Forced oscillations of a linear system

[watty]

Hello,

I am currently working on a lab in which we are studying the behaviour of chain of metal bars attached together with nylon wire in such a way as to to mimic the ability of solids or liquids to transmit a wave.

After studying the normal modes of the system as well as the quality factor, we excited the system at frequencies not equal to normal modes and analysed the frequencies present using an optical detector wired through a computer that can perform a Fourier analysis of the spectrum.

When the system was being driven, we expected to see only one frequency present in the Fourier spectrum: that of the driving oscillator. However we also saw two very small peaks at normal frequencies as well as a significant peak at what appeared to be 3 times the driving frequency.

The two small peaks I can understand as maybe imperfections of the system, ie the forced oscillation does not fully overcome the natural properties of the system but I don't understand why the system is also oscillating at 3 times the driving frequency.

NB. there is also a normal mode reasonable close to this significant unexplained peak.

 

[Bob S]

When you theoretically analyze the propagation of waves in this chain, are you fully accounting for the rotational moment of inertia in the individual metal bars? The metal bars have both center-of-mass motion (linear inertia) and rotational inertia. Could this cause mode-conversion?
Bob S

 

[watty]

no i have not taken this into account. you mean that they are oscillating not just on one axis but in several directions? this could be the case. each metal bar is attached at each end to two long nylon wires. the wires are at high tension but there could be some extension and contraction in the wires and i suppose the bars are not moving exclusively up and down but also left and right too. Is this what you mean?

 

[watty]

ps. mode conversion? what does this mean?