In reply to Pellys questions regarding waves in a thin plate I would like to make some comments that may considerably differ from the traditionally accepted theory. But first of all What do you mean by plate? Is it a really very thin plate or is it a thin layer on a base? We have several different problems here.
Regarding Lamb waves. If the plate serves as a structural element its minimal thickness (or thinness) is always limited by stiffness of the structure. That is why if the ultrasonic wavelength corresponds to the plates thickness, we have two groups of Lamb waves: symmetric and asymmetric. They differ by phase and group velocity, spread of shifts and stresses along the plate thickness. Each of the Lamb wave groups represents a family of different wave modes depending on their frequency. High dispersion of velocity is observed here. According to my physical notion these groups are complex configurations of longitudinal and shear stresses caused by special boarder conditions of the plate. In this case it is impossible to separate them. Then there are no pure longitudinal or shear Lamb waves. Sometimes for very thin plates it is possible to consider only the first modes of symmetric and asymmetric waves, but it is an artificial approach convenient for theoretical modeling. In reality we use ultrasonic impulses for materials testing which theoretically have unlimited spectrum of frequencies. Practically the spectrum is limited only by transducer frequency bands and equipment measuring possibilities (relation of noise to threshold levels). This uncertainty characteristic of the ultrasonic pulse method is one of the main difficulties of measuring the Lamb wave parameters. Regarding transducers. There are different angles of inducing ultrasonic impulses into the material according to Snell law, but this critical angle exists only for one fixed frequency. Impulse signal, as a rule, has a wide frequency spectrum. I do not know a technical solution for getting critical angles for all the spectrum components! Transducer design also affects testing in this case. Traditionally plate (with liquid couplant) contact transducers or air couplant or dry point contact transducers generate stresses in the plate with different directional diagrams, thus different spectrums of pulse ultrasonic waves. Regarding measurements. It is necessary to remember that theoretically we consider only models of the waves, where we use notions of only phase or group velocities. As far as I know, the existing ultrasonic equipment do not measure these parameters in a pure form. It is very strange that this problem seems to be ignored. Do we know what we are measuring? I welcome any discussion and comments for searching the truth. Good luck, Pelly, but keep in mind that your road is full of stones and lambs.