This document discusses the nonlinear dynamics of cable nets. It explores hidden resonant phenomena that can be detected through frequency response curves. An example is given of applying these concepts to the design of a cable net roof, showing how engineers can use nonlinear dynamics principles from nature to create strong yet elegant structural solutions.
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Nonlinear dynamics of cable nets - An engineering course
7. FREQUENCY RESPONSE CURVE FUNDAMENTAL RESONANCE
立 竜
natural frequency
立 loading frequency
|a|
0
frequency detuning
竜 small non-dimensional parameter
2
2
2 2
3留a p
亮
8 4 a
2 3
u 2竜亮u u 竜留u pcos(立t)
Equation of motion
Response curve
a steady-state amplitude
留 factor of nonlinear term
亮 damping
BEYOND THE COMPLEX MATHEMATICS