This chapter examines aperiodic vibrational resonance induced by frequency-modulated signals in bistable systems. We focus on the distinct characteristics of linear and nonlinear frequency-modulated signals, analyzing each form separately. In particular, for nonlinear frequency-modulated signals, we explore three typical types in detail. To achieve aperiodic vibrational resonance, we employ the piecewise re-scaled method for simpler linear frequency-modulated signals, while utilizing a real-time re-scaled theoretical approach for more complex nonlinear signals, underscoring the advantages of this method.