# Cantilever Beam, Tapered in breadth, uniform thickness, natural frequency

Hey there
I need to find the natural frequency of a Cantilever Beam. The beam is tapered in breadth, but has a uniform thickness. So basically the end goal is an equation for f as a function of the angle of the side cut.

Clamped at one end
L=constant
B=changes though the length of the beam and is dependent on the angle from the z axis (along the beam)
H=constant (thickness)
E constant,
So obviously the second moment of area will be a function of x or angle.

The end equation will be used in matlab to for a plot angle vs frequency

Any pointers, or a solution would be most helpful,

Just an incomplete idea -

Find an equivalent system of a massless beam with a point mass at the end. Then use the stiffness of the beam, and the point mass as a simple spring-mass system and get the fundamental frequency from $$\omega = \sqrt{\frac{k}{m}}$$

AlephZero