Shaping of a system's frequency response using an array of subordinate oscillators

Area of Science:

• Mechanical Engineering
• Vibration Analysis
• Structural Dynamics

Background:

• The frequency response of oscillating structures is critical in many engineering applications.
• Tailoring structural response often involves complex design considerations and added mass penalties.

Purpose of the Study:

• To demonstrate how an array of subordinate oscillators can engineer the frequency response of a primary structure.
• To provide analytic methods for shaping magnitude and phase characteristics.
• To explore the advantages of using multiple subordinate oscillators over single ones.

Main Methods:

• Derivation of exact analytic equations of motion for the coupled primary-subordinate system.
• Analysis of frequency response functions based on prescribed dynamic properties of subordinate oscillators.
• Investigation of systems with a small number of oscillators and minimal added mass.

Main Results:

• Achieved precise control over the magnitude and phase of the primary structure's frequency response.
• Demonstrated the ability to engineer nearly linear phase or constant amplitude over specific frequency bands.
• Showcased that increasing the number of subordinate oscillators enhances response shaping capabilities without significant mass increase.

Conclusions:

• Arrays of subordinate oscillators offer a powerful and efficient method for tailoring structural frequency response.
• The analytic framework provides a direct design approach for vibration control.
• This technique surpasses traditional single dynamic vibration absorber designs in reshaping capabilities.