Three-Dimensional Mode-Matching Theory of Rectangular Bar Resonators Using Complex Wave-Numbers

1981 ◽  
Author(s):  
R.F. Milsom ◽  
D.T. Elliott ◽  
M. Redwood
Keyword(s):  
Three Dimensional ◽  
Matching Theory ◽  
Mode Matching ◽  
Wave Numbers ◽  
Complex Wave

Axially Symmetric Waves in Elastic Rods

1960 ◽  
Vol 27 (1) ◽  
pp. 145-151 ◽  
Author(s):  
R. D. Mindlin ◽  
H. D. McNiven
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Rods ◽  
Axially Symmetric ◽  
Elastic Rod ◽  
One Dimensional ◽  
Axial Shear ◽  
Wave Numbers ◽  
Complex Wave

A system of approximate, one-dimensional equations is derived for axially symmetric motions of an elastic rod of circular cross section. The equations take into account the coupling between longitudinal, axial shear, and radial modes. The spectrum of frequencies for real, imaginary, and complex wave numbers in an infinite rod is explored in detail and compared with the analogous solution of the three-dimensional equations.

Extensional Vibrations of Elastic Plates

1959 ◽  
Vol 26 (4) ◽  
pp. 561-569
Author(s):  
R. D. Mindlin ◽  
M. A. Medick
Keyword(s):  
Three Dimensional ◽  
Infinite Plate ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Wave Numbers ◽  
Complex Wave ◽  
Shear Modes ◽  
Thickness Shear

Abstract A system of approximate, two-dimensional equations of extensional motion of isotropic, elastic plates is derived. The equations take into account the coupling between extensional, symmetric thickness-stretch and symmetric thickness-shear modes and also include two face-shear modes. The spectrum of frequencies for real, imaginary, and complex wave numbers in an infinite plate is explored in detail and compared with the corresponding solution of the three-dimensional equations.

scholarly journals COMPLEX WAVE NUMBERS IN THE VICINITY OF THE SCHWARZSCHILD EVENT HORIZON

2008 ◽  
Vol 23 (09) ◽  
pp. 1417-1433 ◽  
Author(s):  
M. SHARIF ◽  
UMBER SHEIKH
Keyword(s):  
Event Horizon ◽  
Plasma Wave ◽  
Cold Plasma ◽  
Dispersion Relations ◽  
Wave Numbers ◽  
Complex Wave ◽  
And Behavior ◽  
Wave Properties

This paper is devoted to investigate the cold plasma wave properties outside the event horizon of the Schwarzschild planar analogue. The dispersion relations are obtained from the corresponding Fourier analyzed equations for nonrotating and rotating, nonmagnetized and magnetized backgrounds. These dispersion relations provide complex wave numbers. The wave numbers are shown in graphs to discuss the nature and behavior of waves and the properties of plasma lying in the vicinity of the Schwarzschild event horizon.

scholarly journals The Complex Rayleigh Waves in a Functionally Graded Piezoelectric Half-Space: An Improvement of the Laguerre Polynomial Approach

Materials ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2320 ◽  
Author(s):  
Ke Li ◽  
Shuangxi Jing ◽  
Jiangong Yu ◽  
Xiaoming Zhang ◽  
Bo Zhang
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Rayleigh Waves ◽  
Three Dimensional ◽  
Wave Mode ◽  
Functionally Graded ◽  
Function Technique ◽  
Complex Wave ◽  
Acoustic Wave Devices ◽  
Functionally Graded Piezoelectric

The research on the propagation of surface waves has received considerable attention in order to improve the efficiency and natural life of the surface acoustic wave devices, but the investigation on complex Rayleigh waves in functionally graded piezoelectric material (FGPM) is quite limited. In this paper, an improved Laguerre orthogonal function technique is presented to solve the problem of the complex Rayleigh waves in an FGPM half-space, which can obtain not only the solution of purely real values but also that of purely imaginary and complex values. The three-dimensional dispersion curves are generated in complex space to explore the influence of the gradient coefficients. The displacement amplitude distributions are plotted to investigate the conversion process from complex wave mode to propagating wave mode. Finally, the curves of phase velocity to the ratio of wave loss decrements are illustrated, which offers extra convenience for finding the high phase velocity points where the complex wave loss is near zero.

