scholarly journals Transfer matrix of a truncated cone with viscothermal losses: application of the WKB method

Acta Acustica ◽  
2020 ◽  
Vol 4 (2) ◽  
pp. 7
Author(s):  
Augustin Ernoult ◽  
Jean Kergomard
Keyword(s):  
Transfer Matrix ◽  
Cross Section ◽  
Thermal Effects ◽  
Classical Problem ◽  
Wkb Method ◽  
Zeroth Order ◽  
Low Frequencies ◽  
Musical Acoustics ◽  
Truncated Cone ◽  
Wkb Expansion

The propagation in tubes with varying cross section and wall visco-thermal effects is a classical problem in musical acoustics. To treat this aspect, the first method is the division in a large number of short cylinders. The division in short conical frustums with uniform averaged wall effects is better, but remains time consuming for narrow tubes and low frequencies. The use of the WKB method for the transfer matrix of a truncated cone without any division is investigated. In the frequency domain, the equations due to Zwikker and Kosten are used to define a reference result for a simplified bassoon by considering a division in small conical frustums. Then expressions of the transfer matrix at the WKB zeroth and the second orders are derived. The WKB second order is good at higher frequencies. At low frequencies, the errors are not negligible, and the WKB zeroth order seems to be better. This is due to a slow convergence of the WKB expansion for the particular case: the zeroth order can be kept if the length of the missing cone is large compared to the wavelength. Finally, a simplified version seems to be a satisfactory compromise.

A macrotransport equation for the particle distribution in the flow of a concentrated, non-colloidal suspension through a circular tube

2013 ◽  
Vol 734 ◽  
pp. 219-252 ◽  
Author(s):  
Arun Ramachandran
Keyword(s):  
Cross Section ◽  
Colloidal Particles ◽  
Particle Distribution ◽  
Circular Tube ◽  
Colloidal Suspension ◽  
Classical Problem ◽  
Taylor Dispersion ◽  
Concentration Gradients ◽  
Concentrated Suspension ◽  
The Cross

AbstractA two-time-scale perturbation expansion is used to derive a cross-section-averaged convection–dispersion equation for the particle distribution in the flow of a concentrated suspension of neutrally buoyant, non-colloidal particles through a straight, circular tube. Since the cross-streamline motion of particles is governed by shear-induced migration, the Taylor-dispersion coefficient ${\mathscr{D}}_{eff} $ scales as ${U}^{\prime } {R}^{3} / {a}^{2} $, ${U}^{\prime } $, $R$ and $a$ being the characteristic velocity scale, the tube radius and the particle radius, respectively. Here ${\mathscr{D}}_{eff} $ is found to decrease monotonically with an increase in the particle concentration. The linear dependence of ${\mathscr{D}}_{eff} $ on ${U}^{\prime } $ implies that changes in the cross-section averaged axial concentration profile are dependent only on the total axial strain experienced by the suspension. This stipulates that the spatial evolution of a fluctuation in the concentration of particles in the flowing suspension, or the width of the mixing zone between two regions of different concentrations in the tube will be independent of the suspension velocity in the tube. A second interesting feature in particulate dispersion is that the effective velocity of the particulate phase is concentration-dependent, which, by itself (i.e. without considering Taylor dispersion), can produce either sharpening or relaxation of concentration gradients. In particular, shocks with positive concentration gradients along the flow direction can asymptotically evolve into time-independent distributions in an appropriately chosen frame of reference, and concentration pulses relax asymmetrically. These trends are contrasted with those expected from the classical problem of Taylor dispersion of a passive tracer in the same geometry. The results in this paper are especially relevant for suspension flows through microfluidic geometries, where the induction lengths for shear-induced migration are short.

scholarly journals CT2A Cell Viability Modulated by Electromagnetic Fields at Extremely Low Frequency under No Thermal Effects

2019 ◽  
Vol 21 (1) ◽  
pp. 152 ◽  
Author(s):  
Olga García-Minguillán ◽  
Raquel Prous ◽  
Maria del Carmen Ramirez-Castillejo ◽  
Ceferino Maestú
Keyword(s):  
Cell Viability ◽  
Frequency Dependence ◽  
Electromagnetic Fields ◽  
Thermal Effects ◽  
Low Frequency ◽  
Human Beings ◽  
Cellular Mechanisms ◽  
Low Frequencies ◽  
Hsp90 Expression

