Mechanical Vibrations, Modal Analysis & Industrial Instrumentation

Continuous Beam Modal Analysis: Determine bending shapes, compare cantilever properties (Steel, Aluminum, Titanium), and inspect non-moving nodal points where deflection drops to zero. Passive Mass Isolation & Anti-Resonance: Tune a secondary absorber ($k_2/m_2$) to match machine excitation ($\omega$), generating an out-of-phase force that stops the primary mass ($X_1 = 0$).

ISO 10816 Severity Gauging: Measure RMS velocity ($v_{\text{rms}}$) across varying forcing conditions to determine equipment safety zones. Fourier & Bode Analysis: Correlate time waveforms with peak spectral frequencies and transmissibility curves using DSA instrumentation.

Active Apparatus Testbed: Mechanical cantilever clamping rig, vice vice stand, electrodynamic shaker, 2-DOF mass-spring-damper, Jeffcott rotor with shaft probes, and modal impact hammer. Signal Instrumentation: Laser Doppler Vibrometer (LDV), strain gauges, piezo accelerometers, Eddy-current proximity probes, and digital scope/FFT analyzer. Reagents & Alloys: Structural Steel, Aircraft Aluminum 7075-T6, and Titanium Ti-6Al-4V. Data Deck: Sliders for Beam Length ($0.4\text{--}2.0\text{ m}$), Forcing Frequency ($5\text{--}350\text{ rad/s}$), Stiffness ($20\text{--}800\text{ N/m}$), Damping, Rotor Speed, and Eccentricity ($10\text{--}200\text{ mm}$).

Step 1: Modal Analysis of a Continuous Cantilever Load Standard Rig and choose Beam Modal. Set excitation to Harmonic and toggle through Mode 1 to Mode 4 bending shapes. Observation: Bending shapes show distinct zero-amplitude nodes (Mode 2 has one node, Mode 3 has two, Mode 4 has three) while the accelerometer traces the motion. Step 2: Tuned Vibration Absorber (TVA) Anti-Resonance TuningSwitch to Tuned Absorber module and set excitation to $10\text{ rad/s}$ to induce resonance on the machine $M_1$ ($v_{\text{rms}}$ spikes into Danger Zone D). Adjust Absorber Stiffness $k_2$ and click Auto-Tune TVA.

Step 3: Finding Rotor Critical SpeedsSwitch to Rotor Whirling and increase speed towards $10\text{ rad/s}$.

Step 4: Observing Supercritical Self-CenteringSet speed above $30.0\text{ rad/s}$.

Step 5: Impact Hammer & Signal Spectrum Testing Run Harmonic or trigger Tap Impact.View the FFT Spectrum or Bode Response on the DSA to inspect natural frequencies, peak resonance, and attenuation