Assignment 1) Compute the natural frequencies of the free-fixed bar of slide 3 (𝜌=2700𝑘𝑔/𝑚3,
𝐸 = 70 𝐺𝑃𝑎, 𝐿 = 2 𝑚, b = h = 0.05 m) in the frequency range [0 10] kHz and plot the corresponding mode shapes.
2) Compute the natural frequencies of the same bar in free-free conditions and plot the corresponding mode shapes.
3) For the free-fixed bar excited at the free-end, plot and comment the FRF for output positions located in 𝑥ҧ = 𝐿/2 and 𝑥ҧ = 𝐿/5. Consider the following cases:
• undamped bar (standing wave solution);
• damped bar (wave propagation solution) – loss factor 𝜂 = 0.01;
• damped bar (modal superposition approach) – loss factor 𝜂 = 0.01.
4) For the free-fixed bar excited at the free-end, plot and comment the driving-point impedance in the following cases:
• damped bar (wave propagation solution) – loss factor 𝜂 = 0.01;
• damped bar (modal superposition approach) – loss factor 𝜂 = 0.01.
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Vibroacoustics - Cesare Lupo Ferrari - Politecnico di Milano
