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I came across the concept of Rayleigh damping. I aqm told it is unrelated to viscoelasticity and as a result is unable to reproduce the behaviour of real materials under harmonic excitation.

I can not understand why.

Considering for simplicity a 1D setting, a ball of mass $$M$$ linked to a rigid wall by a spring of elastic constant $$K$$. Rayleigh damping dictates to model losses via a matrix (in our case, a scalar) given by $$D = \alpha M + \beta K$$.

The motion of the ball under an applied harmonic force is represented by the solution of the ODE

$$M\ddot{x}+D\dot{x}+Kx = F_0 cos(\omega t)$$.

Well it seems to be that this is analogous to considering the material as a Kelvin-type (spring and newtonian dampener in parallel) viscoelastic one. Not the best representation for real materials, but not too bad in some instances. Is all this correct?

Thanks

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# Rayleigh Damping

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