ON THE PROPAGATION OF LONGITUDINAL WAVES IN CYLINDRICAL RODS

1931 ◽  
Vol 5 (2) ◽  
pp. 149-155 ◽  
Author(s):  
R. Ruedy
Keyword(s):  
Coupled System ◽  
Theory Of Elasticity ◽  
Radial Vibrations ◽  
Low Frequencies ◽  
Longitudinal Waves ◽  
Resonance Frequencies ◽  
Solid Circular Cylinder ◽  
Velocity Equation ◽  
Set Up ◽  
Degree Of Coupling

The solution of the velocity equation obtained by Pochhammer on the basis of the mathematical theory of elasticity is determined for the propagation of longitudinal waves of any frequency in a long solid circular cylinder of any diameter. For a given frequency a large number of solutions may be obtained, but when the condition is imposed that for low frequencies the velocity must gradually assume the value found by experiment, a single value is obtained for each frequency. The velocity decreases with increasing frequency, so that, for a cylinder of finite length, the resonance frequencies come closer and closer together. It is also necessary to take into account, however, that in a solid rod longitudinal waves are accompanied by radial vibrations of the particles, and that a cylindrical rod has, regardless of its length, a series of natural frequencies for radial waves, so that for wave-lengths comparable with the diameter of the tube a coupled system of oscillations is set up. The resonant frequencies of such a system depend on the degree of coupling.

ANOMALOUS DISPERSION OF SOUND IN SOLID CYLINDRICAL RODS

1935 ◽  
Vol 13a (1) ◽  
pp. 10-15 ◽  
Author(s):  
R. Ruedy
Keyword(s):  
Mutual Coupling ◽  
Radial Component ◽  
Radial Motion ◽  
Coupled Systems ◽  
Radial Vibration ◽  
Longitudinal Waves ◽  
Velocity Equation ◽  
Hollow Cylinders ◽  
Velocity Of Propagation ◽  
Set Up

The deviation of the overtones from whole multiples of the fundamental note when pure longitudinal waves are set up in a cylindrical rod, one to a few centimetres in thickness, is accounted for to within less than 1% by the drop in the velocity of propagation of longitudinal waves with increasing frequency due to radial motion in the rod. The radial component present in vibrating solid or hollow cylinders determines a second solution of the velocity equation which starts near the resonance frequency of the radial vibration. Although radial motion can take place free from longitudinal components, so that no mutual coupling need exist between the two types of vibration, the equation for thin rods can within certain frequency ranges be reduced to the frequency relations valid for coupled systems.

scholarly journals Employing electro-mechanical analogies for co-resonantly coupled cantilever sensors

2016 ◽  
Vol 5 (2) ◽  
pp. 245-259 ◽  
Author(s):  
Julia Körner ◽  
Christopher F. Reiche ◽  
Bernd Büchner ◽  
Thomas Mühl ◽  
Gerald Gerlach
Keyword(s):  
Harmonic Oscillator ◽  
Electric Circuit ◽  
Coupled System ◽  
Measured Data ◽  
Circuit Model ◽  
Good Representation ◽  
Analytical Treatment ◽  
Resonance Frequencies ◽  
Set Up ◽  
Coupled Harmonic Oscillator

Abstract. Understanding the behaviour of mechanical systems can be facilitated and improved by employing electro-mechanical analogies. These analogies enable the use of network analysis tools as well as purely analytical treatment of the mechanical system translated into an electric circuit. Recently, we developed a novel kind of sensor set-up based on two coupled cantilever beams with matched resonance frequencies (co-resonant coupling) and possible applications in magnetic force microscopy and cantilever magnetometry. In order to analyse the sensor's behaviour in detail, we describe it as an electric circuit model. Starting from a simplified coupled harmonic oscillator model with neglected damping, we gradually increase the complexity of the system by adding damping and interaction elements. For each stage, various features of the coupled system are discussed and compared to measured data obtained with a co-resonant sensor. Furthermore, we show that the circuit model can be used to derive sensor parameters which are essential for the evaluation of measured data. Finally, the much more complex circuit representation of a bending beam is discussed, revealing that the simplified circuit model of a coupled harmonic oscillator is a very good representation of the sensor system.

