scholarly journals Oscillations of elastic plate, located at the end of semi-infinite cylindrical acoustic waveguide

2021 ◽  
pp. 104-111
Author(s):  
В.Д. Лукьянов ◽  
Л.В. Носова ◽  
Г.А. Лебедев ◽  
С.В. Попков
Keyword(s):  
Elastic Plate ◽  
Numerical Study ◽  
Exact Analytical Solution ◽  
Cylindrical Symmetry ◽  
Acoustic Medium ◽  
Compressible Medium ◽  
Plate Edge ◽  
Resonant Frequencies ◽  
Acoustic Waveguide ◽  
Nodal Lines

Получено точное аналитическое решение задачи о гармонических изгибных колебаниях тонкой круглой упругой пластины, расположенной в торце полубесконечного цилиндрического акустического волновода. Кромка пластины жестко заделана в стенку волновода. Волновод с жестким корпусом заполнен идеальной сжимаемой акустической средой. Колебания пластины возбуждаются набегающими на неё нормальными волнами волновода, распределение акустического давления для которых имеет цилиндрическую симметрию. Проведено численное исследование смещения пластины на разных частотах возбуждения. Показано, что наличие сжимаемой среды существенно влияет на форму колебаний пластины. Совместные колебания акустической среды и упругой пластины носят резонансный характер. На резонансных частотах имеет место значительное увеличение амплитуды колебаний пластины. На форму колебания пластины влияют как распространяющиеся, так и неоднородные нормальные волны в волноводе, что приводит к увеличению узловых линий в распределении смещения пластины. An exact analytical solution to the problem of harmonic bending oscillations of a thin round elastic plate located at the end of a semi-infinite cylindrical acoustic waveguide has been obtained. Plate edge is rigidly embedded in waveguide wall. The waveguide with rigid housing is filled with an ideal compressible acoustic medium. The plate oscillations are excited by the normal waveguide waves running to the plate. The distribution of acoustic pressure for waves has cylindrical symmetry. Numerical study of plate displacement at different excitation frequencies was carried out. It has been shown that the presence of a compressible medium significantly affects the waveform of the plate oscillation. Joint oscillations of acoustic medium and elastic plate are resonant. There is a significant increase in amplitude of plate oscillations at resonant frequencies. The waveform of the plate oscillation is influenced by both propagating and inhomogeneous normal waves in the waveguide, which leads to an increase in the nodal lines in the displacement distribution of the plate.

scholarly journals A numerical study for convection in a cylindrical model with continuously varying viscosity

1996 ◽  
Vol 39 (3) ◽  
Author(s):  
F. Fanucci ◽  
A. Megna ◽  
S. Santini ◽  
F. Vetrano
Keyword(s):  
Viscosity Solutions ◽  
Numerical Study ◽  
Viscosity Coefficient ◽  
Cylindrical Symmetry ◽  
The Earth ◽  
Realistic Representation ◽  
Convective Motions ◽  
Constant Viscosity ◽  
Varying Viscosity ◽  
Better Than

In the framework of a cylindrical symmetry model for convective motions in the asthenosphere, a new profile for the viscosity coefficient depending on depth is suggested here. The numerical elaboration of the above mentioned model leads to interesting results which fit well with experimental observations. In particular these continuously varying viscosity solutions probably describe the convective motions within the Earth better than simple constant viscosity solutions. Consequently the temperature values seem to be a realistic representation of the possible thermal behaviour in the upper mantle.

scholarly journals Self-Consistent Models for Small Photospheric Flux Tubes

1983 ◽  
Vol 102 ◽  
pp. 67-71
Author(s):  
W. Deinzer ◽  
G. Hensler ◽  
D. Schmitt ◽  
M. Schüssler ◽  
E. Weisshaar
Keyword(s):  
Magnetic Field ◽  
Flux Tube ◽  
Energy Transport ◽  
Numerical Study ◽  
Momentum Equation ◽  
Mhd Equations ◽  
Compressible Medium ◽  
Solar Photosphere ◽  
Slab Geometry ◽  
Element Technique

