Sound wave scattering in a flow duct with azimuthally non-uniform liners

2018 ◽  
Vol 839 ◽  
pp. 644-662 ◽  
Author(s):  
Hanbo Jiang ◽  
Alex Siu Hong Lau ◽  
Xun Huang
Keyword(s):  
Current Model ◽  
Practical Importance ◽  
Closed Form Solution ◽  
Form Solution ◽  
Theoretical Modelling ◽  
Sound Waves ◽  
Matrix Kernel ◽  
Set Up ◽  
Hopf Method ◽  
Flow Duct

Novel acoustic liner designs often incorporate new materials with non-uniform impedance distributions. Therefore, new methods are required for their modelling and analysis. In this paper, a theoretical model is developed to investigate the scattering of sound waves from an axially symmetrical flow duct with a semi-infinite, azimuthally non-uniform acoustic lining on the duct wall. More specifically, the incorporation of Fourier series expansions into the Wiener–Hopf method leads to an analytical model with a matrix kernel, which is further factorised by using the pole-removal method to obtain a closed-form solution. A new mathematical method is developed to solve the residues associated with the pole-removal technique. The proposed model has been verified and validated by comparing with corresponding computational results. In addition to shedding light on the possible physical effect of azimuthally non-uniform liners along with an axial hard–soft interface, the current model enhances the theoretical modelling capability for a complicated set-up of practical importance, and can be used to investigate new liner designs for passive noise control in flow ducts.

Radiation Loading of a Cylindrical Source in a Fluid-Filled Cylindrical Cavity Embedded Within a Fluid-Saturated Poroelastic Medium

2002 ◽  
Vol 69 (5) ◽  
pp. 675-683 ◽  
Author(s):  
S. M. Hasheminejad ◽  
H. Hosseini
Keyword(s):  
Seismic Waves ◽  
Acoustic Radiation ◽  
Surrounding Medium ◽  
Practical Importance ◽  
Closed Form Solution ◽  
Form Solution ◽  
Radiation Impedance ◽  
Harmonic Field ◽  
Cylindrical Source ◽  
Water Saturated

Radiation loading on a vibrating structure is best described through its radiation impedance. In the present work the modal acoustic radiation impedance load on an infinitely long cylindrical source harmonically excited in circumferentially periodic (axially independent) spatial pattern, while positioned concentrically within a fluid cylinder, which is embedded in a fluid-saturated unbounded elastic porous medium, is computed. This configuration, which is a realistic idealization of an acoustic logging tool suspended in a fluid-filled borehole within a permeable surrounding formation (White, J. E., 1983, Underground Sound Application of Seismic Waves, Elsevier, Amsterdam, Fig. 5.29, p. 183), is of practical importance with a multitude of possible applications in seismo-acoustics and noise control engineering. The formulation utilizes the Biot phenomenological model to represent the behavior of the sound in the porous, fluid-saturated, macroscopically homogeneous and isotropic surrounding medium. Employing the appropriate wave-harmonic field expansions and the pertinent boundary conditions for the given boundary configuration, a closed-form solution in the form of an infinite series is developed and the resistive and reactive components of modal radiation impedances are determined. A numerical example for a cylindrical surface excited in vibrational modes of various order, immersed in a water-filled cavity which is embedded within a water-saturated Ridgefield sandstone environment, is presented and several limiting cases are examined. Effects of porosity, frame stiffness, source size, and the interface permeability condition on the impedance values are presented and discussed.

Derivation of Position-Probability Density for the Transient Nano-Tunnel Problem in SET

2010 ◽  
Author(s):  
Sheam-Chyun Lin ◽  
Hsien-Chang Shih ◽  
Fu-Sheng Chuang ◽  
Ming-Lun Tsai ◽  
Harki Apri Yanto ◽  
...  
Keyword(s):  
Probability Density ◽  
Error Function ◽  
Closed Form Solution ◽  
Form Solution ◽  
Single Electron ◽  
Mathematical Operation ◽  
Similarity Parameter ◽  
Set Up ◽  
Position Probability ◽  
Good Agreement

This theoretical investigation intends to study the nano-tunnel problem of the single electron transistor (SET), which is one of the most important components in the nano-electronics industry. With a combined effort of quantum mechanics and similarity parameter, the partial differential equation of transient position-probability density is attained and can be applied to predict the electron’s position inside the nano tunnel. Also, an appropriate set of the initial and the boundary conditions is set up in accordance to the actual electron behavior for solving this PDE of probability density function. Thereafter, a simple, closed-form solution for the probability density is obtained and expressed in terms of the error function for a new similarity variable η. Note that this analytic similarity solution is easy to perform the calculation and suitable for any further mathematical operation, such as the optimization applications. In addition, it is shown that these predications are reasonable and in good agreement to the physical meanings, which are evaluated from both microscopic and macroscopic viewpoints. In conclusions, this is an innovative approach by using the Schro¨dinger equation directly to solve the nano-tunnel problem. Moreover, with the aids of this analytic position-probability-density solution, it is illustrated that the free single electron in the SET’s tunnel can only appear at some specified regions, which are defined by a dimensionless parameter η within a range of 0 ≤ η ≤ 2. This result can be served as a valuable design reference for setting the practical manufacture requirement.

