SCATTERING OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN MINDLIN'S THICK PLATES WITH A CUTOUT

Using the complex variable method and conformal mapping,scat- tering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout have been studied.The general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of cutouts is obtained. Applying the orthogonal function expansion technique,the dynamic stress problem can be reduced into the solution of a set of infinite algebraic equations.As examples, numerical results for the dynamic stress concentration factor in Mindlin's plates with a circular,elliptic cutout are graphically presented in sequence.

Flexural wave band-gaps in phononic metamaterial beam with hybrid shunting circuits

Periodic arrays of hybrid-shunted piezoelectric patches are used to control the band-gaps of phononic metamaterial beams. Passive resistive-inductive （RL） shunting circuits can produce a narrow resonant band-gap （RG）, and active negative capacitive （NC） shunting circuits can broaden the Bragg band-gaps （BGs）. In this article, active NC shunting circuits and passive resonant RL shunting circuits are connected to the same piezoelectric patches in parallel, which are usually called hybrid shunting circuits, to control the location and the extent of the band-gaps. A super-wide coupled band-gap is generated when the coupling between RG and the BG occurs. The attenuation constant of the infinite periodic structure is predicted by the transfer matrix method, which is compared with the vibration transmittance of a finite periodic structure calculated by the finite element method. Numerical results show that the hybrid-shunting circuits can make the band-gaps wider by appropriately selecting the inductances, negative capacitances, and resistances.

NONLINEAR FLEXURAL WAVES IN LARGE-DEFLECTION BEAMS

The equation of motion for a large-deflection beam in the Lagrangian description are derived using the coupling of flexural deformation and midplane stretching as a key source of nonlinearity and taking into account the transverse, axial and rotary inertia effects. Assuming a traveling wave solution, the nonlinear partial differential equations are then transformed into ordinary differential equations. Qualitative analysis indicates that the system can have either a homoclinic orbit or a heteroclinic orbit, depending on whether the rotary inertia effect is taken into account. Furthermore, exact periodic solutions of the nonlinear wave equations are obtained by means of the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function m→1 in the degenerate case, either a solitary wave solution or a shock wave solution can be obtained.

Controlling flexural waves in thin plates by using transformation acoustic metamaterials

In this study,we design periodic grille structures on a single homogenous thin plate to achieve anisotropic acoustic metamaterials that can control flexural waves.The metamaterials can achieve the bending control of flexural waves in a thin plate at will by designing only one dimension in the thickness direction,which makes it easier to use this metamaterial to design transformation acoustic devices.The numerical simulation results show that the metamaterials can accurately control the bending waves over a wide frequency range.The experimental results verify the validity of the theoretical analysis.This research provides a more practical theoretical method of controlling flexural waves in thin-plate structures.

Numerical study of dispersion characteristics of dipole flexural waves in a cased hole with different cement conditions

Crossed-dipole acoustic logging technology is mainly used to measure shear wave and determine the anisotropy or fractures of formation in the fi eld of acoustic logging.Based on the propagation characteristics of dipole flexural waves in cased holes,and the wavefi eld of fundamental flexural mode at three bonding conditions:good cement bonding,poorly bonded interface I,and poorly bonded interface II.The dispersion curves of flexural waves are calculated,and the eff ects of cement parameters(elastic parameters and geometric dimensions)on dispersion curves are investigated.The RAI method is used to calculate the dipole full waveforms in a cased hole with conventional or ultralight cement surrounded by a soft formation.Then,the weighted spectral semblance is used to conduct the dispersion analysis of the full waves.The numerical results show that the cutoff frequency of flexural waves exceeds the frequency band of the current dipole logging tools in the well-bonded cased hole with conventional cement in soft formations.However,when ultralight cement is used,the cutoff frequency shifts toward low values,and the ultralight cement bonding is conducive to measuring flexural waves in soft formations.When interface I is poorly bonded,the cutoff frequency shifts toward low values,and the change is evident in soft formations.The cutoff frequency in the case of ultralight cement bonding is more evident than that of conventional cement bonding.If only interface II is poorly bonded,regardless of the cement used,the cutoff frequencies are all below 2 kHz.The dipole full-wave analysis of diff erent bonding conditions further illustrates that the dispersion characteristics of flexural waves are sensitive to the cement bonding quality of cased holes.

