“…where (●)′ = ∂(●)/∂ x , (●) = ∂(●)/∂ t , u z,j ( x, t ) = vertical deflection of the j th span, u y,j ( x, t ) = lateral deflection of the j th span, L = span length, K = number of magnets attached to the rigid levitation frame, δ (●) = Dirac’s delta function, H ( t ) = unit step function, k = 1, 2, 3, …, K th moving magnetic wheel on the beam, tk = ( k− 1) d/v = arrival time of the k th magnetic wheel into the beam, xk = position of the k th magnetic wheel on the guideway, and ( G y,k , G z,k ) = lateral guidance and uplift levitation forces of the k th lumped magnet in the vertical and lateral directions [ 17 , 18 ].…”