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3 edition of One-dimensional wave propagation in rods of variable cross section found in the catalog.

One-dimensional wave propagation in rods of variable cross section

One-dimensional wave propagation in rods of variable cross section

a WKBJ solution

  • 367 Want to read
  • 26 Currently reading

Published by National Aeronautics and Space Administration, Scientific and Technical Information Office, For sale by the National Technical Information Service] in [Washington, DC], [Springfield, Va .
Written in English

    Subjects:
  • Piezoelectric transducers.,
  • Ultrasonics.

  • Edition Notes

    Other titlesOne dimensional wave propagation in rods of variable cross section.
    StatementSimeon C. U. Ochi and James H. Williams, Jr.
    SeriesNASA contractor report -- 4086., NASA contractor report -- NASA CR-4086.
    ContributionsWilliams, James H., United States. National Aeronautics and Space Administration. Scientific and Technical Information Office.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL17659424M

    The problem of motion of the rope of variable length consists of solving the boundary value problem with a variable boundary for the one-dimensional wave equation. A change of the rope length is caused by the force acting at the upper cross section of the rope. Studying the wave propagation . in the wave velocity. The purpose of the paper is to determine the propagation velocity of an elastic wave in short rods. Since the wave velocity is increase in short rod, we can use the fact for the acoustic testing. For example, the phenomenon allows us to precise the distance to the defect in small area near the rod boundary.

    Thus the one-dimensional theory for the propagation of disturbances along the rod is governed by the equations () and (). The last term in () represents the effect of the cross-sectional area change, and when S - const. shown in the introduction. In this section we derive homogenized equations including terms up to O(4), which include dispersive terms. Additional terms up to O(6) are derived for a plane wave propagating in the x-direction. Our approach is based on the technique used in [3] for one-dimensional wave propagation.

    Create a job named Bar, and enter Stress wave propagation in a bar (SI units) for the job description. Submit the job, and monitor the results. If any errors are encountered, correct the model and rerun the simulation. Be sure to investigate the cause of any warning messages and take appropriate action; recall that some warning messages can be ignored safely while others require corrective action.   Energy Propagation Velocity and Group Velocity Love Waves Waves in Plane Strain in an Elastic Layer The Rayleigh-Lamb Frequency Spectrum Waves in a Rod of Circular Cross Section The Frequency Spectrum of the Circular Rod of Solid Cross Section Torsional Waves Longitudinal Waves Flexural Book Edition: 1.


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One-dimensional wave propagation in rods of variable cross section Download PDF EPUB FB2

Description As an important step in the characterization of a particular dynamic surface displacement transducer (IQI Model ), a one-dimensional wave propagation in isotropic nonpiezoelectric and piezoelectric rods of variable cross section are : Simeon C.

Ochi, James H. Williams. The wave finite element method (WFEM) is developed to simulate the wave propagation in one-dimensional problem of nonhomogeneous linear micropolar rod of variable cross-section.

For this purpose, two kinds of waves with fast and slow velocities are detected. For micropolar medium, an additional rotational degree of freedom (DOF) is considered besides the classical elasticity’s by: 5. The wave finite element method (WFEM) is developed to simulate the wave propagation in one-dimensional problem of nonhomogeneous linear micropolar rod of variable cross-section Cited by: 5.

Stress Wave Propagation Analysis in One-Dimensional Micropolar Rods with Variable Cross-Section Using Micropolar Wave Finite Element Method Mirzajani, Mohsen Khaji, Naser. Title: Stress Wave Propagation Analysis in One-Dimensional Micropolar Rods with Variable Cross-Section Using Micropolar Wave Finite Element Method.

Wave propagation in rods with an exponentially varying cross-section { modelling and experiments Micha l K Kalkowski, Jen M Muggleton and Emiliano Rustighi University of Southampton, High eld, Southampton SO17 1BJ, UK E-mail: [email protected] Abstract. In this paper we analyse longitudinal wave propagation in exponentially tapered.

Propagation of compression waves in elastic rods of variable cross section. “One-dimensional wave propagation through a short discontinuity,” J. Acoust. Soc. Am.,45, I.G.

Propagation of compression waves in elastic rods of variable cross section. Soviet Applied Mechan – Author: I.

