Equation of Motion
In Dynamic Equilibrium
In Static Equilibrium
Elastic Waves in solids
(Longitudinal Wave)
Also called dilatational waves
Particle motion and wave motion are in the same
direction
Play Animation
Elastic Waves in solids
(Transverse Wave)
Also called equivolumnal waves
Particle motion and wave motion are perpendicular to
each other
Play Animation
1. Flexural Waves
2. Shear (Distortional) Waves
Animation of longitudinal and transverse stress pulses
Elastic Waves in solids
(Interfacial Waves)
Play Animation
1. Rayleigh Waves
(On a free surface)
2. Love Waves
(Interfaces of layered media)
3. Stoneley Waves
(On an internal surface)
Elastic Wave Speeds
1. Flexural Waves
Elastic Waves during earthquakes
Play Animation
Note the velocity of the three waves. Also surface
waves cause most damage because they attenuate the
slowest.
The epicenter can be located by knowing the time
separation between the waves and by triangulation
Reflection and transmission
of elastic waves
The acoustic impedance of A and B are different. In
this case, B has a lower impedance than A. So the
reflected wave is tensile (whereas the incident wave
is compressive). Confirm this with the direction of the
particle velocity and wave velocity
Reflection and transmission
of elastic waves at a free surface.
The profile to the left is for the stress and the one to right is for particle velocity.
The compressive wave meets a free surface. The incident wave is compressive
while the reflected wave is tensile. Particle velocity does not change sign on
reflection. Also recall that a free surface is defined as one without surface
tractions. So the reflected wave has to have the opposite sign as the incident.
Reflection and transmission
of elastic waves at a rigid interface.
The compressive wave meets a rigid interface. The incident wave is compressive
while the reflected wave is also compressive. Particle velocity changes sign on
reflection. Remember that at a rigid interface particles CANNOT move – that is
why the interface is rigid. This zero velocity at the interface, is possible only if the
reflected particle velocity is opposite in sign to the incident.
Reflection and transmission
of elastic waves
More animations
Free Surface
Rigid interface
Reflection and transmission
of elastic waves
More animations
Low impedance
to high
impedance
High
impedance to
low impedance
In the above animations, we have transverse waves being reflected and
transmitted. The change (or no change) in the “phase” on encountering the
interface means a change (or no change) of particle velocity, not stress
Impact in bars
(Length and shape of the pulse)
Length of the pulse
Shape of the pulse.
To the left, we have the theroretical shape of the pulse and to the right we have
the real shape of the pulse.
Impact in bars
Shape of the pulse
Effect of aspect ratio
(a is the bar diameter and Λ is the
length of the pulse). The inertial
effects are minimized when the a/Λ
ratio is small.
Effect of free surfaces
Non planarity of the compressive
wave and repeated reflections
from the free surfaces leads to
the oscillations.