ABSTRACT
The goal of this chapter is to present things in seven folds as follows. (1) Equivalent motion equation of a fractional vibrator in class I. (2) The quasiequivalent mass, quasiequivalent damping, quasiequivalent damping ratio, quasiequivalent damping free natural frequency, quasiequivalent damped natural frequency, quasiequivalent frequency ratio, quasiequivalent Q factor, and quasiequivalent logarithmic decrement for a class I fractional vibrator. (3) The quasiequivalent mass of a fractional vibrator in class I may vary from 0 to ∞, relying on the vibration frequency ω and the fractional order α. (4) The quasiequivalent damping of a fractional vibrator of class I type may vary from −∞ to ∞, depending on ω and α. (5) The conditions for a class I fractional vibrator to be self-vibrated or non-stable. (6) The analytic expressions of free response, impulse response, step response, and frequency transfer function of a class I fractional vibrator. (7) Representing generalized Mittag–Leffler functions by using elementary functions.