Filippov. A numerical procedure to study one-dimensional waves in solids is considered in application to longitudinal loading of elastic-plastic rods of a variable cross section. The procedure assumes direct mathematical modelling of mechanical by: 6. Discussion: “Elastic Wave Propagation in Rods of Arbitrary Cross Section” (Rosenfeld, R.

L., and Miklowitz, Julius,ASME J. Appl. Mech., 32, pp. –) J. Appl. Mech (June, ) Dynamic Bond Stress in a Composite Structure Subjected to a Sudden Pressure RiseCited by: 2. Analytical solutions for vibration analysis of the rods with variable cross section are in general complex and in many cases impossible.

On the other hand, approximate methods such as the weighted residual, Rayleigh-Ritz and finite difference methods also have their own shortcomings such as a limited number of natural frequencies and : M.

Khoshbayani Arani, N. Rasekh Saleh, M. Nikkhah Bahrami. Get this from a library. One-dimensional wave propagation in rods of variable cross section: a WKBJ solution. [Simeon C U Ochi; James H Williams; United States. National Aeronautics and Space Administration.

Scientific and Technical Information Office.]. Introduction. The wave equation is a partial differential equation that may constrain some scalar function u = u (x 1, x 2,x n; t) of a time variable t and one or more spatial variables x 1, x 2, x quantity u may be, for example, the pressure in a liquid or gas, or the displacement, along some specific direction, of the particles of a vibrating solid away from their resting.

In the above section, the transfer matrices for the rod with variable cross-section have been derived from the equations of motion of the rod based upon three different wave theories, and the propagation characteristics of the longitudinal wave have also been discussed briefly by analyzing the eigenvalues of these transfer by: 2 Chapter 1.

Elementary solutions of the classical wave equation The classical wave equation The classical Electro Magnetic eld is described by the classical Wave Equation. A one dimensional mechanical equivalent of this equation is depicted in the gure below.

In the present study, the wave propagation equation of SH waves propagating in waveguide bars of rectangular cross-section is derived theoretically. The equation depicts that the SH waves can go.

The mathematics of PDEs and the wave equation spatial variables, and t for the the time variable. Various physical quantities will be measured by some function u = u(x,y,z,t) which could depend on all three spatial variable and time, In the one dimensional wave equation, when c is a constant, it is interesting to observe thatCited by: 2.

ONE-DIMENSIONAL WAVE PROPAGATION ONE-DIMENSIONAL WAVE PROPAGATION This document describes an example that has been used to verify the wave propagation in a one dimensional soil column.

Used version: •PLAXIS 2D - Dynamics Module - Version •PLAXIS 3D - Dynamics Module - Version The Wave Finite Element Method (WFEM) is developed to simulate the wave propagation in one-dimensional problem of nonhomogeneous linear micropolar rod of variable cross section.

In this paper vibration as propagating waves is used to calculate frequencies of exponentially varying cross‐section rods with various boundary conditions.

From wave standpoint, vibrations propagate, reflect and transmit in structures. The propagation and reflection matrices are combined to provide a concise and systematic approach to free longitudinal vibration analysis of Cited by: Wave propagation in rods with an exponentially varying cross-section modelling and experiments Micha K Kalkowski, Jen M Muggleton and Emiliano Rustighi-Recent citations Almost Complete Transmission of Low Frequency Waves in a Locally Damaged Elastic Waveguide S.

Nazarov-The asymptotics of natural oscillations of a long two-dimensional Cited by:. ONE DIMENSIONAL PLANE WAVE PROPAGATION IN PIEZOELECTRIC ROD OF VARIABLE CROSS SECTION I In this section, a one dimensional longitudinal wave equation is derived for an ~ isotropic piezoelectric rod of variable cross section.

The momentum equation (see eqn.(1)) is unaffected by the piezoelectric effect.Abstract. It is shown that when an acceleration wave propagates in hyperelastic rod with slowly varying cross-section, the transport equation for the wave intensity is a generalized Riccati equation.

The three coefficients in the equation all depend on the material properties, but only the coefficient of the quadratic term is independent of the effect of area by: An example using the one-dimensional wave equation to examine wave propagation in a bar is given in the following problem.

Given: A homogeneous, elastic, freely supported, steel bar has a length of ft. (as shown below). A stress wave is induced on one end of the bar using an instrumented.