# Deriving the frequency in a beam equation.

• kezzstar
In summary, the frequency in a beam equation is derived by considering the properties of the beam, such as its length, mass, and stiffness, and using mathematical equations to solve for the natural frequency. This frequency represents the rate at which the beam can vibrate without any external forces, and is an important factor in understanding the behavior and stability of the beam. The frequency can also be affected by boundary conditions and loading conditions, making it a crucial aspect to consider in engineering and design applications.
kezzstar
1. Deriving frequency in a beam equation, E=Young's Modulus, I = Moment of Inertia, m=mass, L=length, f=frequency.
2. Deriving this equation: (∏/2)√(EI/mL3)
3.(EI(∂4y/∂x4 = -m(∂2y/∂x2) ≈ EI(∂4y/∂x4+ m(∂2y/∂x2 = 0
Don't know where to go from here...

Maybe assume a form of solution and use separation of variables?

The equation in (3) looks wrong. If it is supposed to be "force = mass x acceleration", where is the derivative with respect to time?

You haven't defined the problem clearly. If this is a beam of mass m, how is it fixed? Or is it a cantilever beam (assumed to have no mass) with a mass m at the end?

supported at each end. m in the equation is the mass of the beam itself. Yeah 3. is wrong, just found that too. Argh I'm stumped...

kezzstar said:
supported at each end. m in the equation is the mass of the beam itself. Yeah 3. is wrong, just found that too. Argh I'm stumped...

1 person
Chestermiller said:

Thanks for the reply. Checked that website and still no further forward.

kezzstar said:
Thanks for the reply. Checked that website and still no further forward.
The website gives you the exact equation you need to solve and the method of solution. What specifically are you not able to follow about the development in the reference. It's hard to help without knowing specifically what the stumbling block is.

chet

1 person
Chestermiller said:
The website gives you the exact equation you need to solve and the method of solution. What specifically are you not able to follow about the development in the reference. It's hard to help without knowing specifically what the stumbling block is.

chet

Where abouts in the text am I looking?

kezzstar said:
Where abouts in the text am I looking?
Pages 5.1 through 5.8. Eqn. 5.5 with w = 0 is the equation you are supposed to be solving.

Chet

1 person

## 1. What is the formula for calculating the frequency in a beam equation?

The formula for calculating the frequency in a beam equation is f = (1/2π) √(EI/mL^3), where f is the frequency, E is the modulus of elasticity, I is the moment of inertia, m is the mass per unit length, and L is the length of the beam.

## 2. How is the frequency related to the properties of the beam?

The frequency is inversely proportional to the length and square root of the modulus of elasticity and moment of inertia, and directly proportional to the square root of the mass per unit length. This means that as any of these properties increase, the frequency will decrease, and vice versa.

## 3. What is the significance of calculating the frequency in a beam equation?

Calculating the frequency in a beam equation is important because it helps determine the natural frequency of the beam, which is the frequency at which the beam will naturally vibrate when disturbed. This information is useful in designing and analyzing structures to ensure they can withstand vibrations and avoid resonance.

## 4. Can the frequency in a beam equation be changed?

Yes, the frequency in a beam equation can be changed by altering the properties of the beam such as its length, mass per unit length, or modulus of elasticity. It can also be changed by applying external forces or adding additional supports to the beam.

## 5. How does the frequency in a beam equation affect the stability of a structure?

The frequency in a beam equation is directly related to the stability of a structure. If the frequency of an external force applied to a structure matches the natural frequency of the structure, it can cause resonance and lead to instability or even failure of the structure. Therefore, it is important to consider the frequency in a beam equation when designing structures to ensure they are stable and can withstand any potential vibrations.

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