How Does Thermal Effect Influence Wave Velocity in Piezoelectric Materials?

[Turtle Yuan]

Hello group,

Now I am solving a problem of waves in a piezoelectric body including thermal effect in a infinite domain.

The physical quantities are involved including displcement{u_1,u_2,u_3},electric potential{phi} and temperature increment{T}. The waves are, in general, assumed as forms that all share a common term expi(k*n-v*t) , k---wave number; n---wave normal;v--phase velocity;t--time. This induces a characteristic value and vector problem. The outlines for this problem are 1. input n--->several velocity---->characteristic vector corresponding to each velocity.

what makes me puzzled is along some direction n, all the physical quantities share the same velocity according to the general algorithm. For my instinct it doesn't make any sense. I don't think displacement , electric potential, or thermal diffusion move with the same velocity.

Do you some idea about such issue? any help or discussion are appreciated.

 

[mda]

In general the speeds are different, but if you are looking for a coupled solution then by definition the speeds must all be equal, in order to maintain phase-matching through all space and time.