The effects produced by electromagnetic fields (EMFs) on human beings at extremely low frequencies (ELFs) have being investigated in the past years, across in vitro studies, using different cell lines. Nevertheless, the effects produced on cells are not clarified, and the cellular mechanisms and cell-signaling processes involved are still unknown. This situation has resulted in a division among the scientific community about the adequacy of the recommended level of exposure. In this sense, we consider that it is necessary to develop long-term exposure studies and check if the recommended levels of EMFs are under thermal effects. Hence, we exposed CT2A cells to different EMFs at different ELFs at short and long times. Our results showed frequency dependence in CT2A exposed during 24 h to a small EMF of 30 μT equal to those originated by the Earth and frequency dependence after the exposure during seven days to an EMF of 100 µT at different ELFs. Particularly, our results showed a remarkable cell viability decrease of CT2A cells exposed to EMFs of 30 Hz. Nevertheless, after analyzing the thermal effects in terms of HSP90 expression, we did not find thermal damages related to the differences in cell viability, so other crucial cellular mechanism should be involved.

scholarly journals A new shielding effectiveness measurement method based on a skin-effect transmission line coupler

2007 ◽  
Vol 5 ◽  
pp. 37-42 ◽  
Author(s):  
T. Kleine-Ostmann ◽  
K. Münter ◽  
T. Schrader
Keyword(s):  
Transmission Line ◽  
Cross Section ◽  
Measurement Method ◽  
Skin Effect ◽  
Test Material ◽  
Shielding Effectiveness ◽  
Scattering Parameters ◽  
Low Frequencies ◽  
Outer Conductor ◽  
Effectiveness Measurement

Abstract. We propose a new convenient material shielding effectiveness measurement method based on a skin-effect transmission line coupler. The method is somewhat similar to the arrangement with two coupled TEM cells known from literature. The transmission line coupler consists of a pair of identical transmission line 2-port devices. Each device contains a coaxial waveguide, with a circular inner conductor and an outer conductor having a square cross section. One side of the outer conductor is left completely open as a slot. The slot is surrounded by a large metal housing to contact the two halves. As a measure for the shielding effectiveness the coupling between the two devices is measured in terms of scattering parameters after the test material is brought between the two halves. The devices can be used in a range from low frequencies to a few GHz.

Saint-Venant Decay Rates for the Rectangular Cross Section Rod

2004 ◽  
Vol 71 (3) ◽  
pp. 429-433 ◽  
Author(s):  
N. G. Stephen ◽  
P. J. Wang
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Transfer Matrix ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Decay Rates ◽  
Elastic Rod ◽  
Cross Sectional ◽  
Element Transfer

A finite element-transfer matrix procedure developed for determination of Saint-Venant decay rates of self-equilibrated loading at one end of a semi-infinite prismatic elastic rod of general cross section, which are the eigenvalues of a single repeating cell transfer matrix, is applied to the case of a rectangular cross section. First, a characteristic length of the rod is modelled within a finite element code; a superelement stiffness matrix relating force and displacement components at the master nodes at the ends of the length is then constructed, and its manipulation provides the transfer matrix, from which the eigenvalues and eigenvectors are determined. Over the range from plane stress to plane strain, which are the extremes of aspect ratio, there are always eigenmodes which decay slower than the generalized Papkovitch-Fadle modes, the latter being largely insensitive to aspect ratio. For compact cross sections, close to square, the slowest decay is for a mode having a distribution of axial displacement reminiscent of that associated with warping during torsion; for less compact cross sections, slowest decay is for a mode characterized by cross-sectional bending, caused by self-equilibrated twisting moment.

The Acoustical Impedance at the Junction of Non-Coaxial Cylindrical Ducts

1992 ◽  
Vol 11 (4) ◽  
pp. 114-123 ◽  
Author(s):  
Keith S. Peat
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Plane Waves ◽  
Low Frequency ◽  
Evanescent Waves ◽  
Wave Analysis ◽  
Cross Sectional ◽  
Low Frequencies ◽  
Duct Systems

At low frequencies, only plane waves can continuously propagate along uniform ducts, but evanescent, non-planar waves arise from discontinuities in the duct cross-section. The effect of these evanescent waves can be considered as an acoustical impedance to the propagation of plane waves. It is then possible to increase the accuracy of low frequency plane-wave analysis of duct systems with cross-sectional discontinuities, by inclusion of these impedance corrections. This paper considers the derivation of the acoustical impedance at the junction of non-coaxial circular ducts, a common feature within silencer systems.

