It has been found that the forces on the domain walls (DWs) in ferromagnetic material for measuring internal friction (IF) when the magnetic field (H) is increased at constant rate (a) are: (1) main driving force caused by the H, namely A00+A10at; (2) harmonic perturbation force A30sinωt; (3) interaction force which is proportional to A10at, A30sinωt and a resistant force depending on the internal stress field and anisotropy field A20sinωt. The equation of motion of DWs can be written as ρ(d2 x)/(dt2) + r(dx)/(dt)+κx = A00 + A10at + A20t sinωt + A30 sin ωt where A00,A10,A20,A30 are constants depending on material chosen and test condition; ρ is the mass density, γ is the viscous damping parameter and κ is the coefficient of restoring force. The IF caused by DWs motion can be obtained from the solution of the equation of motion as follows Qm-1=B1 (Eλsδ)/(Ms2Hm) (dM)/(dH)·α/ω (If for α≠0) Q0-1=B2 (γωE)/(κ2) (If for α=0) where E is the modulus, λs is the saturation magnetostriction,Ms is the saturation magnetization, Hm is a critical field at whichthe reversible motion of DWs becomes irreversible B1, B2 are dimensionless positive numbers. When α≠0, the visco-elastic IF may be initiated and the IF varies with α/ω; when α= 0, the low-frequency micro-eddy current IF may be initiated and the IF varies with ω. The calculated results are compared with experimental data and interface dynamics.
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