are given, and the linear velocity of the driving point C is obtained, and the finite differential numerical method for computing the angular velocities of the connecting rod and the rocker is also introduced. The results of the given numerical example show the feasibility of the theoretical conclusions here.

A Technique to Predict the Acoustic Radiation Characteristics of an Automobile Tire

1986 ◽  
Vol 14 (2) ◽  
pp. 102-115 ◽  
Author(s):  
C. Wright ◽  
G. H. Koopmann
Keyword(s):  
Close Agreement ◽  
Sound Pressure ◽  
Acoustic Radiation ◽  
Surface Velocity ◽  
Experimental Measurements ◽  
Far Field ◽  
Radiation Characteristics ◽  
Automobile Tire ◽  
Electrodynamic Vibrator ◽  
Field Sound

Abstract A technique to predict the acoustic radiation characteristics of the predominant structural modes of an automobile tire is presented. A stationary tire is excited by an electrodynamic vibrator and, through conventional modal analysis methods, a description of the surface velocity is obtained. With this information, and a representation of the tire geometry, numerical procedures are used to predict the acoustic surface intensity and field pressure, for a given frequency of interest, based on a Helmholtz integral formulation. Predicted far field sound pressure levels are in close agreement with experimental measurements taken in an anechoic chamber. This provided the necessary validation of the technique.

Analysis of Acoustic Radiation Characteristics of an Infinitely Long Half-Filled Cylindrical Shell

2018 ◽  
Author(s):  
Shuai Zhang ◽  
Tianyun Li ◽  
Xiang Zhu ◽  
Wenjie Guo
Keyword(s):  
Cylindrical Shell ◽  
Numerical Method ◽  
Radial Displacement ◽  
Acoustic Radiation ◽  
Surface Boundary ◽  
Acoustic Structure ◽  
Fluid Structure ◽  
Finite Element Software ◽  
Fluid Load ◽  
Control Equation

The acoustic radiation analysis of a fully-submerged infinitely long half-filled cylindrical shell coupling with fluid field is a typical acoustic-structure problem in the infinite domain, the solution of which is currently mainly based on numerical method. The analytic or semi-analytical method is indispensable for the numerical method and the mechanism to reveal the acoustic-structure coupling characteristics. In this paper, an analytic solution is presented that can calculate the acoustic radiation of infinitely long half-filled cylindrical shell. The displacement of the shell, the fluid load and the excitation force are expressed as the combination of trigonometric series and Fourier series, and displacements of the other two directions are removed by orthogonalizing, only the radial displacement is retained. The control equation of the fluid-structure interaction can be obtained from the relationship between the amplitude of fluid load and the amplitude of radial displacement which can be established by orthogonalizing the continuous conditions of the fluid-structure coupled contact surface and the free surface boundary condition. Solving the control equation, the vibration and acoustic radiation of the coupling system can be determined. Compared with the finite element software Comsol, the results of forced vibration and underwater radiated noise show that the presented method is accurate and reliable. A new way to solve acoustic-vibration problem with partial coupling of elastic structure and sound field is provided in this study.

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