In this paper, the damping force and the damping coefficient of a rotary magnetic damper consisting of several sector magnets and an arbitrarily shaped plate conductor with a circular cavity have been obtained theoretically. The unit step function is applied to solve the differential equations of the electromagnetic field, and the boundary condition of the outer arbitrarily shaped boundary of the plate conductor is satisfied directly by making use of the Fourier expansion collocation method. Numerical calculations have been carried out for the dimensionless damping coefficients with the variations of various factors such as the magnetic flux range, the outer shape and the radius of the inner circular cavity of the conductor, the position and the number of the magnets.

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