# Effect of initial stress on the natural frequency of vibration

• Hassan2
In summary, the conversation discusses the phenomenon of changing natural frequency in a string instrument when the string is tightened. This cannot be explained by linear elasticity theory. Additionally, applying a constant axial load does not affect the vibration frequency in a bar simulation, as external forces do not impact natural frequency. The question arises whether non-linearity is involved when considering the effect of initial stress on vibration characteristics in structures. The correct method for modeling tensioned strings must include tension, mass, length, and deflection. A good starting point for understanding string vibration is provided at the given link.

#### Hassan2

TL;DR Summary
Does initial stress ( preloading) have effect on vibration of linear structures?
Hello all,

We might have observed that by tightening a string of a musical instrument, the natural frequency of the string changes. But I can not describe this phenomenon by the theory of linear elasticity. Also if we simulate the vibration of a bar with the help of structural software tools, applying an constant axial load does not make change on the vibration frequency. This is easy to explain because the preloaded vibration is in fact a force vibration and we know that the external force does not affect the natural frequency. Given that the statements above are right, a question come into mind:

When people talk about the effect of initial stress ( per-loading) on the vibration characteristics of a structure, is some kind of non-linearity included?

Last edited:
Linear elasticity does not apply to tensioned strings. The structural software tools that you mention assume small deflections, therefore those tools do not include the effects of tension in the calculations.

The correct method of modeling tensioned strings must include the tension, the mass of the string, the length, and the effect of deflection. This link is a good place to start: https://en.wikipedia.org/wiki/String_vibration.

etotheipi, berkeman and Hassan2