Displacements and Velocities Produced by the Diffraction of a Pressure Wave by a Cylindrical Cavity in an Elastic Medium

1962 ◽  
Vol 29 (2) ◽  
pp. 385-395 ◽  
Author(s):  
M. L. Baron ◽  
R. Parnes
Keyword(s):  
Cylindrical Cavity ◽  
Integral Transform ◽  
Plane Shock ◽  
Displacement Fields ◽  
Influence Coefficients ◽  
Body Component ◽  
Cavity Boundary ◽  
Component Motion ◽  
The Mean ◽  
Integral Transform Technique

An infinitely long cylindrical cavity in an infinite elastic homogeneous and isotropic medium is enveloped by a plane shock wave whose front is parallel to the axis of the cavity. The displacement and velocity fields produced by the diffraction of the wave by the cavity are determined by means of an integral transform technique. Expressions for the radial and tangential components of the displacements and velocities are derived, and numerical results are presented for these quantities at the cavity boundary. Results for the mean (rigid-body component) motion of the cavity boundary are also presented. The problem is considered for pressure waves with a step distribution in time. The results may be used as influence coefficients to determine, by means of Duhamel integrals, the velocity and displacement fields produced by waves with time-varying pressure.

Diffraction of a Pressure Wave by a Cylindrical Cavity in an Elastic Medium

1961 ◽  
Vol 28 (3) ◽  
pp. 347-354 ◽  
Author(s):  
M. L. Baron ◽  
A. T. Matthews
Keyword(s):  
Shock Wave ◽  
Stress Field ◽  
Cylindrical Cavity ◽  
Hoop Stress ◽  
Integral Transform ◽  
Time History ◽  
Plane Shock ◽  
Influence Coefficients ◽  
History Of ◽  
Stress Concentration Factors

An infinitely long cylindrical cavity in an infinite elastic homogeneous and isotropic medium is enveloped by a plane shock wave whose front is parallel to the axis of the cavity. An integral transform technique is used to determine the stress field produced in the medium by the diffraction of the incoming shock wave by the cavity. Expressions for the radial stress σrr, the hoop stress σθθ, and the shear stress σrθ are derived as inversion integrals, and numerical results are presented for the time-history of the hoop stress σθθ at the boundary of the cavity. The amplifications of the hoop-stress concentration factors due to the dynamic loading are noted. The problem is considered for pressure waves with a step distribution in time. These results may be used as influence coefficients to determine, by means of Duhamel integrals, the stress field produced by waves with time-varying pressures.

Response of Nonlinearly Supported Spherical Boundaries to Shock Waves

1957 ◽  
Vol 24 (4) ◽  
pp. 501-505
Author(s):  
M. L. Baron
Keyword(s):  
Integral Equation ◽  
Integral Transform ◽  
Boundary Value ◽  
Acoustic Medium ◽  
Plane Shock ◽  
Linear Boundary ◽  
Influence Coefficients ◽  
Pressure Time ◽  
Elastically Supported ◽  
Integral Transform Technique

Abstract An integral transform technique is used to solve a boundary-value problem in which the partial differential equation is linear but the associated boundary condition is nonlinear. A spherical cavity in an infinite acoustic medium has an elastically supported boundary such that the pressure-displacement relation on the boundary is nonlinear. The response of the boundary to a plane shock wave which progresses across the cavity and envelops it is obtained by solving two auxiliary boundary-value problems with linear boundary conditions. Using influence coefficients obtained from these solutions, a nonlinear integral equation for the response of the actual boundary is obtained. The integral equation is solved numerically for a set of parameters, and curves for the pressure-time and displacement-time responses of the boundary are presented.

scholarly journals Computational Evaluation of Shock Wave Interaction with a Cylindrical Water Column

2021 ◽  
Vol 11 (11) ◽  
pp. 4934
Author(s):  
Viola Rossano ◽  
Giuliano De Stefano
Keyword(s):  
Shock Wave ◽  
Water Column ◽  
Wave Interaction ◽  
Navier Stokes ◽  
Plane Shock ◽  
Governing Equations ◽  
Computational Evaluation ◽  
Air Water Interface ◽  
The Mean ◽  
The Impact

Computational fluid dynamics was employed to predict the early stages of the aerodynamic breakup of a cylindrical water column, due to the impact of a traveling plane shock wave. The unsteady Reynolds-averaged Navier–Stokes approach was used to simulate the mean turbulent flow in a virtual shock tube device. The compressible flow governing equations were solved by means of a finite volume-based numerical method, where the volume of fluid technique was employed to track the air–water interface on the fixed numerical mesh. The present computational modeling approach for industrial gas dynamics applications was verified by making a comparison with reference experimental and numerical results for the same flow configuration. The engineering analysis of the shock–column interaction was performed in the shear-stripping regime, where an acceptably accurate prediction of the interface deformation was achieved. Both column flattening and sheet shearing at the column equator were correctly reproduced, along with the water body drift.

Hybrid Analytical-Numerical Analysis of SAE 4150 Alloy Steel Rods Cooling

2014 ◽  
Vol 1082 ◽  
pp. 187-190 ◽  
Author(s):  
Marcelo Ferreira Pelegrini ◽  
Thiago Antonini Alves ◽  
Felipe Baptista Nishida ◽  
Ricardo A. Verdú Ramos ◽  
Cassio R. Macedo Maia
Keyword(s):  
Diffusion Equation ◽  
Alloy Steel ◽  
Integral Transform ◽  
Numerical Study ◽  
Physical Parameters ◽  
Analytical Treatment ◽  
Aspect Ratios ◽  
Rectangular Cylinders ◽  
Thermo Physical Properties ◽  
Integral Transform Technique

In this work, a hybrid analytical-numerical study was performed in cooling of rectangular rods made from SAE 4150 alloy steel (0.50% carbon, 0.85% chrome, 0.23% molybdenum, and 0.30% silicon). The analysis can be represented by the solution of transient diffusive problems in rectangular cylinders with variable thermo-physical properties in its domain under the boundary conditions of first kind (Dirichlet condition) and uniform initial condition. The diffusion equation was linearized through the Kirchhoff Transformation on the temperature potential to make the analytical treatment easier. The Generalized Integral Transform Technique (GITT) was applied on the diffusion equation in the domain in order to determine the temperature distribution. The physical parameters of interest were determined for several aspect ratios and compared with the results obtained through numerical simulations using the commercial software ANSYS/FluentTM15.

scholarly journals INTEGRAL TRANSFORM TECHNIQUE FOR MESON WAVE FUNCTIONS

1996 ◽  
Vol 11 (20) ◽  
pp. 1611-1626 ◽  
Author(s):  
A.P. BAKULEV ◽  
S.V. MIKHAILOV
Keyword(s):  
Wave Function ◽  
Sum Rules ◽  
Integral Transform ◽  
Wave Functions ◽  
Sum Rule ◽  
New Approach ◽  
Exactly Solvable ◽  
The Stability ◽  
The Masses ◽  
Integral Transform Technique

In a recent paper1 we have proposed a new approach for extracting the wave function of the π-meson φπ(x) and the masses and wave functions of its first resonances from the new QCD sum rules for nondiagonal correlators obtained in Ref. 2. Here, we test our approach using an exactly solvable toy model as illustration. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance (π′), but also in the estimation of π″-mass.

Sign in / Sign up

Export Citation Format

Share Document