Fault Identification for Shear-Type Structures Using Low-Frequency Vibration Modes

Shear-type structures are common structural forms in industrial and civil buildings,such as concrete and steel frame structures.Fault diagnosis of shear-type structures is an important topic to ensure the normal use of structures.The main drawback of existing damage assessment methods is that they require accurate structural finite element models for damage assessment.However,for many shear-type structures,it is difficult to obtain accurate FEM.In order to avoid finite elementmodeling,amodel-freemethod for diagnosing shear structure defects is developed in this paper.This method only needs to measure a few low-order vibration modes of the structure.The proposed defect diagnosis method is divided into two stages.In the first stage,the location of defects in the structure is determined based on the difference between the virtual displacements derived from the dynamic flexibility matrices before and after damage.In the second stage,damage severity is evaluated based on an improved frequency sensitivity equation.Themain innovations of this method lie in two aspects.The first innovation is the development of a virtual displacement difference method for determining the location of damage in the shear structure.The second is to improve the existing frequency sensitivity equation to calculate the damage degree without constructing the finite elementmodel.Thismethod has been verified on a numerical example of a 22-story shear frame structure and an experimental example of a three-story steel shear structure.Based on numerical analysis and experimental data validation,it is shown that this method only needs to use the low-order modes of structural vibration to diagnose the defect location and damage degree,and does not require finite element modeling.The proposed method should be a very simple and practical defect diagnosis technique in engineering practice.

ELECTROELASTIC FIELD FOR AN IMPERMEABLE ANTI-PLANE SHEAR CRACK IN A PIEZOELECTRIC CERAMICS PLATE

Electroelastic behavior of a cracked piezoelectric ceramics plate subjected to four Cases of combined mechanical-electrical loads is analyzed. The integral transform method is applied to convert the problem involving an impermeable anti-plane crack to dual integral equations. Solving the resulting equations, the explicit analytic expressions for electroelastic field along the crack line and the intensity factors of relevant quantities near the crack tip and the mechanical strain energy release rate we obtained, The known results for an infinite piezoelectric ceramics plane containing an impermeable anti-plane crack are recovered from the present results only if the thickness of the plate h --> infinity.

Dynamic anti-plane analysis for two symmetrically interfacial cracks near circular cavity in piezoelectric bi-materials

The present paper is exposed theoretically to the influence on the dynamic stress intensity factor （DSIF） in the piezoelectric bi-materials model with two symmet- rically permeable interracial cracks near the edges of a circular cavity, subjected to the dynamic incident anti-plane shearing wave （SH-wave）. An available theoretical method to dynamic analysis in the related research field is provided. The formulations are based on Green＇s function method. The DSIFs at the inner and outer tips of the left crack are obtained by solving the boundary value problems with the conjunction and crack- simulation technique. The numerical results are obtained by the FORTRAN language program and plotted to show the influence of the variations of the physical parameters, the structural geometry, and the wave frequencies of incident wave on the dimensionless DSIFs. Comparisons with previous work and between the inner and outer tips are con- cluded.

In-plane shear(ModeⅡ) crack sub-critical propagation of rock at high temperature

In-plane shear crack sub-critical propagation of rock at high temperature was studied by finite element method and shear-box(i.e.compression-shear) test with newly designed electrically conductive adhesive method.Numerical and experimental results show that the normalized shear(Mode Ⅱ) stress intensity factors,K ⅡT/KT0 is decreased as the temperature increases because high temperature can improve stress distribution at crack tip and reduce the Mode Ⅱ stress intensity factor.Microscopic features of fractured surface are of little pits and secondary micro-cracks in the vicinity(1.5-4.0 mm) of the crack tip.The chevron-shape secondary cracks gradually merge in the length of about 4-5 mm and disappear along the direction of crack propagation.Stable shear crack propagation time is increased with the increasing temperature while the stable shear crack propagation rate is decreased with the increasing temperature,since high temperature can increase the shear(Mode Ⅱ) fracture toughness and prevent the crack growth.It is necessary to ensure the ligament of specimen long enough to measure the maximum unstable crack propagation rate of rock.

Effect of holes on in-plane shear(Mode Ⅱ) crack sub-critical propagation of rock

Shear-box(i.e.compression-shear) test and newly designed electrically conductive adhesive method were used to measure shear crack sub-critical propagation time and rate of sandstone specimen.Different cubic specimens with and without holes were tested to study the effect of holes on the shear crack sub-critical propagation.Numerical and experimental results show that three independent variables of hole,the interval distance S,the distance between the center of hole and the crack tip L,and hole radius R,have different contribution to the ratio of stress intensity factor of the specimen with holes to that of the specimen without hole,KⅡ/KⅡ0.Increasing S and decreasing L and R will result in the decrease of KⅡ/KⅡ0 and help crack arrest.The weight relation of the independent variables for KⅡ/KⅡ0 is S>L>R.The specimen DH3 with the largest value of S and the smallest values of L and R has the longest sub-critical crack propagation time and the smallest sub-critical crack propagation rate.Adding two suitable holes symmetrically to the original crack plane in rock specimen is considered to be a potential method for crack arrest of rock.

