圆弧形超表面对透射声波的可调控制与功能转换

基于"螺丝?螺母"的工作原理,设计了可调的透射型三通道螺旋单元,通过调节螺丝的旋拧深度来改变声通道的长度,从而实现对透射声波相位的调节.利用有限元方法计算了单元的透射波相位差和透射系数随频率和旋拧深度的变化规律.在平面广义Snell定律基础上推导了适用于圆弧形曲面的广义Snell定律.设计了圆弧形超表面,包括弧状和圆环...     

On the encounter of an acoustic shear pulse with a phase boundary in an elastic material: energy and dissipation

The fully dynamical motion of a phase boundary is examined for a specific class of elastic materials whose stress-strain relation in simple shear is nonmonotone. Previous work has shown that a preexisting stationary phase boundary in such a material can be set in motion by a finite amplitude shear pulse and that an infinity of solutions is possible according to the present theory. In this work, these solutions are examined in detail from the perspective of energy and dissipation. It is shown that there exists at most two solutions which involve no dissipation (corresponding to conservation of mechanical energy). It is also shown that there exists one solution that maximizes the mechanical energy dissipation rate. The total mechanical energy remaining in the dynamical fields after one such pulse-phase boundary encounter is shown to exceed the total methanical energy after either an energy minimal quasi-static motion or a maximally dissipative quasi-static motion.     

Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates

The governing equation of motion of gradient elastic flexural Kirchhoff plates, including the effect of in-plane constant forces on bending, is explicitly derived. This is accomplished by appropriately combining the equations of flexural motion in terms of moments, shear and in-plane forces, the moment–stress relations and the stress–strain equations of a simple strain gradient elastic theory with just one constant (the internal length squared), in addition to the two classical elastic moduli. The resulting partial differential equation in terms of the lateral deflection of the plate is of the sixth order instead of the fourth, which is the case for the classical elastic case. Three boundary value problems dealing with static, stability and dynamic analysis of a rectangular simply supported all-around gradient elastic flexural plate are solved analytically. Non-classical boundary conditions, in additional to the classical ones, have to be utilized. An assessment of the effect of the gradient coefficient on the static or dynamic response of the plate, its buckling load and natural frequencies is also made by comparing the gradient type of solutions against the classical ones.     

Bending and stability analysis of gradient elastic beams

The problems of bending and stability of Bernoulli–Euler beams are solved analytically on the basis of a simple linear theory of gradient elasticity with surface energy. The governing equations of equilibrium are obtained by both a combination of the basic equations and a variational statement. The additional boundary conditions are obtained by both variational and weighted residual approaches. Two boundary value problems (one for bending and one for stability) are solved and the gradient elasticity effect on the beam bending response and its critical (buckling) load is assessed for both cases. It is found that beam deflections decrease and buckling load increases for increasing values of the gradient coefficient, while the surface energy effect is small and insignificant for bending and buckling, respectively.     

On the encounter of an acoustic shear pulse with a phase boundary in an elastic material: reflection and transmission behavior

The fully dynamical motion of a phase boundary is considered for a specific class of elastic materials whose stress-strain relation in simple shear is nonmonotone. It is shown that a preexisting stationary phase boundary in a prestressed layer composed of such a material can be set in motion by a finite amplitude shear pulse. An infinity of solutions is possible according to the present theory, each of which is characterized by different reflected and transmitted waves at the phase boundary. A global analysis gives exact bounds on the size of the solution family for different shear pulse amplitudes. For certain ranges of shear pulse amplitudes a completely reflecting solution will exist, while for an in general different range of shear pulse amplitudes a completely transmitting solution will exist. The properties of these different solutions are examined. In particular, it is observed that the ringing of a shear pulse between the external boundaries and the internal phase boundary gives rise to periodic phase boundary motion for both the case of a completely reflecting phase boundary and a completely transmitting phase boundary.     

