The differential equation for small amplitude vibrations y(x, t) of a simple beam is given by Where rho beam material density A cross sectional area I area moment of inertia E Youngs modulus Use only the quantities rho , E, and A to non dimensionalize 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 at dx

Question: The differential equation for small-amplitude vibrations y(x, t) of a simple beam is given by Where ρ = beam material density A = cross-sectional area

The differential equation for small-amplitude vibrations y(x, t) of a simple beam is given by

Where ρ = beam material density
A = cross-sectional area
I = area moment of inertia
E = Young€™s modulus
Use only the quantities ρ, E, and A to non-dimensionalize 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?

at dx

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