Upgraded Railway Front Searchlight Design Plastic Deformations by its Vibrations with Resonance Frequencies

2016 ◽  
Vol 684 ◽  
pp. 111-119 ◽  
Author(s):  
Stanislav Rafaelevich Abulkhanov ◽  
Dmitrii Sergeevich Goryainov
Keyword(s):  
Natural Frequencies ◽  
Ansys Software ◽  
Software Environment ◽  
Low Frequencies ◽  
Plastic Deformations ◽  
Vibration Resistance ◽  
First Case ◽  
Resonance Frequencies ◽  
The One ◽  
Electric Lamp

Natural frequencies of the four upgraded front searchlight designs were received in ANSYS software environment. In the first case serial front searchlight incandescent electric lamp was replaced by a LED group which was mounted on the one-piece cylinder backing. The second front searchlight design had the backing which was upgraded by a radial ribs and concentric rigidity ferrules. Analyze of the backing deformation character by vibrations with the natural frequencies established a number of design solutions which make it possible to raise front searchlight vibration resistance. By the front searchlight model were established that the natural frequencies of the searchlight with the one-piece backing appertain to the whole range of the train vibrations. Natural frequencies of the backing with perforation, rigidity ferrules, and radial ribs appertain to the low frequencies of the railway locomotive vibrations spectrum. On basis of devised methodology of analyze of the deformation and natural frequencies of the surface carrying a LED group the vibration-proof searchlight design was introduced and researched.

Optimization of spiral-shaped piezoelectric energy harvester using Taguchi method

2017 ◽  
Vol 24 (19) ◽  
pp. 4484-4491 ◽  
Author(s):  
R Tikani ◽  
L Torfenezhad ◽  
M Mousavi ◽  
S Ziaei-Rad
Keyword(s):  
Taguchi Method ◽  
Energy Harvester ◽  
Piezoelectric Materials ◽  
Mechanical Energy ◽  
Experimental Investigations ◽  
Optimum Level ◽  
Low Frequencies ◽  
Piezoelectric Energy ◽  
Resonance Frequencies ◽  
Design Values

Nowadays, environmental energy resources, especially mechanical vibrations, have attracted the attention of researchers to provide energy for low-power electronic circuits. A common method for environmental mechanical energy harvesting involves using piezoelectric materials. In this study, a spiral multimode piezoelectric energy harvester was designed and fabricated. To achieve wide bandwidth in low frequencies (below 15 Hz), the first three resonance frequencies of the beam were designed to be close to each other. To do this, the five lengths of the substrate layer were optimized by the Taguchi method, using an L27 orthogonal array. Each experiment of the Taguchi method was then simulated in ANSYS software. Next, the optimum level of each design variable was obtained. A test rig was then constructed based on the optimum design values and some experimental investigations were conducted. A good correlation was observed between measured and the finite element results.

VELOCITY OF SOUND IN CYLINDRICAL RODS

1931 ◽  
Vol 5 (6) ◽  
pp. 619-624 ◽  
Author(s):  
Geo. S. Field
Keyword(s):  
Velocity Of Sound ◽  
Low Frequencies ◽  
Longitudinal Waves ◽  
Experimental Knowledge ◽  
Close Analogy ◽  
Theory And Experiment

The experimental knowledge so far available of the velocity of longitudinal waves in cylindrical rods is reviewed, and it is shown that a close analogy most probably exists between waves in cylinders of liquid and in solid rods. The theory for rods due to Pochhammer is considered with reference to a specific case for which experimental velocities have been determined, and it is shown that the agreement at low frequencies is good. At higher frequencies, however, theory and experiment differ widely.

The Study on Harmonic Vibration of Drill String in Horizontal Well

2010 ◽  
Vol 139-141 ◽  
pp. 2397-2400
Author(s):  
Chun Jie Han ◽  
Tie Yan
Keyword(s):  
Horizontal Well ◽  
Drill String ◽  
Harmonic Vibration ◽  
Well Drilling ◽  
Harmonic Vibrations ◽  
String Vibrations ◽  
Resonance Frequencies ◽  
Set Up ◽  
Drill Tool ◽  
Modal Vibration

During exploitation of horizontal well drilling engineering, the problem of drill string failure is very serious, there are many reasons, and drill string vibrations are main reasons. In this paper drill string of horizontal well is object being studied. The models about various vibrations are set up. The vibration rule of drill string is obtained under different situation; the axial and lateral frequency of drill string vibration in free state is studied. The analysis of modal vibration of drill string is the basis of the analysis of harmonic vibration of drill string. The harmonic vibrations rules of drill string of horizontal well are studied. All sorts of resonance frequencies are obtained practicability. This study can prove basic method for optimizing drill tool of horizontal well and reducing drill string failure.

SPECTRAL PROPERTIES OF AN ELASTIC ROD-SPRING COUPLED SYSTEM IMMERSED IN A FLUID

1992 ◽  
Vol 02 (04) ◽  
pp. 441-460 ◽  
Author(s):  
J. SANCHEZ-HUBERT ◽  
S. BÉRÉTÉ ◽  
J. PLANCHARD
Keyword(s):  
Heat Exchangers ◽  
Spectral Properties ◽  
Nuclear Reactor ◽  
Dynamical Behavior ◽  
Coupled System ◽  
Elastic Tube ◽  
Elastic Rod ◽  
Resonance Frequencies ◽  
Continuous Material ◽  
Very High