THEORY AND EXPERIMENTAL INVESTIGAION OF FLEXURAL WAVE PROPAGATION IN THIN RECTANGULAR PLATE WITH PERIODIC STRUCTURE

With the idea of the phononic crystals, a thin rectangular plate with two-dimensional periodic structure is designed. Flexural wave band structures of such a plate with infinite structure are calculated with the plane-wave expansion （PWE） method, and directional band gaps are found in the ΓX direction. The acceleration frequency response in the ΓX direction of such a plate with finite structure is simulated with the finite element method and verified with a vibration experiment. The frequency ranges of sharp drops in the calculated and measured acceleration frequency response curves are in basic agreement with those in the band structures. Thin plate is a widely used component in the engineering structures. The existence of band gaps in such periodic structures gives a new idea in vibration control of thin plates.

AN ANALYSIS FOR DIFFRACTION OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN THICK PLATES WITH A CAVITY

By using the complex variable method and conformal mapping, the diffraction of flexural waves and dynamic stress concentrations in thick plates with a cavity have been studied. A general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of an arbitrary cavity is obtained. By employing the orthogonal function expansion technique, the dynamic stress problem can be reduced to the solution of an infinite algebraic equation series. As an example, the numerical results for the dynamic stress concentration factor in thick plates with a circular, elliptic cavity are graphically presented. The numerical results are discussed.

Propagation Characteristics of Flexural Wave in One-Dimensional Phononic Crystals Based on Lattice Dynamics Model

In this paper, we establish discrete flexural lattice chain models of Bragg and locally resonant phononic crystals by setting mass defect atoms and local resonant elements on the flexural lattice chain. The bandgap characteristics of flexural wave in phononic crystals are studied by establishing the governing equations of the model. The results from models show that with the change of the mass ratio of defective atoms to normal atoms, the bandgap of the flexural wave produced by Bragg scattering shows a certain rule. When the local resonant bandgap and Bragg scattering bandgap are close to each other, the two bandgaps will be coupled to form a wider flexural wave bandgap. The effect of axial strain on bending wave propagation is only the shift of bandgap position. The effect of material damping on the propagation of a bending wave is only energy dissipation at high frequency. In addition, we use finite element simulation to calculate the bandgap of flexural wave in phononic crystals with mass defects, and the results are consistent with lattice chain model. This shows that lattice chain model can effectively guide the bandgap design of phononic crystals. This comprehensive study may help to elucidate the rule of bandgap generation of flexural wave in one-dimensional phononic crystals.

DUAL RECIPROCITY BOUNDARY ELEMENT METHOD FOR FLEXURAL WAVES IN THIN PLATE WITH CUTOUT

The theoretical analysis and numerical calculation of scattering of elastic waves and dynamic stress concentrations in the thin plate with the cutout was studied using dual reciprocity boundary element method （DRM）. Based on the work equivalent law, the dual reciprocity boundary integral equations for flexural waves in the thin plate were established using static fundamental solution. As illustration, numerical results for the dynamic stress concentration factors in the thin plate with a circular hole are given. The results obtained demonstrate good agreement with other reported results and show high accuracy.

Lattice Dynamics Models to Predict Transmission Properties of Flexural Waves in One-Dimensional Atom Chains with Defects

Flexural waves usually propagate in one-and two-dimensional structures.To further our understanding on their transmission properties from the viewpoint of discrete lattice dynamics,we systematically established analytical atom chain models with mass defects and side branches.Both mechanisms of the Bragg scattering and the local resonance corresponding to mass defects and side branches,respectively,are elucidated by means of the present models.The results from the models show that increasing the number of mass defects or side branches decreases the transmission magnitude gradually,and the finite-width phononic bandgap may form due to the periodical arrangement of defects.The interplay between the local resonance and the Bragg scattering gives rise to the narrow phononic bandgap for lattice chains only with periodical side branches.The width of the bandgap strongly depends on the stiffness of side branches.The transmission is insensitive to the tensile strain considered for both kinds of defects,but significantly decreases with an increase in damping or wave frequency.The present work helps further our understanding on the dynamics of flexural waves.

