ABSTRACT
This chapter discusses the contributions in eight folds as follows. (1) Equivalent motion equation for class IV fractional vibrators. (2) The quasiequivalent mass, quasiequivalent damping, quasiequivalent stiffness, quasiequivalent damping ratio, quasiequivalent damping free natural frequency, quasiequivalent damped natural frequency, quasiequivalent frequency ratio, quasiequivalent logarithmic decrement, and quasiequivalent Q factor for fractional vibrators in class IV. (3) The quasiequivalent mass of a fractional vibrator in class IV equals to that of a fractional vibrator in class I. (4) The phenomenon that the quasiequivalent damping of a fractional vibrator in class IV may vary from −∞ to ∞. (5) The condition for a fractional vibrator in class IV to be self-vibrated or non-stable. (6) Asymptotic properties of the quasiequivalent stiffness. (7) A possible mathematical explanation of the Rayleigh damping assumption. (8) The analytic expressions of free response, impulse response, step response, frequency transfer function of a fractional vibrator of class IV.
