Natural frequency of clamped-hinged column

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SUMMARY

The discussion focuses on calculating the natural frequency of a clamped-hinged column, specifically one that is clamped at the bottom and hinged at the top with freedom along the Y-axis. The equation provided for natural frequency is fn=k^2/(2*pi()*L^2)*sqrt(EI/m), where L is the length, E is Young's modulus, I is the moment of inertia, and m is the mass per unit length. The parameter k, which is crucial for determining the natural frequency based on boundary conditions, remains undefined for this specific case. A recommended resource for understanding the fixity parameter k is linked in the discussion.

PREREQUISITES
  • Understanding of natural frequency calculations
  • Familiarity with boundary conditions in structural mechanics
  • Knowledge of Young's modulus and moment of inertia
  • Ability to interpret engineering papers and equations
NEXT STEPS
  • Research the fixity parameter k for clamped-hinged columns
  • Study the effects of boundary conditions on natural frequency
  • Explore additional resources on natural frequency calculations for various cross-sections
  • Review engineering literature on the dynamics of beams and columns
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Structural engineers, mechanical engineers, and students studying dynamics who are involved in calculating the natural frequencies of columns and beams under various boundary conditions.

dyah09
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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?
 
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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.
 
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The cross-section is a rectangle. I tried to write the problem out. Here you go
 

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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 ?
 
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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.
 
Ohh thank you sm sir, i will read it first
 

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