Effects of Magnetic Shear on the Resistive Wall Mode Instability in a Cylindrical Model

The linear evolution of a resistive wall mode(RWM)with magnetic shears was analytically studied in a cylindrical geometry.The incompressible magnetohydrodynamic(MHD)equations were solved by the Fourier analysis method,and various equilibrium magnetic fields were considered.The shear in the magnetic field had an unstable effect on the linear evolution of the RWM.The linear growth rate increased obviously with increase of the magnetic shear rate for higher magnetic shears.Slow plasma rotation could stabilize the RWM with low magnetic shears,but the plasma rotation could not stabilize the RWM with high magnetic shears.The stabilizing effects of the wall conductivity on the RWM are more efficient for lager magnetic shear.

Short beam shear properties and failure modes of the wood-based X-type lattice sandwich structure

A wood-based X-type lattice sandwich structure was manufactured by insertion-glue method.The birch was used as core,and Oriented Strand Board was used as panel of the sandwich structure.The short beam shear properties and the failure modes of the wood-based X-type lattice sandwich structure with different core direction(vertical and parallel),unit specification(120 mm×60 mm and 60 mm×60 mm),core size(50 mm and 60 mm),and drilling depth(9 mm and 12 mm)were investigated by a short beam shear test and the establishment of a theoretical model to study the equivalent shear modulus and deflection response of the X-type lattice sandwich structure.Results from the short beam shear test and the theoretical model showed that the failure modes of the wood-based X-type lattice sandwich structure were mainly the wrinkling and crushing of the panels under three-point bending load.The experimental values of deflection response of various type specimens were higher than the theoretical values of them.For the core direction of parallel,the smaller the unit specification is,the shorter the core size is,and the deeper the drilling depth is,the greater the short beam shear properties of the wood-based X-type lattice sandwich structure is.

Analysis of Low-Frequency Vibrational Modes and Particle Rearrangements in Marginally Jammed Amorphous Solid under Quasi-Static Shear

We present the numerical simulation results of a model granular assembly formed by spherical particles with tIertzian interaction subjected to a simple shear in the athermal quasi-static limit. The stress-strain curve is shown to separate into smooth, elastic branches followed by a subsequent plastic event. Mode analysis shows that the lowest-frequency vibrational mode is more localized, and eigenvalues and participation ratios of low- frequency modes exhibit similar power-law behavior as the system approaches plastic instability, indicating that the nature of plastic events in the granular system is also a saddle node bifurcation. The analysis of projection and spatial structure shows that over 75% contributions to the non-affine displacement field at a plastic instability come from the lowest-frequency mode, and the lowest-frequency mode is strongly spatially correlated with local plastic rearrangements, inferring that the lowest-frequency mode could be used as a predictor for future plastic rearrangements in the disordered system jammed marginally.

Analysis of thickness-shear and thickness-twist modes of AT-cut quartz acoustic wave resonator and filter

The thickness-shear （TS） and thickness-twist （TT） vibrations of partially electroded AT-cut quartz plates for acoustic wave resonator and filter applications are theoretically studied. The plates have structural variations in one of the two in-plane directions of the plates only. The scalar differential equations derived by Tiersten and Smythe for electroded and unelectroded AT-cut quartz plates are used, resulting in free vibration resonant frequencies and mode shapes for both fundamental and overtone fam- ilies of modes. The trapped modes with vibrations, mainly confined in the electroded areas, are found to exist in both the resonator and the filter structures. The numerical results for the trapped modes are presented for different aspect ratios of electrodes and material properties, providing a reference to the design and optimization of quartz acous- tic wave resonators and filters.

Electric admittance analysis of quartz crystal resonator in thickness-shear mode induced by array of surface viscoelastic micro-beams

The electric admittance of a compound system composed of a thickness-shear mode （TSM） quartz crystal resonator （QCR） and an array of surface viscoelastic micro-beams （MBs） is studied. The governing equations of the MBs are derived from the Timoshenko-beam theory in consideration of shear deformation. The electrical admittance is described directly in terms of the physical properties of the surface epoxy resin （SU-8） MBs from an electrically forced vibration analysis. It is found that both the inertia effect and the constraint effect of the MBs produce competitive influence on the resonant frequency and admittance of the compound QCR system. By further comparing the numerical results calculated from the Timoshenko-beam model with those from the Euler-beam model, the shear deformation is found to lead to some deviation of an admittance spectrum. The deviations are revealed to be evident around the admittance peak（s） and reach the maximum when a natural frequency of the MBs is identical to the fundamental frequency of the QCR. Besides, a higher order vibration mode of the MBs corresponds to a larger deviation at the resonance.