Bending and buckling of thin strain gradient elastic beams

Bending of strain gradient elastic thin beams is studied adopting Bernoulli-Euler principle. Simple linear strain gradient elastic theory with surface energy is employed. The governing beam equations with its boundary conditions are derived through a variational method. It turns out that new terms are introduced, indicating the importance of the cross-section area in bending of thin beams. Those terms are missing from the existing strain gradient beam theories. Those terms increase highly the stiffness of the thin beam. The buckling problem of the thin beams is also discussed.     

Wave dispersion in gradient elastic solids and structures: A unified treatment

Analytical wave propagation studies in gradient elastic solids and structures are presented. These solids and structures involve an infinite space, a simple axial bar, a Bernoulli–Euler flexural beam and a Kirchhoff flexural plate. In all cases wave dispersion is observed as a result of introducing microstructural effects into the classical elastic material behavior through a simple gradient elasticity theory involving both micro-elastic and micro-inertia characteristics. It is observed that the micro-elastic characteristics are not enough for resulting in realistic dispersion curves and that the micro-inertia characteristics are needed in addition for that purpose for all the cases of solids and structures considered here. It is further observed that there exist similarities between the shear and rotary inertia corrections in the governing equations of motion for bars, beams and plates and the additions of micro-elastic (gradient elastic) and micro-inertia terms in the classical elastic material behavior in order to have wave dispersion in the above structures.     

Size effects on strength, toughness and fatigue crack growth of gradient elastic solids

The present study investigates the microstructural size effect on the strength of a bar under axial loading, and on the toughness and crack growth of a beam under three-point bending within the framework of strain gradient elasticity. The gradient responses have been found considerably tougher as compared to the classical theory predictions and the observed deviation increases with increasing values of the non-dimensional parameter g/L (microstructural length over structural length). Based on the analytical solution of the strain energy release rate for the three-point bending case, a new, simple and universal, strain gradient elasticity, brittle fracture criterion and a new, size adjusted fatigue crack growth law have been established. Finally, the analytical predictions of the current modeling compare well with previous experimental data, based on three-point bending tests on single-edge notched concrete beams.     

Torsional vibrations of a column of fine-grained material: A gradient elastic approach

The gradient theory of elasticity with damping is successfully employed to explain the experimentally observed shift in resonance frequencies during forced harmonic torsional vibration tests of columns made of fine-grained material from their theoretically computed values on the basis of the classical theory of elasticity with damping. To this end, the governing equation of torsional vibrations of a column with circular cross-section is derived both by the lattice theory and the continuum gradient elasticity theory with damping, with consideration of micro-stiffness and micro-inertia effects. Both cases of a column with two rotating masses attached at its top and bottom, and of a column fixed at its base carrying a rotating mass at its free top, are considered. The presence of both micro-stiffness and micro-inertia effects helps to explain the observed natural frequency shift to the left or to the right of the classical values depending on the nature of interparticle forces (repulsive or attractive) due to particle charge. A method for using resonance column tests to determine not only the shear modulus but also the micro-stiffness and micro-inertia coefficients of gradient elasticity for fine-grained materials is proposed.     

Reflection and transmission of elastic waves at five types of possible interfaces between two dipolar gradient elastic half-spaces

Reflection and transmission of an incident plane wave at five types of possible interfaces between two dipo-lar gradient elastic solids are studied in this paper. First, the explicit expressions of monopolar tractions and dipolar trac-tions are derived from the postulated function of strain energy density. Then, the displacements, the normal derivative of displacements, monopolar tractions, and dipolar tractions are used to create the nontraditional interface conditions. There are five types of possible interfaces based on all possible combinations of the displacements and the normal derivative of displacements. These interfacial conditions with consid-eration of microstructure effects are used to determine the amplitude ratio of the reflection and transmission waves with respect to the incident wave. Further, the energy ratios of the reflection and transmission waves with respect to the incident wave are calculated. Some numerical results of the reflection and transmission coefficients are given in terms of energy flux ratio for five types of possible interfaces. The influences of the five types of possible interfaces on the energy parti-tion between the refection waves and the transmission waves are discussed, and the concept of double channels of energy transfer is first proposed to explain the different influences of five types of interfaces.