Theoretical model of scattering from flow ducts with semi-infinite axial liner splices

2015 ◽  
Vol 786 ◽  
pp. 62-83 ◽  
Author(s):  
Xin Liu ◽  
Hanbo Jiang ◽  
Xun Huang ◽  
Shiyi Chen
Keyword(s):  
Fourier Series ◽  
Theoretical Model ◽  
Numerical Solutions ◽  
Practical Importance ◽  
Numerical Test ◽  
Closed Form Solution ◽  
Fourier Series Expansion ◽  
Constant Matrix ◽  
Acoustic Effect ◽  
Matrix Kernel

In this paper we present a theoretical model to study sound scattering from flow ducts with a semi-infinite lining surface covered by some equally spaced rigid splices, which is of practical importance in the development of silent aeroengines. The key contribution of our work is the analytical and rigorous description of axial liner splices by incorporating Fourier series expansion and the Wiener–Hopf method. In particular, we describe periodic variations of the semi-infinite lining surface by using Fourier series that accurately represent the layout of rigid splices in the circumferential direction. The associated matrix kernel involves a constant matrix and a diagonal matrix. The latter consists of a series of typical scalar kernels. A closed-form solution is then obtained by using standard routines of Wiener–Hopf factorisation for scalar kernels. A couple of appropriate approximations, such as numerical truncations of infinite Fourier series, have to be adopted in the implementation of this theoretical model, which is validated by comparing favorably with numerical solutions from a commercial acoustic solver. Finally, several numerical test cases are performed to demonstrate this theoretical model. It can be seen that the proposed theoretical model helps to illuminate the essential acoustic effect jointly imposed by axial and circumferential hard–soft interfaces.

Predicting Equation of Transient Position-Probability Density for Nano-Tunnel Problem in SET

2013 ◽  
Vol 284-287 ◽  
pp. 2570-2574
Author(s):  
Sheam Chyun Lin ◽  
Hsien Chang Shih
Keyword(s):  
Probability Density ◽  
Dimensionless Parameter ◽  
Error Function ◽  
Closed Form Solution ◽  
Form Solution ◽  
Single Electron ◽  
Analytic Investigation ◽  
Similarity Parameter ◽  
Set Up ◽  
Position Probability

This analytic investigation intends to study the nano-tunnel problem of the single electron transistor (SET), which is the most important component in the nano-electronics industry. With a combined effort of quantum mechanics and similarity parameter, the PDE equation of transient position-probability density is attained and can be applied to predict the electron’s position inside the nano tunnel. Also, appropriate initial and the boundary conditions are set up in accordance to the actual electron behavior for solving this PDE of probability density function. Thereafter, a simple, closed-form solution for the probability density is obtained and expressed in terms of the error function for a new similarity variable η. In conclusions, this is an innovative approach by using the Schrödinger equation directly to solve the nano-tunnel problem. Moreover, with the aids of this analytic position-probability-density solution, it is illustrated that the free single electron in the SET’s tunnel can only appear at some specified regions, which are defined by a dimensionless parameter η within a range of 0≤η≤2. This result can be served as a valuable design reference for setting the practical manufacture requirement.

Closed-Form Inverse Kinematic Analysis of Variable-Geometry Truss Manipulators

1992 ◽  
Vol 114 (3) ◽  
pp. 438-443 ◽  
Author(s):  
B. Padmanabhan ◽  
V. Arun ◽  
C. F. Reinholtz
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Practical Importance ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Variable Geometry ◽  
Inverse Kinematic Problem ◽  
Inverse Kinematic Analysis ◽  
Variable Geometry Truss

A variety of applications for variable-geometry truss manipulators (VGTMs) have been demonstrated or proposed in the literature. Most of these applications require solution to the inverse kinematic problem, yet only a few isolated examples of closed-form solution methods have been presented to date. This paper provides an overview to the general problem of inverse kinematic analysis of variable-geometry truss manipulators and presents new closed-form solution techniques for problems of practical importance.

scholarly journals Comparison of closed-form solutions to experimental magnetic force between two cylindrical magnets

2021 ◽  
pp. 141-146
Author(s):  
Sampart Cheedket ◽  
Chitnarong Sirisathitkul
Keyword(s):  
Magnetic Field ◽  
Closed Form ◽  
Magnetic Force ◽  
Permanent Magnets ◽  
Magnetic Levitation ◽  
Closed Form Solution ◽  
Vertical Tube ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Set Up