Three-dimensional mode growth in boundary layers with tuned and detuned subharmonic resonance

1995 ◽  
Vol 352 (1700) ◽  
pp. 453-471 ◽  
Keyword(s):  
Three Dimensional ◽  
Low Frequency ◽  
Phase Speed ◽  
Subharmonic Resonance ◽  
Oblique Waves ◽  
Periodic Disturbances ◽  
Wave Numbers ◽  
Interaction Order ◽  
Tollmien Schlichting ◽  
Low Amplitude

This work involves the use of controlled periodic disturbances to excite a plane Tollmien-Schlichting (TS) wave at one frequency ( f 2D) along with pairs of oblique waves with equal but opposite wave angles at a different frequency ( f 3D) in order to study the resonant growth of 3D modes in a Blasius boundary layer. In our earlier work (Corke & Mangano 1989; Corke 1990), the frequency of the oblique modes was exactly the subharmonic of the plane Tollmien-Schlichting (TS) mode. These modes were also phase-speed locked so that in terms of their streamwise wave numbers, α2D=1/2 α3D. This so-called ‘tuned’ subharmonic resonance leads to the enhanced growth of the otherwise linearly damped oblique waves, as well as the growth of higher harmonic 3D modes with frequencies and wave numbers: (3/2 f2d, 3/2 α2D, ±β3D), (5/2 f2d, 5/2 α2D, ±β3D), (f2d, α2D, ±2β3D) and (0, 0, ±2β3D). Even when the initial 3D oblique waves have frequencies which are close to the TS subharmonic frequency, a ‘detuned’ subharmonic resonance leads to the enhanced growth of the 3D mode. In addition, it promotes the growth of numerous discrete modes produced by successive sum and difference interactions. These interacted modes are also three dimensional, with higher amplification rates that increase with the interaction order. The growth of these modes accounts for the rapid spectral filling, and low-frequency modulation commonly observed in natural subharmonic transition. Starting from a ‘tuned' resonance, this scenario then provides a mechanism for the generation of a broad spectrum at the later stages of subharmonic mode transition. However, the results also suggest that with ‘natural’ transition, starting from low-amplitude broadband disturbances, the most likely 2D/3D resonance will be ‘detuned’.

Evaluation of Intracranial Pressure Response in Rats Exposed to Complex Shock Waves

2012 ◽  
Author(s):  
Alessandra Dal Cengio Leonardi ◽  
Nickolas Keane ◽  
Cynthia Bir ◽  
Pamela VandeVord
Keyword(s):  
Intracranial Pressure ◽  
Shock Waves ◽  
Blast Wave ◽  
Preliminary Investigation ◽  
Free Field ◽  
Three Dimensional ◽  
Head Orientation ◽  
Reflected Shock ◽  
Complex Wave ◽  
The Individual

Studies on blast neurotrauma have focused on investigating the effects of exposure to free-field blast representing the simplest form of blast threat scenario without considering any reflecting surfaces. However, in reality personnel are often located within enclosures or nearby reflecting walls causing a complex blast environment, that is, involving shock reflections and/or compound waves from different directions. In fact, when a blast wave interacts with nearby structures, reflected shock waves are generated and complex three-dimensional shock waves are formed. Complex shock wave overpressure-time traces are significantly different from free-field profiles because reflections can cause super-positioning of shock waves resulting in increased pressure magnitudes and multiple pressure peaks. Very importantly, the shocks arrive from different directions which would invoke a different biomechanical response than a one-dimensional exposure. It has been reported that in complex wave environments, the extent of the injuries becomes a function of the location related to the surrounding structures rather than a function of the distance from the center of the explosion, as it is for free-field conditions (Yelverton et al. 1993; Mayorga 1997; Stuhmiller 1997). Furthermore, the resulting injuries when the individual is in confined spaces are noted to be more severe (Yelverton et al. 1993; Leibovici et al. 1996). The purpose of this study was to design a complex wave testing system and perform a preliminary investigation of the intracranial pressure (ICP) response of rats exposed to a complex blast wave environment. Furthermore, we explored the effects of head orientation in the same environment.

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