Cyclic symmetry - harmonic load components

In summary, the speaker has a homework problem that involves solving for the displacements of a system using cyclic symmetry. They need to find the harmonic load components, but are unsure of how many harmonics the system has. They are not looking for help with solving the problem, but rather clarification on the number of harmonics and why. The system has three independent forces, so it requires three coefficients for a Fourier series. The zero harmonic has one coefficient, while higher harmonics have two each for the sin and cos terms. Alternatively, the speaker suggests using superposition and the cyclic symmetry of the system to solve the problem without Fourier coefficients, unless using computer software.
  • #1
blue24
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I have a homework problem where I have to solve for the displacements of the attached system using cyclic symmetry. To do this, I know that I have to find the harmonic load components of the system. One thing that my professor did not make clear (or if he did, I missed it) is how to determine how many harmonics a system has. Can anyone tell me how to determine this?

I am not looking for help solving for the displacements. I'll sweat through that on my own :) I just want clarification on how many harmonics this system has, and why.

Thanks for the help!
 

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  • #2
You have three independent forces, so you need three coefficients to represent them as a Fourier series.

The zero harmonic has one coefficient, and higher harmonics have 2 each, for the sin and cos terms (or real and imaginary parts of a complex coefficient, or phase and quadrature, depending how you want to think about the problem).

Personally I wouldn't bother with Fourier coefficients here. I would consider a unit load at one vertex of the triangle, and then rotate the solution through 120 degrees and use superposition. That is using the cyclic symmetry of the system directly. Introducing Fourier coefficients doesn't seem to make it any easier, if you are doing it by hand. If you are using computer software, maybe that will force you to use Fourier coefficients.
 

1. What is cyclic symmetry in structural engineering?

Cyclic symmetry is a property of a structure where the geometry and loading conditions repeat themselves around a central axis or point. This allows for simplification of analysis and design, as only a portion of the structure needs to be considered and the results can be extrapolated to the rest of the structure.

2. What is a harmonic load component?

A harmonic load component is a type of load that varies sinusoidally with time. It is often used to model cyclic loads, such as wind or seismic forces, in structural analysis. Harmonic loads have a frequency and amplitude that can be adjusted to simulate different loading scenarios.

3. Why is cyclic symmetry important in structural analysis?

Cyclic symmetry allows for simplification of analysis, as the structure can be divided into smaller sections and the results can be extrapolated to the entire structure. This reduces the computational effort and time required for analysis, making it more efficient.

4. How is cyclic symmetry applied in real-world structural design?

Cyclic symmetry can be applied in real-world structural design by taking advantage of the simplification it offers. This can lead to more efficient and cost-effective designs, as well as reducing the risk of errors or oversights in the analysis process.

5. What are some challenges associated with analyzing structures with cyclic symmetry?

One of the main challenges with analyzing structures with cyclic symmetry is ensuring that the simplifications made do not significantly affect the accuracy of the results. Additionally, dealing with discontinuities or changes in geometry within the cyclically symmetric structure can also be challenging. It may also be difficult to accurately model and account for the effects of imperfections or irregularities in the structure.

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