The force between permanent magnets implemented in many engineering devices remains an intriguing problem in basic physics. The variation of magnetic force with the distance x between a pair of magnets cannot usually be approximated as x-4 because of the dipole nature and geometry of magnets. In this work, the force between two identical cylindrical magnets is accurately described by a closed-form solution. The analytical model assumes that the magnets are uniformly magnetized along their length. The calculation, based on the magnetic field exerted by one magnet on the other along the direction of their orientation, shows a reduction in the magnetic force with the distance x and a dependence on the size parameters of magnets. To verify the equation, the experiment was set up by placing two cylindrical neodymium iron boron type magnets in a vertical tube. The repulsive force between the identical upper and lower magnets of 2.5 cm in diameter and 7.5 cm in length was measured from the weight on the top of the upper magnet. The resulting separation between the magnets was recorded as x. The forces measured at x=0.004-0.037 m differ from the values calculated using the analytic solution by -0.55 % to -13.60 %. The calculation also gives rise to a practical remnant magnetic field of 1.206 T. When x is much large than the equation of force is approximated as a simple form proportional to 1/x-4. The finding can be directly used in magnetic levitation as well as applied in calculating magnetic fields and forces in other systems incorporating permanent magnets.

Theoretical model of acoustic scattering from a flat plate with serrations

2017 ◽  
Vol 819 ◽  
pp. 228-257 ◽  
Author(s):  
Xun Huang
Keyword(s):  
Theoretical Model ◽  
Practical Importance ◽  
Acoustic Scattering ◽  
Low Noise ◽  
Test Cases ◽  
Sound Waves ◽  
Rigorous Description ◽  
Parametric Studies ◽  
Closed Form Analytical Solution ◽  
Hopf Method

A theoretical model is proposed in this work to study the scattering of sound waves from a serrated flat plat in the presence of a uniform flow, which is of both scientific significance and practical importance. The key contribution is the analytic and rigorous description of the scattering from the laterally periodic serrations by incorporating Fourier series expansions and the Wiener–Hopf method, which collectively give a closed-form analytical solution. To validate and demonstrate the model, a couple of test cases with some representative sinusoidal- and sawtooth-shaped serrations are studied by comparing with a commercial finite element solver. The comparisons show quite good agreement for various set-ups. The subsequent parametric studies further demonstrate the efficiency of the model and the effect of the serrations for noise control. Overall, the proposed theoretical model should be able to assist in studies of low-noise aerofoils and the silent flying capabilities of owls.

Effect of rotation on wave propagation through a poroelastic wet bone with cavity

2019 ◽  
Vol 16 (1) ◽  
pp. 53-72
Author(s):  
A.M. Abd-Alla ◽  
S.M. Abo-Dahab ◽  
Roqia Ateeq ◽  
Moaiad A. Khder
Keyword(s):  
Wave Propagation ◽  
Large Scale ◽  
Mechanical Response ◽  
Practical Importance ◽  
Engineering Application ◽  
Closed Form Solution ◽  
Form Solution ◽  
Long Bone ◽  
Content Type ◽  
Bio Engineering

Purpose The purpose of this paper is to investigate the wave propagation of wave in an infinite poroelastic cylindrical bone. The dynamic behavior of a wet long bone that has been modeled as a piezoelectric hollow cylinder of crystal class 6 is investigated. Design/methodology/approach An exact closed form solution is presented by employing an analytical procedure. The frequency equation for poroelastic bone is obtained when the boundaries are stress free and is examined numerically. Findings The study of wave propagation over a continuous medium is of practical importance in the field of engineering, medicine and bio-engineering. Application of the poroelastic materials in medicinal fields such as orthopedics, dental and cardiovascular is well known. In orthopedics, wave propagation over bone is used in monitoring the rate of fracture healing. There are two types of osseous tissue, such as cancellous or trabecular and compact or cortical bone, which are of different materials, with respect to their mechanical behavior. Originality/value The frequencies are calculated for poroelastic bone for various values for different values of rotation, angular velocity and density. In wet bone little velocity dispersion was observed, in contrast to the results of earlier studies on wet bone. Large values of attenuation were observed. Such a model would in particular be useful in large-scale parametric studies of bone mechanical response.

Formulation of a Strain Hardening Model for Gasket Creep Relaxation

2011 ◽  
Author(s):  
Antoine Abboud ◽  
Sayed A. Nassar
Keyword(s):  
Strain Hardening ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Duration ◽  
Experimental Procedure ◽  
Hardening Model ◽  
Pressure Step ◽  
Step Loading ◽  
Gasket Material ◽  
Set Up

This paper proposes a novel strain hardening model for investigating gasket creep relaxation under compressive step-loading at room temperature. A closed form solution is developed for predicting the steady-state gasket pressure. Step-loading of the gasket may be directly achieved and controlled, or indirectly estimated through the bolt tightening and re-tightening torque. The effect of gasket material, time duration at each stress level, as well as the geometric parameters of the gasket is investigated. An experimental procedure and test set-up are used to validate the proposed gasket model.

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