General procedure for finding stiffness in vibration problems

Then, divide that force by the displacement to find the stiffness.In summary, To find the natural frequency of a single degree of freedom system, the formula ω=√k/m is used. However, for finding the stiffness "k" in most SDOF problems, a general procedure can be followed. This involves determining the force on the system when it is moved from its equilibrium position and dividing it by the displacement. This procedure can be applied to various systems such as a rigid massless bar with springs attached, an L-shaped bar with gravity acting, or a water column in a U-shaped test tube.
  • #1
bda23
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Hi, I have forgotten quite a bit of my vibration studies, so I have a fairly basic question. Essentially, when you want to find the natural frequency of a single dof system, you use ω=√k/m. However, does anyone know a general procedure (not problem-specific) for finding "k" that is applicable to most SDOF problems. Examples would be something along the lines of a a rigid massless bar, hinged at one end, with a few springs attached and a mass at one end, or a rigid L-shaped bar hinged somewhere and gravity acting, or a water column in a U-shaped test tube (height vibrating with gravity)... I think you get the idea. Basically, I am looking for a series of steps that you would go through in all these situations in order to find the stiffness. Thanks.
 
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  • #2
Stiffnesss = Force / displacement.

Work out the force on the system when it is moved a small distance from its equilibrium position.
 

1. How do you determine the stiffness in a vibration problem?

The stiffness in a vibration problem is determined by calculating the ratio of the applied force to the resulting displacement. This is known as the stiffness constant and is typically denoted by the letter k.

2. What is the general procedure for finding stiffness in a vibration problem?

The general procedure for finding stiffness in a vibration problem involves setting up the equations of motion for the system, which includes the mass, damping, and stiffness terms. These equations can then be solved using numerical or analytical methods to determine the stiffness value.

3. Can stiffness be determined experimentally in a vibration problem?

Yes, stiffness can be determined experimentally in a vibration problem by using various methods such as impact testing or modal analysis. These methods involve applying a known force or excitation to the system and measuring the resulting displacement or response.

4. What factors can affect the stiffness in a vibration problem?

The stiffness in a vibration problem can be affected by various factors such as material properties, geometry, and boundary conditions. For example, increasing the stiffness of a material or changing the shape of a component can result in a higher stiffness value for the system.

5. How does stiffness impact the behavior of a vibrating system?

Stiffness plays a critical role in determining the natural frequencies and mode shapes of a vibrating system. A higher stiffness value typically results in higher natural frequencies and shorter periods of vibration. It also affects the amplitude and damping of the system's response to external forces or excitations.

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