Size and temperature effects on band gaps in periodic fluid-filled micropipes

A new model is proposed for determining the band gaps of flexural wave propagation in periodic fluid-filled micropipes with circular and square thin-wall cross-sectional shapes, which incorporates temperature, microstructure, and surface energy effects. The band gaps depend on the thin-wall cross-sectional shape, the microstructure and surface elastic material constants, the pipe wall thickness, the unit cell length, the volume fraction, the fluid velocity in the pipe, the temperature change,and the thermal expansion coefficient. A systematic parametric study is conducted to quantitatively illustrate these factors. The numerical results show that the band gap frequencies of the current non-classical model with both circular and square thin-wall cross-sectional shapes are always higher than those of the classical model. In addition,the band gap size and frequency decrease with the increase of the unit cell length according to all the cases. Moreover, the large band gaps can be obtained by tailoring these factors.

Bending and wave propagation analysis of axially functionally graded beams based on a reformulated strain gradient elasticity theory

A new size-dependent axially functionally graded(AFG) micro-beam model is established with the application of a reformulated strain gradient elasticity theory(RSGET). The new micro-beam model incorporates the strain gradient, velocity gradient,and couple stress effects, and accounts for the material variation along the axial direction of the two-component functionally graded beam. The governing equations and complete boundary conditions of the AFG beam are derived based on Hamilton's principle. The correctness of the current model is verified by comparing the static behavior results of the current model and the finite element model(FEM) at the micro-scale. The influence of material inhomogeneity and size effect on the static and dynamic responses of the AFG beam is studied. The numerical results show that the static and vibration responses predicted by the newly developed model are different from those based on the classical model at the micro-scale. The new model can be applied not only in the optimization of micro acoustic wave devices but also in the design of AFG micro-sensors and micro-actuators.

A Transversely Isotropic Magne to -Elec tro-Elastic Circular Kirchhoff Plate Model Incorporating Microstructure Effect

A non-classical model for transversely isotropic magneto-electro-elastic circular Kirchhoff plates is established based on the extended modified couple stress theory.The Gibbs-type variational principle is used to obtain the governing equations and boundary cond计ions.To illustrate the newly derived model,the static bending problem of a clamped circular plate subjected to a uniformly distributed constant load is solved numerically by Fourier-Bessel series.The numerical results show that the values of transverse displacement,electric and magnetic potentials predicted by the current model are always smaller than those of the classical model,and the differences are diminishing as the plate thickness increases.In addition,it is shown that the magneto-electro-elastic coupling effect plays an important role in the transverse displace-ment,elec trie pot ential and magnetic pot ential of the magne to-elec tr o-elastic circular Kirchhoff plates.Furthermore,several reduced specific models are provided for simpler cases.

Microstructure-dependent Band Gaps for Elastic Wave Propagation in a Periodic Microbeam Structure

A new model for producing band gaps for flexural elastic wave propagation in a periodic microbeam structure is developed using an extended transfer matrix method and a non-classical Bernoulli–Euler beam model that incorporates the strain gradient,couple stress and velocity gradient effects.The band gaps predicted by the new model depend on the three microstructure-dependent material parameters of each constituent material,the beam thickness,the unit cell length and the volume fraction.A parametric study is conducted to quantitatively illustrate these factors.The numerical results reveal that the first band gap frequency range increases with the increases of the three microstructure-dependent material parameters,respectively.In addition,the band gap size predicted by the current model is always larger than that predicted by the classical model,and the difference is large for very thin beams.Furthermore,both the unit cell length and volume fraction have significant effects on the band gap.

Magnetically induced electric potential in first-order composite beams incorporating couple stress and its flexoelectric effects

A new model of a first-order composite beam with flexoelectric and piezomagnetic layers is developed.The new model is under a transverse magnetic field and can capture the couple stress and its flexoelectric effects.The governing equations are obtained through a variational approach.To illustrate the new model,the static bending problem is analytically solved based on a Navier’s technique.The numerical results reveal that the extension,deflection,and shear deformation of the current or couple stress relevant flexoelectric model are always smaller than those of classical models at very small scale.It is also found that the electric potentials only appear with the presence of the flexoelectric effect for this non-piezoelectric composite beam model.Furthermore,various electric potential distributions can be manipulated by the particular magnetic fields,and remote/non-contact control at micro-and nano-scales can be realized by current functional composite beams.

Bandgap Analysis of Periodic Composite Microplates with Curvature-Based Flexoelectricity:A Finite Element Approach

A finite element model is proposed permitting prediction of elastic wave bandgaps of periodic composite microplates incorporating flexoelectric effect.In this model,we applied curvature-based flexoelectricity and Mindlin plate theories and derived a finite element formulation that has been implemented for bandgap analysis.The finite element model utilizes a three-node triangle element with 30 degrees of freedom satisfying Mindlin kinematics assumptions.It is based on a non-conforming interpolation scheme which provides nodal C^(1) continuity and ensures compatibility with curvature-based flexoelectricity.The approach accounts for microstructure effects and,owing to the triangular element topology,can be used to assist the design of microplates with complex microstructures.Validation of the approach is performed through comparison with both analytical and numerical models,in which the effect of flexoelectricity on the bandgap is studied based on cases demonstrating size dependence.