Chapter 5, Problem 5.47P

The differential equation for small-amplitude vibrations y(x, t) of a simple beam is given by $\rho A\frac{{\partial }^{2}y}{\partial t^2}+EI\frac{{\partial }^{4}y}{\partial x^4}=0$ where $\rho$ = beam material density

A = cross-sectional area

I = area moment of inertia

E = Young’s modulus

Use only the quantities $\rho$ , E, and A to nondimensionalize y, x, and t, and rewrite the differential equation in dimensionless form. Do any parameters remain? Could they be removed by further manipulation of the variables?