Euler Bernoulli to second order ode

In summary, the conversation discusses the replacement of a cantilever beam with a spring mass system for analyzing the movement of the tip when the base is excited at the first eigen mode frequency. The speaker is seeking a paper or book that proves this concept, and a helpful resource is provided for further information and references.
  • #1
umarkhan
8
0
hello,
I have read in a number of papers that if we have a cantilever beam and are only interested in the movement of the tip when the base is being excited at the frequency of the first eigen mode , then the whole beam can be replaced by a spring mass system. Can anyone tell me of a paper or book where this is actually proved?

Thanks.
 
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  • #2
The paper will help clarify the basics and the references at the bottom will help in finding information on the various proofs.

http://faculty.uml.edu/pavitabile/22.403/web_downloads/Final_Project_Cantilever_101806.pdf
 

1. What is an Euler Bernoulli to second order ODE?

An Euler Bernoulli to second order ODE (ordinary differential equation) is a mathematical equation that relates a function to its derivatives up to the second order. It is commonly used in engineering and physics to model systems that involve time and displacement.

2. How is an Euler Bernoulli to second order ODE solved?

An Euler Bernoulli to second order ODE can be solved using various methods such as separation of variables, variation of parameters, and Laplace transforms. The specific method used depends on the complexity of the equation and the initial conditions given.

3. What are the applications of an Euler Bernoulli to second order ODE?

An Euler Bernoulli to second order ODE has many applications in engineering and physics, including analyzing the behavior of structures such as beams, bridges, and plates. It can also be used to model mechanical systems, electrical circuits, and fluid flow.

4. What is the difference between a first and second order ODE?

The main difference between a first and second order ODE is the number of derivatives present in the equation. A first order ODE has only one derivative, while a second order ODE has two. This means that a second order ODE is usually more complex and requires additional techniques for solving.

5. Are there real-world examples of systems that can be modeled using an Euler Bernoulli to second order ODE?

Yes, there are many real-world examples of systems that can be modeled using an Euler Bernoulli to second order ODE. Some common examples include the vibration of a guitar string, the bending of a diving board, and the oscillation of a pendulum.

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