Lab 05: Vibration Testing of Beams

Lab Overview

Course: AE 417 – Aerospace Structures and Instrumentation Laboratory (David Sypeck / Reshma Kubsad) | November 14, 2025
Objective: Experimentally determine resonance frequencies and nodal positions for multiple bending modes of short and long Al-6061-T651 cantilever beams; compare to Euler-Bernoulli beam theory predictions.
Specimens: Short beam — L = 761 mm, h = 5.05 mm, b = 25.55 mm; Long beam — L = 1275 mm, h = 5.01 mm, b = 25.52 mm
Instrumentation: Electrodynamic shaker, sweep sine generator, power supply amplifier, ICP® accelerometer + signal conditioner, digital oscilloscope, digital stroboscope on tripod
Material properties used: E = 68.90 GPa, ρ = 2700 kg/m³ (Al-6061)

Short and long Al-6061 beam samples (Fig. 1)

Electrodynamic shaker with beam (Fig. 7)

Oscilloscope and sine generator (Fig. 5)

Procedure & Methodology

The short beam was clamped to the electrodynamic shaker and the sweep sine generator frequency was increased from zero until large-amplitude beam deflection was observed (Mode 1 resonance). Resonance frequency was recorded simultaneously from: the sine generator display (F_SSG), the digital oscilloscope period reading (F_piezo from the ICP accelerometer), and the digital stroboscope (F_strobe, which froze the beam motion at resonance). Node positions were measured with a ruler from the clamped end. This was repeated for Modes 2 and 3 on the short beam, and Modes 1–4 on the long beam.

Theoretical resonance frequencies were calculated using Euler-Bernoulli beam theory: ω_n = (λ_n L)² / L² · √(EI/ρA), where eigenvalues λL were 1.88, 4.69, 7.85, and 11.00 for modes 1–4. Theoretical nodal distance ratios x/L for each mode shape were used to compute expected node positions.

Stroboscope and ICP accelerometer (Fig. 6)

Aerospace structures — rib and model airplane (Fig. 2)

Beam mounted on shaker — test in progress

Results & Analysis

Short beam frequencies (Hz):

Mode	F_SSG	F_piezo	F_strobe	Theoretical
1	6.5	6.41	6.5	7.15
2	40.1	40.32	40.06	44.5
3	111.5	111.1	111.4	124.72

Short beam % difference from theory: 9.5–11.6% across all modes; long beam 5.3–8.0%. Long beam consistently closer to theory.
At Mode 1, F_SSG and F_piezo differed by 13.6% for the short beam — the piezo oscilloscope struggles below 10 Hz. Higher modes converged to <3% between all three measurement methods.
Nodal positions matched theoretical ratios within 3.32% for both beams — consistent with human measurement error in ruler-based node location.
Aerospace structures (wing rib and model airplane) were also tested qualitatively, showing multiple complex mode shapes at distinct frequencies.

Experimental vs theoretical frequencies

Nodal distance comparison — short and long beams

% difference summary tables