Modification of Resonant Frequencies in Mechanical Systems through Effective Mass Adjustment

Abstract

Resonance in mechanical systems can lead to excessive vibration and premature component failure when operating frequencies coincide with a system’s natural frequency. While vibration is often mitigated by reducing excitation forces through balancing and alignment, such approaches are ineffective when resonance is the root cause. This paper presents a practical method for identifying and modifying resonant behaviour by altering the effective mass of a system. Using static deflection measurements and bump test data, system stiffness, damping, amplification factor, and effective mass are estimated. A detailed case study of a gearbox experiencing resonance at the gear meshing frequency demonstrates how adding a calculated inertial mass shifts the resonance away from the excitation frequency. This paper tells how to make a calculated change in a resonance frequency of a structure by changing its effective mass and includes two documented case histories that illustrate the technique. Experimental results show a significant reduction in vibration levels after retuning the system. The study confirms that controlled mass modification is an effective and economical method for mitigating resonance in localized mechanical subsystems.

Introduction

The text explains how resonance in mechanical systems can cause excessive vibration and premature component failure, not because of large forcing forces, but because modest forces coincide with a system’s natural (resonant) frequency, leading to high vibration amplification. The amplification factor depends on the ratio of forcing frequency to natural frequency and the level of damping.

The resonant frequency of a system is primarily determined by its effective stiffness and effective mass. While damping and large displacements can affect accuracy, simplified resonance equations are generally sufficient for typical machinery vibrations. Instead of reducing the forcing function, the article focuses on mitigating resonance by deliberately shifting the natural frequency—specifically by changing the effective mass of the system.

Two case studies illustrate this approach:

1. Motor Resonance
   A motor exhibited resonance at twice its running speed. By measuring stiffness through applied force and displacement, the effective mass was calculated. The result closely matched a common engineering approximation (90% of total mass), validating the method for simple systems where the entire machine vibrates as a single mass.

2. Gearbox Resonance
   A more complex case involved a gearbox with localized resonance near the input shaft bearing at the gear meshing frequency. Because only part of the machine was involved, the effective mass could not be estimated directly. Instead, bump test data were used to derive system compliance, dynamic stiffness, damping ratio (via half-power and transfer-function slope methods), and amplification factor. From these, the static stiffness and effective mass were calculated, revealing that only a small portion of the gearbox mass participated in the resonance.

Using these parameters, the system was retuned by adding a concentrated inertial mass to shift the resonant and anti-resonant frequencies away from the excitation frequency. After installing the added mass, follow-up bump tests confirmed the frequency shift, and vibration levels were reduced by up to four times, with further improvement after continued operation.

Conclusion

Because the resonant frequency is a function of the square root of both the effective mass and stiffness, it is often not practical to cause a significant change in the resonance by changing either of these parameters when the entire structure is part of the vibration system. Such was the case with the motor mentioned earlier. In such a case, it would be necessary to add a much larger mass relative to the mass of the primary system. In the case of the motor, it was not practical to change the resonance by adding mass to the system, and other methods were employed to control the vibration. However, in the case of the gearbox, the effective mass of the vibrating system was a relatively small part of the entire system, and adding an inertial mass was very effective in controlling the vibration.

References

[1] Vance, John M. Machinery vibration and rotordynamics / John Vance, Brian Murphy, Fouad Zeidan.p. cm. [2] Baker Hughes MDM Literature. [3] Mobius VCAT-III vibration analysis literature. [4] Mobius VCAT-IV vibration analysis literature.

Copyright

Copyright © 2025 Sushil Sharma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.