Propagation of flexural waves in phononic crystal thin plates with linear defects

The band structures of flexural waves in a phononic crystal thin plate with straight, bending or branching linear defects are theoretically investigated using the supercell technique based on the improved plane wave expansion method. We show the existence of an absolute band gap of the perfect phononic crystal and linear defect modes inside the gap caused by localization of flexural waves at or near the defects. The displacement distributions show that flexural waves can transmit well along the straight linear defect created by removing one row of cylinders from the perfect phononic crystals for almost all the frequencies falling in the band gap, which indicates that this structure can act as a high efficiency waveguide. However, for bending or branching linear defects, there exist both guided and localized modes, and therefore the phononic crystals could be served as waveguides or filters.

Hydroelastic Response of A Circular Plate in Waves on A Two-Layer Fluid of Finite Depth

The hydroelastic response of a circular, very large floating structure(VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the platecovered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presented to investigate the effects of different physical quantities, such as the thickness of the plate, Young’s modulus, the ratios of the densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid. Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode.

Rough interfaces and ultrasonic imaging logging behind casing

Ultrasonic leaky Lamb waves are sensitive to defects and debonding in multilayer media. In this study, we use the finite-difference method to simulate the response of flexural waves in the presence of defects owing to casing corrosion and rough fluctuations at the cement-formation interface. The ultrasonic obliquely incidence could effectively stimulate the flexural waves. The defects owing to casing corrosion change the amplitude of the early- arrival flexural wave, which gradually decrease with increasing defect thickness on the exterior walls and is the lowest when the defect length and wavelength were comparable. The scattering at the defects decreases the energy of flexural waves in the casing that leaks directly to fluids. For rough cement-formation interface, the early-arrival flexural waves do not change, whereas the late-arrival flexural waves have reduced amplitude owing to the scattering at rough interface.

Possible Collapse Mode for Slender Reinforced Concrete Plates Subjected to Blast Load

This paper discusses the collapse mode of thin reinforced concrete (RC) plates sub-jected to blast load. To extend the well known plastic-mode method to analyze, not only perfect-plastic plates , but also RC plates, it is needed to investigate the effect of material cracking on the collapse mode because the plate might have been cracked on both upper and lower surface before the plastic-mode fully develops, creating an unexpected type of collapse mode shape. A new fail-ure mode is proposed and verified by numerical analysis in this paper. The new mode is a result of the material cracking and has an un-negligible effect on the reaction mechanism of the RC plate to the blast load.

Propagation of flexural modal waves in a fluid-filled borehole

The propagation of multipole modal waves along the well-axis in a fluid-filled borehole surrounded by elastic and nonelastic, infinite and finite formation is analysed by using the wave equations. The phase velocity dispersion and the excitation curves are numerically calculated. The waveforms excited by attenuating bursts are also calculated. The measurements with long-spaced dipole transducers made of PZT thin disks vibrating in bending mode are carried out in a concrete model well and the experimental results are compared with the theoretical results.

Extreme transmission of elastic metasurface for deep subwavelength focusing

In this paper,elastic metasurfaces composed of zigzag units are proposed to manipulate flexural waves at a deep subwavelength scale.Through the parameter optimization of the genetic algorithm,units with full transmission and full phase control can be found,while the width is only one-fifth of the wavelength.The outstanding capability of the units is explained by analyzing.their wave fields.The flat and the curved metasurfaces for focusing are designed and simulated,showing excellent performance.Experimental results of the flat metasurface show that the incident wave energy at the focal point is enhanced over 6 times,verifying the simulation results.The proposed metasurfaces could be useful in the design of.compact and efficient elastic devices.