A Symmetry Property of Transfer Matrices

1969 ◽  
Vol 73 (704) ◽  
pp. 686-688
Author(s):  
D. S. Whitehead
Keyword(s):  
Transfer Matrix ◽  
Cross Section ◽  
State Vector ◽  
Turbine Blades ◽  
Axial Compressor ◽  
The State ◽  
Compressor Blades ◽  
Turbo Generator ◽  
The Matrix ◽  
Propeller Blades

The transfer matrix method of vibration analysis is widely used for the calculation of the natural frequencies of turbo-generator rotors, and of propeller blades, axial compressor blades, turbine blades, and helicopter rotors. A comprehensive account of the method has been given by Pestel and Leckie. The basis of the method is to deine a state vector, which gives all the generalised displacements and forces at a given cross-section of the system. The state vector at one cross-section is then related to the state vector at a neighbouring cross-section by means of a transfer matrix. It is found that, by a suitable choice of the order and signs of the elements of the state vector, the transfer matrix can in many cases be made symmetrical about the secondary diagonal; that is the diagonal running from the top right corner to the bottom left corner of the matrix and is also often called the “cross diagonal”.

Excimer laser-assisted etching of polysilicon at 193 nm

1987 ◽  
Vol 2 (6) ◽  
pp. 895-901 ◽  
Author(s):  
M. D. Armacost ◽  
S. V. Babu ◽  
S. V. Nguyen ◽  
J. F. Rembetski
Keyword(s):  
Gas Phase ◽  
Excimer Laser ◽  
Cross Section ◽  
Thermal Effects ◽  
Etch Rate ◽  
Sem Analysis ◽  
Surface Roughening ◽  
193 Nm ◽  
Limiting Value ◽  
Scanning Electron

Excimer laser-assisted etching of polysilicon at 193 nm was studied in the presence of CF3Br, CF2Cl2, and NF3. In the presence of 193 nm radiation, CF3Br showed some propensity to etch polysilicon, while CF2Cl2 did not show any appreciable etching. In the presence of NF3, maximum etch rates of 0.6 Å/pulse were obtained for pressures greater than 500 Torr and fluences exceeding 200 mJ/(cm2 pulse). The etch rate increased with both fluences and pressure to a limiting value of 0.6 Å/pulse. An adsorptive etch mechanism was proposed, where NF3 molecules diffuse to the surface, adsorb, and then react after absorbing laser radiation. Thermal effects enhance this process and appear to dominate at lower pressures (<400 Torr) and higher fluences. Etching caused by the gas phase formation of F atoms is minimal due to the low absorption cross section of NF3 at 193 nm. Etching of submicron profiles in polysilicon was also examined. Polysilicon samples masked by patterned SiO2 were exposed to NF3 and 193 nm ArF radiation. Subsequent scanning electron microscopy (SEM) analysis demonstrated directional etching with some surface roughening.

Numerical analysis of the transmission loss of dissipative mufflers with polygonal cross-section

2021 ◽  
Vol 263 (3) ◽  
pp. 3108-3117
Author(s):  
Thomas Geyer ◽  
Christopher Mai ◽  
Anna-Sophia Henke
Keyword(s):  
Cross Section ◽  
Transmission Loss ◽  
Broadband Noise ◽  
The Finite Element Method ◽  
Practical Application ◽  
Cross Sectional ◽  
Low Frequencies ◽  
Maximum Transmission ◽  
Calculation Procedures ◽  
Good Agreement

Dissipative mufflers are often used for the reduction of broadband noise transmitted in ducts. Many common calculation procedures for the transmission loss of such mufflers require conventional shapes like rectangular or circular cross-sectional areas. In an effort to analyze the effect of the cross-sectional area of dissipative mufflers on the resulting noise reduction, the transmission loss of axially uniform mufflers with polygonal cross-sectional areas was investigated using the finite element method. The mufflers are designed to have the same open area, and hence in a practical application would lead to a similar pressure drop. The results were compared to those obtained with the well known approximative method of Piening. Good agreement between simulation and estimation was found regarding basic trends at low frequencies, while notable differences were revealed regarding the maximum transmission loss.

Sign in / Sign up

Export Citation Format

Share Document