Soft magnetorheological elastomers (s-MRE) are a kind of smart material with soft magnetic particles embedded in an elastomer matrix. Under a magnetic field, there is pronounced magnetostriction and magnetically controllable mechanical properties for s-MRE, offering broad application prospects in soft robotics, surface pattern control and vibration control. While most existing literature on s-MRE focuses on the quasi-static behaviour, neglecting inertia effect, the dynamic behaviour and potential nonlinear oscillation phenomenon in certain scenarios of s-MRE-based actuators remain underexplored. In order to addressing this gap, a novel dynamic model which incorporates the magnetization, nonlinear viscoelasticity and inertia effects of isotropic s-MRE is proposed to explore the interplay among magnetic field, inertia and viscoelasticity on its dynamic behaviour. After developing the corresponding two-dimensional finite element implementation platform, this study examines the magnetic-induced dynamic behaviour of an isotropic s-MRE-based bilayer beam through numerical simulation. The influence of inertia and viscoelasticity on the magnetic-induced deformation as well as the unique nonlinear vibration characteristics of isotropic s-MRE-based system, such as superharmonic and resonance jump, are explored. Furthermore, to further enhance practical applications, novel magnetic field control algorithms aimed at mitigating harmonic distortion and tuning the vibration frequency of isotropic s-MRE-based magnetic actuation systems are introduced. These findings significantly advance the understanding the dynamic behaviour of s-MRE, paving the way for practical applications of s-MRE in magnetic field-driven loudspeakers and active noise control devices.