I am trying to simulate the impact of a sinusoidal force on a Beam, yet I registred this beating signal (Displacement by time).
The freaquency of excitation was the same as the first natural frequency.
for me I find it strange to have this beating signal since I thought it would take a sinus shape.
The attached picture is the one for Displacement by time evolution
Hi Mohammed,
Do you have a homogeneous medium and uniform shape throughout the beam? If not, that might be a contributing factor.
Romik
Romik Khajehtourian Yes a rectangular beam with a uniform thickness and no twist
Considering that this beam is equivalent to a simple harmonic oscillator, that is the expected result if the excitation frequency is close to the natural frequency of the system. If you have an undamped (or very lightly damped) system and excite it harmonically near the natural frequency, the total response would be a summation of two harmonics with very closely spaced frequencies f1 and f2. Then, consider the "sum to product" trigonometric identity:
cos(2\pi f1t) + cos(2\pi f2t) = 2cos( 0.5(f1 +f2)2\pi t)*cos(0.5(f1 - f2)2\pi t)
So you end up with slowly varying amplitude (beats) at the frequency abs(0.5(f1 - f2)), while the high frequency oscillations occur at the frequency 0.5(f1 +f2), which is basically the average of the two frequencies.
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