Fundamental frequency of an object with nonlinear stiffness.

In summary, the conversation discusses the topic of finding the fundamental frequency of objects with varying stiffness, specifically a simply supported beam resting on curved supports. The person asking for resources is directed towards the Duffing equation or Duffing oscillator, which can be easily researched through Google.
  • #1
jasc15
162
5
Hi all. It's been a few years since I've posted here, but it's remained a great go-to resource for me.

Any time I have dealt with mechanical vibrations, the fundamental frequency was based on a constant stiffness. However, I have never encountered the subject of finding the fundamental frequency of objects where the stiffness varies with displacement from equilibrium (i.e., a simply supported beam resting on curved supports, such that the supported length changes as the beam deflects.)

Could someone point to a resource that deals with this subject?

Much appreciated.
 
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  • #2
The simplest system mathematically is usually called a Duffing equation or Duffing oscillator, after the person who first studied it. Now you know what it's called, Google is your friend.
 
  • #3
Thanks for the reply. That should be enough of a foot in the door to look into this further.
 

FAQ: Fundamental frequency of an object with nonlinear stiffness.

What is the fundamental frequency of an object with nonlinear stiffness?

The fundamental frequency of an object with nonlinear stiffness refers to the lowest natural frequency at which the object can vibrate. It is determined by the stiffness of the object and can be affected by factors such as material properties, shape, and boundary conditions.

How is the fundamental frequency calculated for an object with nonlinear stiffness?

The fundamental frequency can be calculated using the formula f = (1/2π)√(k/m), where f is the fundamental frequency, k is the stiffness of the object, and m is its mass. This formula assumes that the object's stiffness is linear, but for objects with nonlinear stiffness, a more complex calculation may be needed.

Can the fundamental frequency of an object with nonlinear stiffness change?

Yes, the fundamental frequency of an object with nonlinear stiffness can change depending on various factors such as changes in material properties, shape, or boundary conditions. This is because these factors can affect the stiffness of the object, which in turn affects its fundamental frequency.

How does the fundamental frequency of an object with nonlinear stiffness affect its behavior?

The fundamental frequency of an object with nonlinear stiffness plays a crucial role in determining its dynamic behavior. If an external force is applied to the object at its fundamental frequency, it will experience resonance, which can lead to excessive vibrations and potential damage. Understanding the fundamental frequency is essential for designing structures and machines that can withstand dynamic loads.

Can nonlinear stiffness be beneficial for certain applications?

Yes, nonlinear stiffness can be beneficial for certain applications, such as shock absorbers or vibration dampers. In these cases, the nonlinear stiffness allows the object to absorb and dissipate energy, reducing the impact of external forces and protecting the object from damage. Nonlinear stiffness can also be used to tune the fundamental frequency of an object to a desired value for specific applications, such as musical instruments.

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