# Need help in solving SDOF cantilever

• Engineering
• pjotrjanusz
In summary, the conversation discusses methods for calculating various parameters for a SDOF system, such as force, damping, mass, and stiffness. The confusion arises when trying to apply a SDOF model to a continuous beam with infinite natural frequencies. The solution is to use curve fitting to match the natural frequency and damping rate of the data plot, and to measure stiffness and mass directly.

#### pjotrjanusz

Homework Statement
Calculate force, mass, damping and stiffness of horicontally oscillated IPE beam, completely fixed on the one end and free on the other
Length: 5990mm ;Deflection: 1cm, 3cm, 5cm, 7cm
Relevant Equations
I am given data of our project that includes the measurement of the acceleration of the beam after being deflected as named above each and left to swing for 1 minute.
1.) I'd calculate the force needed to deflect the beam by using the method of virtual work for t=0 which is u[L] = FL^3/3EI. From there on I am completely clueless.
2.) Task is to calculate damping, mass and stiffness of the SDOF by using the data sheets which is basicly the u''(t) function of each experiment. I thought the mass of the SDOF can be generalised by putting the mass of the IPE beam (V*p) concentrated in a singular dot which represents the SDOF. Am I wrong by assuming this?
3.) Bending-stiffness in statics is always a combination of young's modulus and moment of inertia, but how do I find out the stiffness the beam has when experiencing dynamic stress? I don't know how to calculate the stiffness.
4.) I'd calculate the damping of the system by solving the differential equation of motion. But how am I supposed to get the inputs for that equations?
-> Basically I am confused because we are only given the acceleration graphs of the tip of that beam after being deflected by us. I just need a good tip on how to start. Do I have to select some critical coordinates in those graphs and use them as input for the ODE to or three times as damping and stiffness is going to be constant anyways? each of the 8 graphs contain more than 60k coordinates... You can cleary see how lost I am so I'd be so thankfull for any help or tips!

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Have you learned that continuous beams have an infinite number of natural frequencies? And that a SDOF model applies to only one of those natural frequencies, normally the lowest frequency? The confusion seems to be that a SDOF model has three parameters, and you have 60,000 data points. These type of problems are solved by curve fitting.

pjotrjanusz said:
From there on I am completely clueless.
Well, here are some clues:
1) The data plot shows the natural frequency, and the damping rate.
2) Natural frequency of a SDOF system is the ratio of stiffness to mass.
3) You can measure the stiffness directly by pulling on the beam with a known force and measuring the deflection with a ruler.
4) That allows you to calculate the mass of a SDOF with the same natural frequency of the beam. That mass will not be equal to the mass of the beam. Do you know why?
5) Now that you have stiffness and mass, find the damping that matches the rate of damping in the data. Plot the response of the resulting equation on the same axes as your experimental data. They should match.

berkeman

## 1. What is a SDOF cantilever?

A SDOF (single degree of freedom) cantilever is a structural element that is supported at only one end and has one degree of freedom, meaning it can only move in one direction.

## 2. How do I solve a SDOF cantilever?

To solve a SDOF cantilever, you will need to use equations of motion, such as the Euler-Bernoulli beam equation, and apply boundary conditions to determine the deflection and stress at different points along the cantilever.

## 3. What are the common applications of SDOF cantilevers?

SDOF cantilevers are commonly used in structural engineering for various applications, such as bridges, buildings, and aerospace structures. They are also used in mechanical engineering for components like springs and beams.

## 4. What factors affect the behavior of a SDOF cantilever?

The behavior of a SDOF cantilever is affected by factors such as the material properties, geometry of the cantilever, applied loads, and boundary conditions. These factors can influence the deflection, stress, and natural frequency of the cantilever.

## 5. How can I improve the performance of a SDOF cantilever?

To improve the performance of a SDOF cantilever, you can modify the material properties, change the geometry, or add supports or reinforcements to reduce stress and increase stiffness. You can also optimize the design using numerical methods or experimental testing.