The Couple-stress Effects Of Elastic Wave Propagation In Solid

The couple stress elastic theory is derived according to Mindlin's linear elastic theory with microstructure in this dissertation.Several problems are investigated based on this theory,i.e.,reflection of elastic waves at the elastically/visco-elastically supported boundary of couple stress half-sapce,reflection and transmission of elastic wave through couple-stress slab sandwiched between elastic half-spaces,Bloch wave propagation in one-dimenssional couple stress laminated structure phononic crystals formed by periodically repeating of two different couple stress solids,the dispersion characteristics of Bloch waves and band gap properties of elastic waves,reflection and refraction of thermo-elastic waves at the interface between two different couple stress elastic solids.The specific research contents are:(1)The reflection elastic waves at the surface of a couple stress elastic half-space with a elastic/viscoelastic support boundary are studied.The visco-elastically supported boundary is modeled as a boundary with a distributed spring and dashpot.Each mass point at the boundary surface is subjected to the normal and tangent translational constraints and the rotational constraint.Three elastic boundary parameters and three viscous boundary parameters are introduced to represent the respective constraint degrees.The boundary conditions at the visco-elastically supported surface of a couple stress elastic half-space include the couple stress vector and the rotation vector,which disappear in the classical elastic solids.The reflection waves are determined by the boundary condition with consideration of the force-stress,the couple stress,the instantaneous elasticity,and the delayed viscosity.The free-surface and the fixed surface can be recovered as two special cases of the presented surface model.These boundary conditions are used to obtain a linear algebraic equation set,from which the amplitude ratios of reflection waves with respect to the incident wave can be determined.Then,the reflection coefficients in terms of energy flux ratios are calculated numerically under the couple stress effect,and the normal energy flux conservation is used to validate the numerical results.At last,based on these numerical results,the influences of the boundary parameters,which reflect the mechanical behavior of a viscoelastic support,on the amplitude ratio,the phase shift and the energy partition of reflection waves are discussed.Both the incident longitudinal displacement wave(the P wave)and incident transverse displacement wave(the SV wave)are considered.It is found that the instantaneous elasticity and the delayed viscosity of a viscoelastic support have different influences on the reflection waves.(2)The reflection and transmission of the elastic waves through a couple stress elastic slab that is sandwiched between two classical elastic or couple stress elastic half-spaces are studied.The interface conditions between the couple stress elastic slab and classical elastic or couple stress elastic half-space are studied.The interface conditions between two couple stress solids involve the surface couple and rotation apart from the surface traction and displacement.The role of the micro-rotation and the couple-stress in the interface conditions are mainly discussed.The nontraditional interface conditions between the slab and two solid half-spaces are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection and transmission waves to the incident wave can be determined.Then,the energy fluxes carried by the various reflection and transmission waves are calculated numerically.The energy flux ratio of the reflection and transmission waves with respect to the incident wave are calculated numerically for various combination situations.The normal energy flux conservation is used to validate the numerical results.The special case,couple stress elastic slab sandwiched by the classical elastic half-spaces,is also studied and compared with the situation that the classical elastic slab sandwiched by the classical elastic half-spaces.Incident longitudinal wave(P wave)and incident transverse wave(SV wave)are both considered.Based on these numerical results,the influences of couple-stress elastic constants and the non-dimensional thickness of slab are mainly discussed.It is found that the couple-stress mainly influences the transverse modes of elastic waves.(3)The elastic wave(the in-plane Bloch waves and the anti-plane Bloch waves,the oblique propagation situation and the normal propagation situation)propagation in one-dimensional layered composite structures formed by the periodical and infinite repeat of two different couple-stress elastic solids are studied by method of transfer matrix.Its each sublayer is homogeneous medium,the transfer matrix of single layer can be used to connect the state vectors of the right and left interfaces of the sub layer.The transfer matrix of a unit cell will be obtained when all the transfer matrix of the sub layers in a unit cell are multiplied together obtained by inserting the continuous state parameters into the basic equations.Then by the theory of Bloch,the elastic wave dispersion equation of periodic layered crystal structures will be derived and the dispersion curves will be drawn.The influences of different boundary conditions and the couple-stress parameters on the dispersion characteristics of elastic wave and the band gap properties of elastic waves are discussed.(4)From the energy conservation law,The basic equations(for example,the coupled governing equations and constitutive equations)of couple-stress solid are derived based on Lord-Shulman generalized thermoelastic theory.In contrast to the classical thermoelastic solid,there exist four kinds of wave modes by solving the governing equation,three of them are bulk wave:coupled longitudinal waves(CP-waves),coupled thermo waves(CT-waves),transversal waves(SV-waves),and surface wave of S type(SS-waves).Various interface conditions are given,for example,perfect interface,isothermal interface,adiabatic interface,mechanically imperfect interface and thermally imperfect interface.The reflection and refraction of coupled thermo-elastic waves which incorporates simultaneously the microstructure effects and thermal wave effects across a mechanically and thermally imperfect interface,and the influence of the incident energy distribution are considered.The amplitude of the reflection and transmission ratio can be derived from different interface conditions of linear algebraic equations.Both the incident longitudinal wave(the P wave)and incident transverse wave(the SV wave)are considered,the reflection and transmission coefficients of various wave in terms of energy are obtained.The influences of the thermal relaxation time and the imperfect interface conditions,the relationship between the various modes of wave velocity and wave type are discussed.At last,the numerical results are checked by the energy conservation at the interface.The influence of the couple-stress effect and thermal-mechanical coupling effect on high frequency elastic wave propagation in couple stress solid material is revealed through the above researches.The propagation of elastic wave through multi-layer structure are studied theoretically for couple-stress effect,and it can be used as theoretical instructor for the acoustic application of materials.