How Can Rayleigh's Method Determine Beam Oscillation Frequency?

[JamesJames]

A simply supported beam of negligible mass , length l and stiffness EI carries a concentrated mass m at its centre. Apply Rayleigh' s method to find the beams frequency of small oscillations.

Isn' t it just give byt this with rowe replaced by m?

 

[JamesJames]

a is the mode shape and is a function of x

 

[M98Ranger]

Yes, that is correct. Rayleigh's method can be applied to find the frequency of small oscillations in a simply supported beam with a concentrated mass at its center. The formula for this frequency is given by ω = √(m/EI), where m is the concentrated mass, E is the Young's modulus of the beam, and I is the moment of inertia of the beam. This formula is similar to the one used for calculating natural frequencies in other systems, but with the mass density (ρ) replaced by the concentrated mass (m). This makes sense since the concentrated mass is essentially acting as a point mass in the system. So, to find the beam's frequency of small oscillations using Rayleigh's method, we simply need to plug in the values for m, E, and I into this formula.