Natural frequency of clamped-hinged column

[dyah09]

Homework Statement

I have a column clamped at the bottom and for the top, I use hinged BC but free at the Y axis. I have the dimension and the material properties. How to calculate its natural frequency?

Relevant Equations

I'm looking for the equation

I have a column clamped at the bottom and for the top, I use hinged BC but free at the Y axis. I have the dimension and the material properties. How to calculate its natural frequency?

 

[Baluncore]

Welcome to PF.

There will be several modes and frequencies of oscillation.
Is the column circular, or does it have different second moment of inertia in different directions?
Please attach a diagram showing the freedom-of-movement connection details to your next post.

 

[dyah09]

The cross-section is a rectangle. I tried to write the problem out. Here you go

 

[Baluncore]

Now that the problem is better defined, it is a case of finding the equation you seek.
We do not directly answer the question, and cannot learn for you. This question requires that you investigate the sources, to identify the relevant equation.
What texts do you have available for this subject ?

 

[dyah09]

I found many equations in some papers. Mostly it's about the cantilever beam. For example, this equation: fn=k^2/(2*pi()*L^2)*sqrt(EI/m)

I know L is for the length of the beam/column; E is for young's modulus of the material; I is for the moment of inertia of the cross-section; and m is for the mass of the column per unit length. And then there is k, a parameter that depends on the boundary condition (BC) and the mode shapes. The paper doesn't have k value for my problem's BC. That's the problem sir, I don't know where to find the k value for clamped-hinged column or beam

Also, the units in this equation aren't really explained well in the paper. So, I'm a bit confused.

 

[Baluncore]

Without a link to your paper, I cannot really comment.

Here is a short paper, downloadable as pdf, that explains the BC fixity K.
https://pubs.aip.org/asa/jasa/article/42/4/900/747870/Effect-of-End-Conditions-on-the-Lateral
Your situation is clamped-hinged = CH.

 

[dyah09]

Ohh thank you sm sir, i will read it first