Elastic Theory

Question 1

what are the components of the wave equation in vector notation? (navier’s equation)

Answer 1

a volumetric deformation and an angular deformation component

Question 2

describe in words what we use the wave equation for

Answer 2

quantifies the variation in time and space of the wave in order to get speed of the wave

Question 3

what is the generic wave equation?

Answer 3

d2u/dx2 = 1/c^2 d2u/dt2 where c is speed - a 1 d scalar case!

Question 4

what is wave speed equal to?

Answer 4

c = lamda/T (speed = wavelength/period)

Question 5

what is helmholtz theorem and why is it important for this class?

Answer 5

states that any vector field can be separated into scalar and vectr fields (Del*Phi + Del x Psi = u) . subbing this into the wave equation (navier’s equation) we can rearrange to get a term that has no angular distortion, but does have volumetric distortion, and another term that has no volumetric distortion, but does have angular distortion. P AND S WAVES

Question 6

what is the velocity of p waves governed by?

Answer 6

alpha = sqrt(lamba + 2mu/rho) - depends on hooke’s law parameters for angular rotation of material and elasticity, as well as the medium.

Question 7

what is the velocity of p waves governed by?

Answer 7

beta = sqrt(mu/rho) only determined by angle of rotation of material

Question 8

what direction is the ground motion in p and s waves?

Answer 8

p waves: ground motion is parallel to wave direction

s waves: ground motion is perpendicular to wave direction