Presentation is loading. Please wait.

Presentation is loading. Please wait.

A New Use of the Elastodynamic Reciprocity Theorem Jan D. Achenbach McCormick School of Engineering and Applied Sciences Northwestern University Evanston,

Similar presentations


Presentation on theme: "A New Use of the Elastodynamic Reciprocity Theorem Jan D. Achenbach McCormick School of Engineering and Applied Sciences Northwestern University Evanston,"— Presentation transcript:

1 A New Use of the Elastodynamic Reciprocity Theorem Jan D. Achenbach McCormick School of Engineering and Applied Sciences Northwestern University Evanston, IL, 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 ( ) 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

10

11 Lamb’s Problem P z x

12 Comparison of LAMB’s and Rec. Thm. Results Result of FIT: Result of Rec. Thm.:

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.


Download ppt "A New Use of the Elastodynamic Reciprocity Theorem Jan D. Achenbach McCormick School of Engineering and Applied Sciences Northwestern University Evanston,"

Similar presentations


Ads by Google