The study of vibrations of elastic tube bundles immersed in a fluid is very important in Engineering, for example concerning the dynamical behavior of heat exchangers, nuclear reactor cores, etc. This paper is concerned with the investigation of the resonance frequencies when the number of rods is very high. That requires us to use the homogenization technique for modelling this coupled system by an equivalent continuous material. We then show that this equivalent system may have an essential spectrum.

scholarly journals Vibro-acoustic analysis of a trapezoidal cavity with a clamped flexible wall

2018 ◽  
Vol 37 (4) ◽  
pp. 801-815 ◽  
Author(s):  
Yuan Wang ◽  
Jianrun Zhang ◽  
Xinzhou Zhang ◽  
Bo Wu
Keyword(s):  
Acoustic Analysis ◽  
Coupled Model ◽  
Coupled System ◽  
Coupling Theory ◽  
Incident Plane ◽  
Resonance Frequencies ◽  
Modal Coupling ◽  
Cavity Coupling ◽  
Flexible Wall ◽  
Matching Degree

The coupled model between trapezoidal cavity and its clamped flexible wall is developed using classical modal coupling theory. Based on the coupled model, the resonance frequencies of coupled system are obtained and compared with the corresponding uncoupled one. Meanwhile, the reason for the variation of resonance frequencies of coupled system modes is analyzed in detail. Then, the response of coupled system is investigated using the acoustic potential energy in the cavity and panel vibration kinetic energy when it is excited by an incident plane wave outside of the cavity. Coupling coefficient between trapezoidal cavity and its clamped flexible wall is proposed to assess the modal matching degree between them. It is shown that the coupling selection is not satisfied except in the axis direction which is parallel to the inclined wall. In addition, a rectangular cavity with a clamped flexible wall is also considered and compared with that of the trapezoidal one.

Elasto-Dynamic Behavior of a Two-Dimensional Square Lattice With Entrained Fluid II: Microstructural and Homogenized Models

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Vladimir Dorodnitsyn ◽  
Alessandro Spadoni
Keyword(s):  
Relative Density ◽  
Coupled System ◽  
Element Model ◽  
Square Lattice ◽  
Porous Solids ◽  
Cellular Solid ◽  
Resonance Frequencies ◽  
Shear Modes ◽  
Structural Deformations ◽  
Analysis Of Dispersion

This paper presents a detailed study of the pressure waves and effective mechanical properties of a closed-cell cellular solid with entrained fluid. Plane-harmonic-waves are analyzed in a periodic square with a finite-element model of a representative-volume element, which explicitly considers fluid-structure interactions, structural deformations, and the fluid dynamics of entrained fluid. The wall, cavity, and coupled-system resonance frequencies are identified as key parameters that describe the propagation characteristics. A tube-piston model based on computed microstructural deformations allows us to determine the effective stiffness tensor of an equivalent continuum at the macroscale. The analysis of dispersion surfaces indicates a single isotropic pressure mode for frequencies below resonance of the lattice walls, unlike Biot's theory which predicts two pressure modes. Shear modes are instead strongly anisotropic for all values of relative density ρ* describing both cellular ρ*<0.3 and porous solids ρ*≥0.3. The dependence of the pressure wave phase velocity on the relative density is analyzed for varying properties of the entrained fluid. Depending on the relative density and mass coupling of the solid and fluid phases, the microstructural deformations can be of three types: bending, through-the-thickness, and the combination of the two. For heavy and stiff entrained fluid, the bending regime is confined to extremely small values of relative density, whereas for light fluid such as a gas, deformations are of the bending-type for ρ*<0.1. Through-the-thickness deformations appear only for the heavy entrained fluid for large values of ρ*.

Modelling a Structural-Acoustic Coupled System with an Equivalent Lumped Parameter Mechanical System

1999 ◽  
Vol 121 (4) ◽  
pp. 453-459 ◽  
Author(s):  
S. M. Kim ◽  
M. J. Brennan
Keyword(s):  
Coupled System ◽  
Acoustic Mode ◽  
Physical Parameters ◽  
Acoustic System ◽  
Acoustic Modes ◽  
Lumped Parameter ◽  
Resonance Frequencies ◽  
Mechanical Models ◽  
Equivalent Mass ◽  
Physical Insight

This paper describes the way in which a structural acoustic coupled system can be modelled using an equivalent lumped parameter mechanical model. The impedance-mobility approach is first used to model the system, and by relating the physical parameters to equivalent mass and stiffness, lumped parameter models can be derived provided that damping in the acoustic system is neglected in all modes, but the first (zero order) mode. A limitation of this approach, however, is that these simple mechanical models formulated in terms of the uncoupled structural and acoustic modes are only possible for either a single structural mode coupled to many acoustic modes, or a single acoustic mode coupled to many structural modes. These models facilitate physical insight into the dynamic behavior of a lightly-damped structural-acoustic system at frequencies close to the resonance frequencies of the coupled system.

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