We give a short summary of some results of a numerical study of magnetic field concentrations in the solar photosphere and upper convection zone. We have developed a 2D time dependent code for the full MHD equations (momentum equation, equation of continuity, induction equation for infinite conductivity and energy equation) in slab geometry for a compressible medium. A Finite-Element-technique is used. Convective energy transport is described by the mixing-length formalism while the diffusion approximation is employed for radiation. We parametrize the inhibition of convective heat flow by the magnetic field and calculate the material functions (opacity, adiabatic temperature gradient, specific heat) self-consistently. Here we present a nearly static flux tube model with a magnetic flux of ∼ 1018 mx, a depth of 1000 km and a photospheric diameter of ∼ 300 km as the result of a dynamical calculation. The influx of heat within the flux tube at the bottom of the layer is reduced to 0.2 of the normal value. The mass distribution is a linear function of the flux function A: dm(A)/dA = const. Fig. 1 shows the model: Isodensities (a), fieldlines (b), isotherms (c) and lines of constant continuum optical depth (d) are given. The “Wilson depression” (height difference between τ = 1 within and outside the tube) is ∼ 150 km and the maximum horizontal temperature deficit is ∼ 3000 K. Field strengths as function of x for three different depths and as function of depth along the symmetry axis are shown in (e) and (f), respectively. Note the sharp edge of the tube.

Numerical Study of a 3-Axis Stage for Application of Fast Tool Servo

2014 ◽  
Vol 625 ◽  
pp. 219-223 ◽  
Author(s):  
Yung Tien Liu ◽  
Bo Jheng Li
Keyword(s):  
Numerical Study ◽  
Fast Response ◽  
Maximum Deviation ◽  
Stress And Strain ◽  
Fast Tool Servo ◽  
The Finite Element Method ◽  
Resonant Frequencies ◽  
Calculation Results ◽  
Flexural Hinges ◽  
Maximum Stresses

In this paper, a 3-axis stage consisted of a XY stage and Z-axis feeding tool holder is proposed for the application of fast tool servo (FTS). The XY stage actuated by six piezoelectric (PZT) actuators is designed with symmetric flexural hinges featuring low interference motions, high stiffness, and fast response. Numerical design using the finite element method (FEM) was conducted to investigate the steady characteristics (displacement, stiffness, stress, and strain) and dynamic characteristic of resonance frequency. According to calculation results, the major characteristics obtained along XYZ axes are as follows: displacements induced are 10.06, 10.28, and 20.31 μm due to the applied voltage being 50 V; stiffness are 112.84, 110.31, and 223.34 kN/mm; the maximum stresses at the hinges are 9.78, 10.9, and 100.56 N/mm2, which are lower than the allowable stress of aluminum used; and the resonant frequencies are 1.0, 0.64, and 0.4 kHz, respectively. Experimental examinations regarding to the resonant frequencies were performed with a maximum deviation of 16% along the Z-axis compared to the simulation result. As a result of the investigation, it is expected that the 3-axis stage can be effectively applied to implement a FTS.

Investigation of Fixed-Free Annular Plate Resonant Frequency Predictions

1988 ◽  
Vol 110 (3) ◽  
pp. 408-410 ◽  
Author(s):  
Alison Flatau ◽  
G. A. Flandro ◽  
W. K. Van Moorhem
Keyword(s):  
Free Boundary ◽  
Resonant Frequency ◽  
Elastic Plate ◽  
Annular Plate ◽  
Plate Theory ◽  
Outer Radius ◽  
Resonant Frequencies ◽  
Free Boundary Conditions ◽  
Annular Plates ◽  
Analytical Frequency

Nondimensional frequency parameters for predicting the resonant frequencies of annular plates with fixed-free boundary conditions as the plate inner to outer radius ratio approaches unity have been investigated experimentally. Frequency parameters have been determined by using modal analysis to measure resonant frequencies for annular plates of varied materials, thicknesses, and with radius ratios of 0.5 to 0.9. The data are compared to two different analytical frequency predictions which have been presented as solutions for resonance of fixed-free annular plates based on classical elastic plate theory.

