Vibration Testing & Experimental Modal Analysis (EMA)

1. Vibration Testing & Experimental Modal Analysis (EMA) • Purpose of vibrations measurements: • Natural frequencies of a structure or machine are important for system’s dynamic behavior. • Verify an analytical model (frequencies and mode shapes) • Experimentally determine dynamic durability • Machinery diagnostics for maintenance (monitoring) • EMA frequencies, mode shapes, damping ratios.

2. Vibration Testing & EMA (continued) Vibration test assumption: testing system is linear Modal testing requires instrumentation, dsp, parameter estimation, vibration analysis. Measurement Hardware:

3. Increasing hammer head mass Decreasing upper frequency Increasing stiffness of tip of hammer Increasing upper frequency Vibration Testing & EMA (continued) Exciters Shaker (electromagnetic, electrohydraulic) – stinger Impulse hammer – tip Signal generator – sweep sinusoidal, random, … Mass loading: added mass due to shaker and its attachment Stinger – minimizes mass loading Impact hammer – avoid mass loading Cut off frequency( ) – the largest value of frequency reasonably well excited by the hammer hit.

4. Vibration Testing & EMA (continued)

5. Vibration Testing & EMA (continued) Transducers – piezoelectric material is the most popular Strain gauges – metallic or semi conductor material part of Wheatstone bridge circuit Signal conditioner – amplifier For low frequency motion, accelerometers are not suitable.

6. A/D FFT digital freq signal analog time signal (Acc, force, vel, disp, strain) digital time signal Digital Signal Processing Signal analyzer – FFT analyzer aliasing: improper sampling time error Shannon’s sampling theorem: To avoid aliasing, 2.5 samples per cycle antialiasing filter – low pass filter  cut off frequencies higher than half the maximum frequencies of interest (Nyquist frequency)

7. Digital Signal

8. Aliasing

9. Discrete Fourier Transform

10. Window Leakage – error due to finite time (cut off mid period) use window to avoid it Difficulty of modal analysis is choosing the sampling frequency and data size N. x(t) t Sampling time

11. Window x(t) t Sampling time x(t) Hanning window t Sampling time

12. Random Signal Analysis Since the transducer contains noise, averaging is necessary. Autocorrelation function of random signal x(t)

13. For random f(t) For deterministic f(t) Expected value (or ensemble average) Random Signal Analysis k m

14. Random Signal Analysis Coherence function (measurement of noise in the signal)