where ζ i is the damping ratio, ω i is the natural frequency, β i and γ i are the electromechanical coupling coefficients, α i is the coefficient for mass normalization, η i is the modal resistance, and a dot indicates a time derivative. Herein, the magnetic coupling force, denoted by f mi , brings position-dependent nonlinearities. The magnetic coupling force was truncated by the Taylor series expansion up to the third order with respect to zero as follow: