140 Friction-Induced Vibration and Self-Organization
where γ
1
, γ
2
, γ
3
, and γ
4
are determined from the characteristic equation of the
system.
Adams (1996) presented results by applying the mathematical model to
several cases. He obtained the maximum ratios of the real part of λ to the
absolute value of the imaginary pan of λ as a function of dimensionless
speed v and presented results for various values of the friction parameter
(α) for different values of the foundation stiffness (k) for various values of
beam tension (T) and for different values of the asperity spring stiffness
(K). Of particular importance were the existences of eigenvalues with pos-
itive real parts that indicate a dynamic instability. In these results, as the
speed was i ...