Wave Propagation in the Linear Theory of Elastic Shells

1976 ◽  
Vol 43 (2) ◽  
pp. 281-285 ◽  
Author(s):  
H. Cohen
Keyword(s):  
Wave Propagation ◽  
Circular Cylinder ◽  
Linear Theory ◽  
Wave Mode ◽  
Mode Shapes ◽  
Elastic Shells ◽  
Special Cases ◽  
Cosserat Surface ◽  
Singular Wave ◽  
The Right

The problem of wave propagation in elastic shells within the framework of a linear theory of a Cosserat surface is treated using the method of singular wave curves. The equations for determining the speeds of propagation and their associated wave mode shapes are obtained in a form involving the speeds of propagation in Cosserat plates and the curvature of the shell. A number of special cases in which the speeds and mode shapes simplify are considered. In particular, these special cases are shown to include as examples, certain systems of waves in elastic shells whose middle surfaces are the surface of revolution, the circular cylinder, the sphere, and the right helicoid.

Surface waves on water of non-uniform depth

1958 ◽  
Vol 4 (6) ◽  
pp. 607-614 ◽  
Author(s):  
Joseph B. Keller
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Linear Theory ◽  
Gravity Waves ◽  
Geometrical Optics ◽  
Surface Wave Propagation ◽  
Special Cases

Gravity waves occur on the surface of a liquid such as water, and the manner in which they propagate depends upon its depth. Although this dependence is described in principle by the equations of the ‘exact linear theory’ of surface waves, these equations have not been solved except in some special cases. Therefore, oceanographers have been unable to use the theory to describe surface wave propagation in water whose depth varies in a general way. Instead they have employed a simplified geometrical optics theory for this purpose (see, for example, Sverdrup & Munk (1944)). It has been used very successfully, and consequently various attempts, only partially successful, have been made to deduce it from the exact linear theory. It is the purpose of this article to present a derivation which appears to be satisfactory and which also yields corrections to the geometrical optics theory.

Wave-Mode Coordinates and Scattering Matrices for Wave Propagation.

1986 ◽  
Author(s):  
James H. Williams ◽  
Nagem Jr. ◽  
Yeung Raymond J. ◽  
Hubert K.
Keyword(s):  
Wave Propagation ◽  
Wave Mode ◽  
Scattering Matrices

scholarly journals Refinements of the Lower Bounds of the Jensen Functional

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Iva Franjić ◽  
Sadia Khalid ◽  
Josip Pečarić
Keyword(s):  
Lower Bounds ◽  
Jensen Inequality ◽  
Left Hand ◽  
Right Hand ◽  
Special Cases ◽  
Jensen Functional ◽  
The Difference ◽  
The Right

The lower bounds of the functional defined as the difference of the right-hand and the left-hand side of the Jensen inequality are studied. Refinements of some previously known results are given by applying results from the theory of majorization. Furthermore, some interesting special cases are considered.

scholarly journals Wave Propagation Analysis in Composite Laminates Containing a Delamination Using a Three-Dimensional Spectral Element Method

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Fucai Li ◽  
Haikuo Peng ◽  
Xuewei Sun ◽  
Jinfu Wang ◽  
Guang Meng
Keyword(s):  
Wave Propagation ◽  
Lamb Wave ◽  
Composite Laminates ◽  
Composite Structures ◽  
Spectral Element Method ◽  
Three Dimensional ◽  
Spectral Element ◽  
Wave Mode ◽  
Diagonal Form ◽  
Element Method

A three-dimensional spectral element method (SEM) was developed for analysis of Lamb wave propagation in composite laminates containing a delamination. SEM is more efficient in simulating wave propagation in structures than conventional finite element method (FEM) because of its unique diagonal form of the mass matrix. Three types of composite laminates, namely, unidirectional-ply laminates, cross-ply laminates, and angle-ply laminates are modeled using three-dimensional spectral finite elements. Wave propagation characteristics in intact composite laminates are investigated, and the effectiveness of the method is validated by comparison of the simulation results with analytical solutions based on transfer matrix method. Different Lamb wave mode interactions with delamination are evaluated, and it is demonstrated that symmetric Lamb wave mode may be insensitive to delamination at certain interfaces of laminates while the antisymmetric mode is more suited for identification of delamination in composite structures.

