Lamb waves

Lamb waves are vibrations of a plate in which displacements occur in both perpendicular to the plate and in the propagation direction ( parallel to the plate ). Lamb waves are therefore pressure and mixed shear waves.

There are symmetric and antisymmetric Lamb waves (the latter also called " asymmetrical " hereinafter). With symmetric Lamb waves move at a position of the plate at the same time the top and bottom of the plate mid- way (or at this to be ); in anti-symmetric Lamb waves move at a position at the same time the upper side away from the center and the bottom to the center (ie, both up or both down).

The wavelength substantially longer than the thickness of the plate, are symmetrical Lamb waves with substantially longitudinal waves propagation direction in the plate plane; the motion transverse to it is due to the transverse contraction. Antisymmetric Lamb wave of long wavelength, bending vibrations of the disk.

For Lamb waves of short wavelength ( corresponding to high frequency, see accompanying chart, are for high frequencies added more lines ) occur several vibrational modes for a wavelength; these are for symmetric and antisymmetric Lamb waves with S0, S1, S2, ..., and A0, A1, A2 ... numbered. At the higher modes occur in the thickness direction of the plate to a plurality of mutually oscillating fields.

When the wavelength is significantly smaller than the thickness of the plate, the Lamb wave to the superposition of two Rayleigh waves, one at the top and at the bottom of the plate. Especially in this case it is also called Lamb -Rayleigh waves.

Lamb waves are dispersive, that is, the propagation velocity ( phase velocity and group velocity ) depends on the wavelength. Only in the limit of very short wavelength ( Rayleigh waves ), and symmetric Lamb waves, even with very long wavelength, the propagation velocity is substantially constant.

Technical application, see Lamb waves for ultrasonic inspection of thin-walled structures, such as for the study of sheet metal in the maintenance of aircraft.

Lamb waves were mathematically correct first described by Horace Lamb in 1917; based on earlier work by John William Strutt, 3rd Baron Rayleigh. Significant work was later performed by Igor Aleksandrovich Viktorov; D.C. Worlton has these waves for the first time experimentally produced in the megahertz range and detected, thus enabling the application for material testing.