Adjustments to Address Resonance

June 8, 2023

Back to: Resonance in Product Development

The Basics of Resonance lesson introduced the three properties a system’s resonant frequency depends on: stiffness, mass, and damping. If an engineering team identifies resonances, they can adjust these system properties or the driving speed/frequency to mitigate the potential for failure. The design decision will depend on the excitation frequency, packaging constraints, and available materials.

Calculating Natural Frequency

Equation 2 is the calculation for the natural frequency of a single-degree-of-freedom system.

(1) $\begin{equation*} f=\frac{\omega}{2\pi} \end{equation*}$

Equation 2

In this equation, omega (ω) is the angular frequency of the system’s oscillation. Equation 3 is the calculation for angular frequency.

(2) $\begin{equation*} \omega=\sqrt{(k/m)} \end{equation*}$

Equation 3

When Equation 3 is substituted for ω, Equation 4 becomes the calculation for natural frequency.

(3) $\begin{equation*} f=\frac{\sqrt{(k/m)}}{2\pi}} \end{equation*}$

Equation 4

Stiffness

Stiffness determines an object’s resistance to deformation following external force. Increasing the stiffness raises the resonant frequency. The stiffer an object, the less displacement it will experience during excitation.

Selecting a different material for design can increase an object’s stiffness, or there are stiffeners engineers can apply to the resonating component, including adding additional fasteners. When considering a whole system, an engineer may choose instead to adjust the stiffness of components that connect the resonating object to the base structure, such as a shaft or belt.

Actions to adjust stiffness—such as changing materials or adding stiffeners—can increase the system’s mass, which could cancel out the effects of an increase in stiffness. Engineers must consider the changes in the system mass when increasing stiffness.

Mass

Increasing the mass of a system lowers its resonant frequency. With more weight, the object has less displacement as it oscillates.

Determining and adjusting the mass of a component can vary in difficulty depending on its weight contribution to the whole system. In [1], Smith offers several approaches to calculating the effective mass of a resonating component.

Adding mass to a system can alter its mode shapes and functionality. The engineer must also consider the force rating of their vibration shaker, as an increase in mass reduces the force a shaker can exert.

Damping

Certain materials, such as rubber, dissipate vibration well. If an engineer can add an absorber to the design, it can reduce the magnitude of resonant vibration. They might apply the material directly to the resonating component or between the structure and a constraint. It is not always necessary to cover the entire surface with dampeners. Sometimes, strategic placement in some areas is enough.

Tuned absorbers, another type of dampener, produce an anti-resonance tuned to the resonating frequency to reduce the component’s response. An anti-resonance is a sharp peak between two resonance peaks. As the system oscillates, the absorber oscillates in accord with it, helping to dampen the resonance peaks.

Considerations

Engineers should consider the system’s other resonant frequencies when adjusting a system to avoid encountering another resonance.

If the component vibrating at the resonant frequency is controllable, then adjusting the excitation frequency may be a plausible solution to resonance. Adjustments may include alignment or balancing. However, the magnitude of the force is not typically an issue, but it matches a resonant frequency [1]. Therefore, adjusting the resonating component is usually an engineer’s first choice.

Factors such as temperature, pressure, fluid flow, and other environmental factors can impact material properties and have significant effects on stiffness. Changes in resonant frequency can arise under various operating conditions as a result and need to be addressed both at the product design stage and during testing.