The Circular Cylinder With a Band of Uniform Pressure on a Finite Length of the Surface

1941 ◽  
Vol 8 (3) ◽  
pp. A97-A104 ◽  
Author(s):  
M. V. Barton
Keyword(s):  
Circular Cylinder ◽  
Finite Length ◽  
Infinite Series ◽  
Fundamental Problem ◽  
The Other ◽  
Complete Picture ◽  
Uniform Pressure ◽  
Uniform Tension ◽  
Special Cases ◽  
Stress And Deformation

Abstract The solution to the fundamental problem of a cylinder with a uniform pressure over one half its length and a uniform tension on the other half is found by using the Papcovitch-Neuber solution to the general equations. In this paper, the results, given analytically in terms of infinite-series expressions, are exhibited as curves giving a complete picture of the stress and deformation. The case of a cylinder with a band of uniform pressure of any length, with the exception of very small ones, is then solved by the method of superposition. The stresses and displacements are evaluated for the special cases of a cylinder with a uniform pressure load of 1 diam and 1/2 diam in length. The problem of a cylinder heated over one half its length is solved by the same means.

Development of Bionic Design Concepts for Structure Optimisation of Forming Tools According to Production and Stress Constraints

2011 ◽  
Vol 473 ◽  
pp. 209-216
Author(s):  
Eugen Oswald ◽  
Mathias Liewald ◽  
Oliver Stephan
Keyword(s):  
Automotive Industry ◽  
Stress Constraints ◽  
Bionic Design ◽  
Design Concepts ◽  
Special Cases ◽  
Current Design ◽  
The Right ◽  
Forming Tools ◽  
Current Standards ◽  
Made In

In the automotive industry, current design and dimensioning of forming tools and bearing tool components occurs according to guidelines. Possible interactions between arising loads as well as dimensioning are empirically estimated. Simulative computations, which are based on CAE-methods, are only realized in special cases. Therefore, most often current standards lead to oversized tools. In consequence, new studies based on CAE-analyses are supposed to investigate new possibilities to design forming tools and components optimized in their structure corresponding to the right distribution of forces and stress. This is made in order to increase reliability during the manufacturing process, as well as the tools’ stiffness and contribute to decrease of investment costs.

Wave Propagation in a Piezoelectric Coupled Solid Medium

2002 ◽  
Vol 69 (6) ◽  
pp. 819-824 ◽  
Author(s):  
Q. Wang
Keyword(s):  
Wave Propagation ◽  
Wave Velocity ◽  
Electric Potential ◽  
Solid Medium ◽  
Electric Displacement ◽  
Piezoelectric Medium ◽  
Wave Number ◽  
Mode Shapes ◽  
Coupled Structures ◽  
Shear Horizontal

Shear horizontal (SH) wave propagation in a semi-infinite solid medium surface bonded by a layer of piezoelectric material abutting the vacuum is investigated in this paper. The dispersive characteristics and the mode shapes of the deflection, the electric potential, and the electric displacements in the thickness direction of the piezoelectric layer are obtained theoretically. Numerical simulations show that the asymptotic phase velocities for different modes are the Bleustein surface wave velocity or the shear horizontal wave velocity of the pure piezoelectric medium. Besides, the mode shapes of the deflection, electric potential, and electric displacement show different distributions for different modes and different wave number. These results can be served as a benchmark for further analyses and are significant in the modeling of wave propagation in the piezoelectric coupled structures.

Intentional Response Reduction by Harmonic Mistuning of Bladed Disks With Aerodynamic Damping

2018 ◽  
Author(s):  
Sebastian Willeke ◽  
Lukas Schwerdt ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Wave Train ◽  
Wave Mode ◽  
Forced Response ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Nodal Diameter ◽  
Aerodynamic Damping ◽  
Mode Pair ◽  
Localized Mode ◽  
Amplitude Level

A harmonic mistuning concept for bladed disks is analyzed in order to intentionally reduce the forced response of specific modes below their tuned amplitude level. By splitting a mode pair associated with a specific nodal diameter pattern, the lightly damped traveling wave mode of the nominally tuned blisk is superposed with its counter-rotating complement. Consequently, a standing wave is formed in which the former wave train benefits from an increase in aerodynamic damping. Unlike previous analyses of randomly perturbed configurations, the mode-specific stabilization is intentionally promoted through adjusting the harmonic content of the mistuning pattern. Through a re-orientation of the localized mode shapes in relation to the discrete blades, the response is additionally attenuated by an amount of up to 7.6 %. The achievable level of amplitude reduction is analytically predicted based on the properties of the tuned system. Furthermore, the required degree of mistuning for a sufficient separation of a mode pair is derived.

Sign in / Sign up

Export Citation Format

Share Document