# Vibrations problem - Deriving the natural frequencies

1. Feb 14, 2010

### alexisonsmith

1. The problem statement, all variables and given/known data

A thin beam of length L (flexural Stufness EI, cross-sectional area A, density p) is connected to a linear spring of stiffness K_s at each end. Derive the governing equation for the natural frequencies of transverse vibrations from the beam equation and boundary conditions

2. Relevant equations

Not sure

3. The attempt at a solution

I am really not sure how to start this one, can someone help please

#### Attached Files:

• ###### scan0010.jpg
File size:
9.2 KB
Views:
71
Last edited: Feb 15, 2010
2. Feb 15, 2010

### magwas

Try to use
Flexural stiffness definition (EI=E*I/L),
Hooke's law (F=-kx)
Beam equation
$$\frac{\partial^2}{\partial x^2}\left(EI \frac{\partial^2 u}{\partial x^2}\right) = w$$
, in the simple case
$$EI \frac{d^4 u}{d x^4} = w(x)$$