Download presentation

Presentation is loading. Please wait.

Published byMayra Belcher Modified over 2 years ago

1
A New Use of the Elastodynamic Reciprocity Theorem Jan D. Achenbach McCormick School of Engineering and Applied Sciences Northwestern University Evanston, IL, 60208 Symposium in Honor of Ted Belytschko April 18-20, 2013

2
Elastodynamic Reciprocity Betti (1872), Rayleigh (1873), Graffi (1947) time-harmonic fields:,, Consider two elastodynamic states Then for a region V with boundary S Linear stress-strain relation: Solids may be: anisotropic inhomogeneous linearly viscoelastic

3
Lamb’s Problem (1904) Time Harmonic line load radiates: Circular longitudinal wave Circular transverse wave Wedge wave Surface (Rayleigh wave)

4
Guided Waves

5
Lord Rayleigh (1842-1919) J.W.S. Raleigh, “On waves propagated along the plane surface of an elastic solid,” Proc. London Math. Soc., Vol. 17 (1885) pp. 4-11

6
Surface Waves

7
Equation for Phase Velocity The condition that yields the well known equation

8
STEADY-STATE TIME-HARMONIC CASE State A: State B: Applied body or surface force

9
State A: State B: virtual surface wave

11
Lamb’s Problem P z x

12
Comparison of LAMB’s and Rec. Thm. Results Result of FIT: Result of Rec. Thm.: 0.10001.50000.8931 -0.9651 -0.9651 0.16001.57180.9090 -0.8682 -0.8682 0.20001.63300.9110 -0.8068 -0.8068 0.26001.75590.9210 -0.7199 -0.7199 0.30001.87080.9274 -0.6655 -0.6655 0.40002.44950.9422 -0.5420 -0.5420

13
Conclusion For every configuration that supports guided waves: e.g., surface waves (Rayleigh) waves in a layer (Lamb) waves in a film/substrate configuration (Sezawa) and if the free time-harmonic form of such waves is known, then the reciprocity theorem of elastodynamics provides a simple approach to determine the amplitude of guided waves that radiate from time-harmonic external excitation. For pulsed excitations such as laser generated heating, Fourier superposition gives the signal strength of the radiated guided waves.

Similar presentations

OK

Physics of fusion power Lecture 11: Diagnostics / heating.

Physics of fusion power Lecture 11: Diagnostics / heating.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on bluetooth technology downloads Ppt on p&g products brands list Electronic paper display ppt online Ppt on online banking system in php Ppt on electric meter testing Ppt on earned value management Ppt on bank lending interest Ppt on chapter iv of companies act 2013 Ppt on adr and drive Ppt on tuberculosis