The Response of a Plate on an Elastic Foundation

1968 ◽  
Vol 35 (1) ◽  
pp. 186-187 ◽  
Author(s):  
J. P. Jones
Keyword(s):  
Elastic Foundation ◽  
Elastic Plate ◽  
Pressure Pulse ◽  
Specific Problem ◽  
Underground Structure ◽  
Approximate Equation ◽  
Step Function ◽  
Simple Expression ◽  
Acoustic Medium ◽  
Recent Interest

There has been much recent interest in the possibility of hardening an underground structure by means of an elastic plate placed on the ground above the structure. To obtain a simple expression for the interaction pressure between the ground and the plate, the present analysis treats the problem of a plate on top of an acoustic medium subjected to a uniformly moving pressure pulse. It is found that an approximate equation suggested by S. B. Baldorf is quite valid in the superseismic range of load speed. The specific problem of a step function loading traveling with uniform velocity, superseismic to the foundation, is treated. The extension of this problem to an actual elastic foundation is straightforward and is not treated.

Optimization of a Peristaltic Micropump with Multiple Moving Actuators

2009 ◽  
Vol 6 (4) ◽  
pp. 189-197
Author(s):  
Ravi Bhadauria ◽  
Ramana M. Pidaparti ◽  
Mohamed Gad-el-Hak
Keyword(s):  
Interaction Analysis ◽  
Numerical Study ◽  
Exact Analytical Solution ◽  
Navier Stokes ◽  
Actuation Frequency ◽  
Navier Stokes Equation ◽  
Specific Flow ◽  
Flow Rates ◽  
Fluid Analysis ◽  
Peristaltic Micropump

A design optimization based on coupled solid–fluid analysis is investigated in this paper to achieve specific flow rate through a peristaltic micropump. A micropump consisting of four pneumatically actuated nozzle/diffuser shaped moving actuators on the sidewalls is considered for numerical study. These actuators are used to create pressure difference in the four pump chambers, which in turn drives the fluid through the pump in one direction. Genetic algorithms along with artificial neural networks are used for optimizing the pump geometry and the actuation frequency. A simple example with moving walls is considered for validation by developing an exact analytical solution of the Navier–Stokes equation and comparing it with numerical simulations. Possible applications of these pumps are in microelectronics cooling and drug delivery. Based on the results obtained from the fluid–structure interaction analysis, three optimized geometries result in flow rates that match the predicted flow rates with 95% accuracy. These geometries need further investigation for fabrication and manufacturing issues.

Resonant frequencies of a combination of split rings: Experimental, analytical and numerical study

2005 ◽  
Vol 46 (5) ◽  
pp. 473-476 ◽  
Author(s):  
A. Radkovskaya ◽  
M. Shamonin ◽  
C. J. Stevens ◽  
G. Faulkner ◽  
D. J. Edwards ◽  
...  
Keyword(s):  
Numerical Study ◽  
Resonant Frequencies

Effect of an Acoustic Medium on the Dynamic Buckling of Plates

1956 ◽  
Vol 23 (2) ◽  
pp. 201-206
Author(s):  
F. L. DiMaggio
Keyword(s):  
Elastic Plate ◽  
Infinite Plate ◽  
Approximate Solutions ◽  
Dynamic Buckling ◽  
Steel Plates ◽  
Acoustic Medium ◽  
Middle Plane ◽  
Numerical Example ◽  
Compressive Stresses ◽  
Surrounding Fluid

Abstract The effect of a surrounding fluid on the dynamic buckling of an elastic plate under suddenly applied compressive stresses in its middle plane is studied. Assuming an infinite plate supported at regular intervals and a semi-infinite acoustic medium, exact and approximate solutions are obtained. By a numerical example, it is shown that for steel plates in water, with dimensions usually encountered in ship structures, the compressibility of water can be neglected.

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