ABSTRACT
This chapter addresses a theory of six classes of vibrators with variable-order fractional forces of inertia, damping, and restoration. The novelty and contributions are reflected in six aspects. (1) Equivalent motion equations of those variable-order fractional vibrators. (2) The analytical expressions of the effective mass, damping, and stiffness of those variable-order fractional vibrators. (3) The asymptotic properties of the effective mass, damping, and stiffness of a class of variable-order fractional vibrators. (4) The restricted effective parameters (damping ratio, damping free natural frequency, damped natural frequency, and frequency ratio) of the variable-order fractional vibrators. (5) The analytical representations of the free responses, the impulse responses, and the frequency transfer functions of those variable-order fractional vibrators. (6) Mathematical explanation of Rayleigh damping assumption.
