On wave propagation in finitely deformed magnetoelastic solids

QC Physics;QA Mathematics

Saxena, Prashant ; Ogden, Ray W.

University:University of Glasgow

Department:School of Mathematics and Statistics

关键词: Nonlinear magnetoelasticity, nonlinear elasticity, wave propagation, finite deformation, solid mechanics, magnetorheological elastomer;   

Others  :  http://theses.gla.ac.uk/3611/1/2012saxenaphd.pdf

来源: University of Glasgow

【 摘 要 】

In this thesis we consider some boundary value problems concerningnonlinear deformations and incremental motions inmagnetoelastic solids. Three main problems have been addressed relating towaves propagating on the surface ofa finitely deformed half-space andwaves propagating along the axis of athick-walled tube.First, the equations and boundary conditions governing linearized incremental motions superimposed on an initial motion and underlying electromagnetic field are derived and then specialized to the quasimagnetostatic approximation. The magnetoelastic material properties are characterized in terms of a ``total'' isotropic energy density function that depends on both the deformation and a Lagrangian measure of the magnetic field.In the first problem, we analyze thepropagation ofRayleigh-type surface wavesfor different directions of the initial magnetic field and for a simple constitutive model of a magnetoelastic material in order to evaluate the combined effect of the finite deformation and magnetic field on the surface wave speed. Numerical results for a Mooney--Rivlin type magnetoelastic material show that a magnetic field in the considered (sagittal) plane in general destabilizes the material compared with the situation in the absence of a magnetic field.A magnetic field applied in the direction of wave propagation is more destabilizing than that applied perpendicular to it.In the second problem, the propagation of Love-type waves in a homogeneously and finitely deformed layered half-space is analyzed for a Mooney--Rivlin type and a neo-Hookean type magnetoelastic energy function. The resulting wave speed characteristics in general depend significantly on the initial magnetic field as well as on the initial finite deformation, and the results are illustrated graphically for different combinations of these parameters. In the absence of a layer, shear horizontal surface waves do not exist in a purely elastic material, but the presence of a magnetic field normal to the sagittal plane makes such waves possible, these being analogous to Bleustein--Gulyaev waves in piezoelectric materials.Then, we consider nonlinear axisymmetric deformations and incremental motions of a cylindrical magnetoelastic tube. The effects of internal pressure, axial stretch, and magnetic field are studied for two different kinds of energy density functions. It is found that in general an underlying azimuthal magnetic field increases the total internal pressure, affects the axial load, and induces stability in the tube. Dependence of the incremental motion on internal pressure, axial stretch,thickness of tube, and the applied magnetic field is illustrated graphically.Finally, we consider the general equations of Electrodynamics and Thermodynamics in continua. In particular, we write theequations governing mechanical waves, electromagnetic fields and temperature changes ina magnetoelastic conductor with a motivation todescribe the electromagnetic acoustic transduction (EMAT) process. This is a work in progress and an open research problem for the future.