Elastic wave amplitude

[WARose]

As I have mentioned on other threads on this board: I have been reading several texts on the propagation of elastic waves in isotropic media lately. (And I appreciate the discussions we’ve had here on this topic.) If I could prevail upon someone again……..a question crossed my mind this weekend………….

In a lot of the afore mentioned texts……equations defining the motion of a variety of wave types are given. (I.e. Rayleigh, lamb, P-wave, etc, etc.) But one thing I am noticing in a lot of them is: the amplitude is typically a undefined variable/constant. The only case I have seen it defined for (outside of longitudinal waves from axial impact) is in the case of Rayleigh waves. In one text I have (on soil dynamics), the motion was a function of a initial amplitude…..and that amplitude was a localized displacement from a vertical load.

So I guess my question is: is this true for other wave types? Are these undefined constants typically all some sort of a function of a local displacement/deformation……possibly do to contact?

By the way, this is not considering vibration.....this is just considering the initial wave at the beginning of motion.

Thanks in advance.

 

[Erik Panos Kostson]

In books of waves in solids e.g., Graff, there are solutions to the wave equations (say plates or rods,..) with different force terms - say excited by different simple point loads (say harmonic or impulsive point loads).

https://www.amazon.co.uk/Motion-Elastic-Solids-Dover-Physics/dp/0486667456

example:
Infinite rod (so standard long. wave equation describes it, no losses), with a point force in the centre exciting long. waves (F= Famp*exp(i*omega*t)*DiracDelta(x-xo))

The amplitude of the longitudinal wave is ~ Famp/(E_Youngs*Cross_Area*wave_number)

 

[WARose]

Actually, that was one of the texts I am reading. And these thoughts occurred when I got to the section on lamb waves. It is somewhat vague on this point.

Thanks for the reply.

 

[Erik Panos Kostson]

Not sure if there is a closed solution for point force excitation with Lamb waves - perhaps there is one, but could be a bit nasty .

 

[WARose]

Could I get some more opinions on this (my question [in bold] in the OP)? We've got some pretty sharp people here so I'd like to hear some more. Thanks.

[red]EDIT[/red]: I guess what I am after is: forgetting about the dynamic amplification (and other things that happen with complex waves at certain frequencies), is the localized [Hertzian] displacement a maximum initial amplitude? (Sort of a ceiling if you will.) Thanks again.