Structural Model and Diagram of Multilayer Electro Magneto Elastic Actuator for Nanotechnology

The multilayer electro magneto elastic actuator nano and micro displacement with the piezoelectric, piezomagnetic, electrostriction, magnetostriction effects is used in the control system for nanotechnology in scanning tunneling microscopy, atomic force microscopy and adaptive optics in the range of movement from few nanometers to tens of micrometers [1−32]. We obtained the structural model and the structural diagram of the multilayer electro magneto elastic actuator in contrast to electrical equivalent circuits of the piezo transducer, the vibration piezo motor [1–11]. We used the equation of the electro magneto elasticity, the equivalent mechanical quadrupole and the boundary conditions of the multilayer actuator for the structural model and the structural diagram of the multilayer actuator [8−28]. We received the matrix transfer function of the multilayer electro magneto elastic actuator from its structural model.

We determined the structural model and the structural diagram of the multilayer electro magneto elastic actuator for nanotechnology and nanomedicine in difference from Cady and Mason electrical equivalent circuits of the piezo transducer. We used the method of the mathematical physics with Laplace transform for the determination the structural model and the structural diagram of the multilayer electro magneto elastic actuator for nanotechnology and nanomedicine [8,14,32].

The equation [8,9,11,25,26] of the electro magneto elasticity has the following form

Where S_i is the relative displacement, ν _mi is the coefficient of electro magneto elasticity: d_mi piezo module or magneto strictive coefficient, Ψ_m is control parameter in the form of electric E_m , magnetic H_m field strengths or electric D_m induction, s_ij^Ψ is the elastic compliance with Ψ = const , T_j is the mechanical stress, i, j, m are the indexes.

We received for the multilayer electro magneto elastic actuator the causes force in the form

where S₀ is the cross sectional area of the actuator.

We have matrix the equivalent mechanical quadrupole of the multilayer electro magneto elastic actuator [25] in the following form

where l is length of the multilayer actuator for the longitudinal piezo effect l = nδ , for the transverse piezo effect , for the shift piezo effect l = nb , and δ,h,b are the thickness, the height, the width for the piezo layer.

We obtained the system of the equations for the structural model and the structural diagram of the multilayer electro magneto elastic actuator on Figure 1. We have the structural model of the multilayer electro magneto elastic actuator in result analysis the equation of the force that causes deformation, the equivalent mechanical quadrupole and the boundary conditions equations with the forces on faces of the actuator in the following form

From the structural model we have the matrix transfer function of the multilayer electro magneto elastic actuator for nanotechnology in the form

where I EQUA are the matrices of the displacements the faces, the transfer functions, and the control parameters.

We have at the static displacements the faces of the voltage-controlled multilayer piezo actuator for the longitudinal piezo effect and the inertial load for where m is the mass of the multilayer piezo actuator, M1 ,M2 are the load masses, and the forces on faces in the form

where U is the voltage on the actuator.

Therefore, the static displacements the faces of the multilayer piezo actuator at and we obtained the static displacements of the faces the multilayer piezo actuator

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