Resonance & Structural Analysis Flashcards

What is resonance in the context of machinery vibration?

Answer: A condition where an excitation frequency coincides with a system natural frequency, causing amplified vibration response

Resonance occurs when an excitation frequency matches a structural or mechanical natural frequency, causing the vibration amplitude to be amplified by a factor related to the system's damping ratio.

What is a natural frequency (also called resonant frequency)?

Answer: The frequency at which a system vibrates freely after an initial disturbance, determined by its mass and stiffness

A natural frequency is a property of the system itself (fn = (1/2π)√(k/m)) that determines the rate at which it oscillates freely; it depends only on mass and stiffness, not on the excitation.

What is the damping ratio, and how does it affect vibration at resonance?

Answer: The ratio of actual damping to critical damping; lower ratios produce higher amplitude amplification at resonance

The damping ratio (ζ = c/cc) is the ratio of actual damping to critical damping; at resonance the dynamic amplification factor is approximately 1/(2ζ), so lower damping produces much higher resonant peaks.

What is a mode shape in structural dynamics?

Answer: The pattern of deformation that a structure exhibits when vibrating at a specific natural frequency

A mode shape describes the relative deflection pattern of all points on a structure when it vibrates at a particular natural frequency; each natural frequency has an associated unique mode shape.

What is a frequency response function (FRF) used for in structural analysis?

Answer: Calculating the ratio of output response (vibration) to input force as a function of frequency, used to characterize system dynamics

The FRF (H(ω) = X(ω)/F(ω)) describes how a structure responds to excitation at each frequency, revealing natural frequencies as peaks and providing the basis for modal analysis.

What is experimental modal analysis (EMA) used for?

Answer: Determining a structure's natural frequencies, mode shapes, and damping ratios from measured vibration responses

EMA is a testing procedure that measures FRFs at multiple structural points to extract natural frequencies, mode shapes, and damping ratios, which are used to diagnose resonance problems and validate finite element models.