Vibratory exciters are essential in technical systems for their vast possibilities of applications. A new exciter with a pair of inertially coupled unbalanced rotors with an additional viscous coupling between them is proposed in the present work. It is capable of producing slowly modulated vibrations with large amplitudes in resonant regime. An asymptotic analysis is conducted to investigate the slow dynamics of the system using an averaging method for partially strongly damped systems. Different types of solutions are shown. The dependency of modulated vibrations on parameters is studied.