New scaling of critical damping and reduced frequency for mechanically excited systems

Md. Mahbub Alam

doi:10.59400/sv2600

New scaling of critical damping and reduced frequency for mechanically excited systems

Md. Mahbub Alam Mechanical and Automation Engineering Department, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China

Article ID: 2600

DOI: https://doi.org/10.59400/sv2600

Keywords: damped vibration; excited system; frequency ratio; damping ratio; maximum amplitude

Abstract

This paper introduces a universal framework for understanding the vibration responses of systems subjected to harmonic excitation. By examining a simplified cylinder-spring-damper model, the study refurbishes traditional scaling methods for the excitation frequency ratio and critical damping ratio. The findings indicate that in damped systems, the maximum amplitude of vibration does not align with the natural frequency. This observation leads to the introduction of a new scaling method for reduced frequency. This new approach aligns resonance peaks at the new reduced velocity of 1.0 across different damping ratios, providing a consistent characterization of vibration behavior. A new critical damping ratio of 0.707 is identified for an excited system as opposed to the traditional damping ratio of 1.0 for an unexcited system. Key properties such as maximum amplitude, phase lag, bandwidth, and quality factor are analyzed, demonstrating that the proposed reduced frequency and critical damping ratio effectively capture the dynamics of both damped and undamped excited systems. The findings offer significant insights for practical applications in engineering and various scientific fields.

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Published

2025-03-18

How to Cite

Alam, M. M. (2025). New scaling of critical damping and reduced frequency for mechanically excited systems. Sound & Vibration, 59(2), 2600. https://doi.org/10.59400/sv2600

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