Radiation conditions for a semi-infinite elastic strip

2005 ◽  
Vol 461 (2056) ◽  
pp. 1163-1179 ◽  
Author(s):  
E Babenkova ◽  
J Kaplunov
Keyword(s):  
High Frequency ◽  
Thin Plates ◽  
Elastic Strip ◽  
Resonance Frequencies ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Plates And Shells ◽  
High Frequency Vibrations ◽  
Thin Plates And Shells ◽  
Radiation Conditions

High-frequency vibrations of a semi-infinite elastic strip with traction-free faces are considered. The conditions on end data that are derived do not allow non-radiating in Sommerfeld's sense of polynomial modes at thickness resonance frequencies. These represent a high-frequency analogue of the well-known decay conditions in statics that agree with the classical Saint-Venant principle. The proposed radiation conditions are applied to the construction of boundary conditions in the theories of high-frequency long-wave vibrations describing slow-varying motions in the vicinity of thickness resonance frequencies. The derivation is based on the Laplace transform technique along with the asymptotic methodology that is typical for thin plates and shells.

A New Rate Principle Suitable for Analysis of Inelastic Deformation of Plates and Shells

1985 ◽  
Vol 52 (3) ◽  
pp. 533-535 ◽  
Author(s):  
S. Mukherjee ◽  
F. G. Kollmann
Keyword(s):  
Variational Principle ◽  
Linear Elasticity ◽  
Inelastic Deformation ◽  
Thin Plates ◽  
Independent Functions ◽  
Rate Form ◽  
Plates And Shells ◽  
Thin Plates And Shells

A variational principle for linear elasticity, using displacements and strains as independent functions, is presented in this paper. An extension of this principle in rate form is claimed to be extremely useful for the analysis of inelastic deformation of thin plates and shells.

Impact of High-Frequency Vibrations on Metal Items Resistance to Cyclic and Axial Loads

2018 ◽  
Vol 284 ◽  
pp. 587-592 ◽  
Author(s):  
I.R. Kuzeev ◽  
E.A. Naumkin ◽  
S.A. Pankratiev ◽  
R.R. Tlyasheva
Keyword(s):  
Fatigue Life ◽  
Resonance Frequency ◽  
Axial Compression ◽  
High Frequency ◽  
Forced Vibrations ◽  
Compression Force ◽  
Simultaneous Application ◽  
Resonance Frequencies ◽  
High Frequency Vibrations ◽  
Force Calculation

It was shown that the forced vibrations of objects on resonance frequencies could significantly change resistance of these objects to cyclic loads in a low-cycle loading range and decrease critical compression load under axial compression. We carried out a procedure of fatigue testing performance with simultaneous application of high-frequency vibrations. We developed and produced a device allowing carrying out testing aimed to check shape stability of cylindrical shells and their resistance to forced vibrations. Dependence of fatigue life capability within the low-cycle range on the frequency of applied forced vibrations in four harmonics of resonance frequency was experimentally determined. Fatigue life capability decreased by 1,6 times. Decrease of life capability particularly occurs on frequencies which are presumably connected with minimum in size elements of hierarchy of polycrystalline material structures. It was found out that the forced vibrations on resonance frequency contribute the increase of a number of vibrations, that leads to decrease of critical axial compression force value. Decrease can be by up to 40%. Experimental determination of critical load during application of vibrations allowed obtaining formula for adjusting factor calculation in the formula for permitted compression force calculation.

Thin Plates and Shells: Theory, Analysis, and Applications

2002 ◽  
Vol 55 (4) ◽  
pp. B72-B73 ◽  
Author(s):  
E Ventsel, ◽  
T Krauthammer, ◽  
E Carrera,
Keyword(s):  
Thin Plates ◽  
Theory Analysis ◽  
Plates And Shells ◽  
Thin Plates And Shells

Buckling of Simply Supported Oblique Plates

1963 ◽  
Vol 30 (3) ◽  
pp. 363-366 ◽  
Author(s):  
Y. Yoshimura ◽  
K. Iwata
Keyword(s):  
General Theory ◽  
Coordinate System ◽  
Thin Plates ◽  
Simply Supported ◽  
Critical Stresses ◽  
Plates And Shells ◽  
Thin Plates And Shells

Based on the general theory of thin plates and shells previously developed by the first author, which holds also for oblique coordinate system, the problem of buckling of simply supported parallelogram plates is treated. Numerical values of the critical stresses of buckling under compression and shear are calculated, respectively, for plates having angles between 45 and 135 deg, and for side ratios 1 and 2.

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