c1, c2 = Smart Spring viscous damping coefficients associated with primary and secondary load paths F = external (input) force applied to the Smart Spring k = effective dynamic stiffness of the Smart Spring k1, k2 = Smart Spring constants associated with primary and secondary load paths m = effective inertia of the Smart Spring m1, m2 = mass of external and internal sleeves in the Smart Spring N = contact force applied by piezoelectric stack T = Smart Spring period of actuation t = time x = displacement (output) yielded by the Smart Spring y = displacement associated with the Smart Spring secondary load path = dynamic stiffness complex coefficients = dry friction coefficient = Smart Spring control frequency, 2 =T ! = Smart Spring frequency of excitation
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Oxley et al. (2009) studied this question.