Vibration Theory And Computational Analysis Of Magnetostrictive Composite Cantilever Actuator

With the developments of modern intelligent control and structural health detection technology,magnetostrictive actuators with good magneto-mechanical coupling properties have been used in related engineering fields.Their dynamic behaviors are important research topics in mechanics,mechanical engineering and electro-magnetic devices.The thin-film magnetostrictive composite cantilever actuator as smart structure was widely used in micro-electro-mechanical systems.Based on this engineering background,the related theoretical models on the vibrations of one-dimensional and two-dimensional magnetoelastic double-layer composite cantilever beams under electromagnetic excitation are systematically proposed,and the analytical results of dynamic response are obtained.The main research works are summarized as follows:(1)For the linear vibration of magnetostrictive double-layer composite cantilever beam,based on displacement assumptions of Levinson beam theory,a mathematical model considering high-order shear effect is built.The governing equations of vibration with the basic unknown variables of interlaminar deflection and interlaminar shear stress are derived.The model can satisfy all continuity conditions on the interface of double-layer beam and the stresses free conditions on upper and lower surface.The natural frequency equation and analytical solutions of deflection response for excited vibration are given.The corresponding vibration modes and dynamic characteristics under harmonic magnetic field excitation are analyzed.The effects of material and geometric parameters on natural frequency,the deflection response and the magneto-mechanical coupling factor are discussed.The results of parameter optimum are obtained,which the magneto-mechanical coupling factor reaches its maximum for a given excitation frequency.(2)Based on the displacement assumptions of Euler beam and Timoshenko beam,the standard square nonlinear constitutive relations of magnetostrictive material are introduced.Two mathematical models of nonlinear vibration problem are established by Hamilton variational principle,and the forced vibration problem is solved analytically.The natural frequency of the magnetostrictive biosensor is calculated,and the results agree well with the experimental datas in literature and finite element calculation values,which validates the correctness of the proposed theoretical model and calculation method.Analysis for the excitatied vibration in harmonic magnetic field indicates that the magnetostrictive double-layer composite cantilever beam exhibits obvious nonlinear vibration characteristics,thus as,the amplitude-frequency curve,the deflection-time and the stress-time history response curves have frequency multiplying effect.The effect of bias magnetic field on vibration performance of magnetostrictive composite cantilever actuator is also investigated.Results show that increasing the bias magnetic field could weaken the frequency multiplying effect.(3)The dynamic characteristics of magnetostrictive composite cantilever beam with microsize are studied by using nonlocal field theory.The vibration governing equations and boundary conditions of the magnetostrictive composite cantilever Euler beam are derived.The influence of non-local(micro-scale)effect on natural frequency and deflection response for the composite cantilever beam are analyzed.Numerical results show that the non-local(micro-scale)effect reduces the low-order natural frequencies and increases the high-order natural frequencies.(4)With the magnetoelastic plane assumption,a two-dimensional mathematical model for the vibration of magnetostrictive double-layer cantilever beam is established.The analytical solutions of the two-dimensional bi-directional orthogonal series of the displacement and stress components are constructed.The problem is reduced to solving infinite dimensional algebraic equations about series coefficients.Analytic results indicate that there is obvious boundary layer feature for the normal(spalling)stress distribution on the interface near the free end,that is the sharp variarion of normal(spalling)stress appears in the narrow area near the free end.Compared with the finite element results,the correctness of the proposed two-dimensional theoretical model and approach is verified.