- #1

Howlin

- 55

- 0

I am looking over deflection in materials and came across the following for a bar u(x,t) and I need some help in understanding it:

F(x,t) = ρA[itex]\frac{∂^{2}u}{∂t^{2}}[/itex] + EI [itex]\frac{∂^{4}u}{∂x^{4}}[/itex]

where ρ is the density of the bar, A is the cross-section, F is the force per unit length, E is Youngs modulus and I is the moment of inertia for the cross-section of the bar.

What I can't understand in this is the [itex]\frac{∂^{2}u}{∂t^{2}}[/itex] and [itex]\frac{∂^{4}u}{∂x^{4}}[/itex].

What do they mean and how do you find out what u(x,t) is to work out the 2nd and 4th diritive of it?