The multilayer engine with the piezoelectric or electrostriction
effects is used for microsurgery and nano biomedicine [1-9]. We
received the structural circuit of the multilayer engine in contrast
to Cady’s and Mason’s equivalent circuits [9-32]. We determined
the mathematical model and the structural circuit of the multilayer
engine with the equation of the electro elasticity and the matrix of
the quadripole for the multilayer engine.
We received the structural circuit of the multilayer engine for
microsurgery and nano biomedicine in difference from Cady’s and
Mason’s equivalent circuits [1–14]. We have the matrix equation
electro elasticity [7,8,14] in the form
Si = vmi Ψm + sijΨ Tj
In this equation we write the relative displacement, the
coefficient of electro elasticity, the control parameter, the elastic
compliance, the mechanical stress in the forms Si, vmi, Ψm, sijΨ, Tj
The causes force for the multilayer engine has the form
where S0 is the area of the multilayer engine
The matrix of the quadripole for the multilayer engine [7, 29,
31] has the form
In this equation we write l is the length of the multilayer
engine and γ is the coefficient propagation.
We have the structural circuit of the multilayer engine
for microsurgsery and nano biomedicine on Figure 1 from its
mathematical model in the form
We have the matrix equation of the multilayer engine for
microsurgery and nano biomedicine in the form
Figure 1: Structural circuit of the multilayer engine for microsurgery and nano biomedicine.
In this equation we write the matrixes [Ξ(p)], [W(p)], [P(p)].
In static for the multilayer engine with longitudinal piezo effect
and one fixed end we received displacement in the form
where Ce , CE33 are the rigidity of the load and the rigidity of the
multilayer engine for E = const . We received for the multilayer engine
at d33 = 4⋅10−10 m/V, n=12, U=200V,
CE33 = 2⋅107 N/m, Ce = 0.4∙107 N/m
the static displacement ξ2 = 800 nm.
We obtained the transfer function with lumped parameters of
the multilayer engine with longitudinal piezo effect and one fixed
end in the form
where Tt , ξt are the time constant, the damping coefficient
of the multilayer engine. Therefore, for the multilayer engine at d33 = 4⋅10−10 m/V, n = 12, U = 200 V, M2 = 4 kg, 7 CE33 = 2∙107 N/m,
Ce= 0.4∙107 N/m we have ξ2 = 800 nm and Tt = 0.4∙10-3 s.
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