Energetic-ion excited internal kink modes with weak magnetic shear in q0> 1 tokamak plasmas

The energetic particle driven internal kink mode is investigated in this paper for q0〉 1 tokamak plasma with weak magnetic shear. With the effect of energetic particles, the m/n = 1/1 internal mode structure in tokamak plasma does not appear as a rigid step-function when safety factor passes through q = 1 rational surface. It is found that even when the rational surface is removed, the mode may be still unstable under the low magnetic shear condition if the energetic particle drive is strong enough; with the low shear region of safety factor profile widening, the mode becomes more unstable with its growth-rate increasing. Furthermore, we find that the existence of the q = 1 rational surface does not have a significant effect on the stability of the plasma if energetic particles are present, which is very different from the scenarios of the ideal-MHD modes.

Effect of shear equilibrium flow in Tokamak plasma on resistive wall modes

A code named LARWM with non-ideal magnetohydrodynamic equations in cylindrical model is used to describe the instability in Tokamak plasma surrounded by a conducting wall with finite resistivity. We mainly take three factors related to the shear equilibrium plasma flow into consideration to study the stabilizing effect of the shear flow on the resistive wall modes （RWMs）. The three factors are the velocity amplitude of flow, the shear rate of flow on plasma surface, and the inertial energy of equilibrium plasma flow. In addition, a local shear plasma flow is also calculated by the LARWM code. Consequently, it is found that the inertial energy of the shear equilibrium plasma flow has an important role in the stabilization of the RWMs.

Numerical linear analysis of the effects of diamagnetic and shear flow on ballooning modes

The linear analysis of the influence of diamagnetic effect and toroidal rotation at the edge of tokamak plasmas with BOUT++ is discussed in this paper. This analysis is done by solving the dispersion relation, which is calculated through the numerical integration of the terms with different physics. This method is able to reveal the contributions of the different terms to the total growth rate. The diamagnetic effect stabilizes the ideal ballooning modes through inhibiting the contribution of curvature. The toroidal rotation effect is also able to suppress the curvaturedriving term, and the stronger shearing rate leads to a stronger stabilization effect. In addition,through linear analysis using the energy form, the curvature-driving term provides the free energy absorbed by the line-bending term, diamagnetic term and convective term.

Nonlinear excitation of a geodesic acoustic mode by reversed shear Alfvén eignemodes

The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold,which could be readily satisfied in burning plasmas operated in steady-state advanced scenario.This decay process can contribute to thermal plasma heating and confinement improvement.

Rear-Surface Deformation of a Water Drop in Aero-Breakup of Shear Mode

Deformation of water drops in shock-induced high-speed flows is investigated with a focus to the influence of primitive flow parameters on the rear-surface deformation features. Two typical deformation patterns are discovered through high-speed photography. A simple equation to evaluate the radial acceleration of the drop surface is derived. The combined use of this equation and outer flow simulation makes it possible for us to reconstruct the profiles of the early deformed drops. The results agree well with the experiments. Further analysis shows that the duration of flow establishment with respect to the overall breakup time shapes the rear side profile of the drop. Thereby the ratio of the two times, expressed as the square root of the density ratio, appears to be an effective indicator of the deformation features.

Maximum twin shear stress factor criterion for sliding mode fracture initiation

Previous researches on the mixed mode fracture initiation criteria were mostly focused on opening mode fracture. In this study, the authors proposed a new criterion for mixed mode sliding fracture initiation, which is the maximum twin shear stress factor criterion. The authors studied a finite width plate with central slant crack, subject to a far field uniform uniaxial tensile or compressive stress.

ROUGHNESS-INDUCED SHEAR RESISTANCE OF MODE Ⅱ CRACK GROWTH

It is obtained in this paper that the fatigue threshold value of mode H was 1.9 times of that of mode Ⅰ in dual-phase steel(DPS),and the normal stress intensity factor range oJ mode Ⅱ branch crack tip was 2.2 times of that of mode Ⅰ.Above results illustrate that the resistance of mode Ⅱ crack growth was higher than that of mode Ⅰ,the former resulting from roughness-induced shear resistance,the latter,crack closure. The mode Ⅱ component can play two important roles in near-threshold fatigue crack growth:(1)increasing crack tip plasticity which accelerates the crack growth and(2)intro- ducing crack surface contact and rubbing to reduce the crack propagation rate.By means of crack closure,the quantity of shear resistance was easily solved in this paper.The friction shear stress strength factor range of mode Ⅱ,K_,is still much higher than the closure stress strength factor range of mode Ⅰ,K_(Ⅰ,cl).This illustrated that the roughness enlarged the second role and played a role of shielding crack tip from mode Ⅱ crack.

Elastic-viscoplastic field at mixed-mode interface crack-tip under compression and shear

For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface crack- tip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.

Investigations of thickness-shear mode elastic constant and damping of shunted piezoelectric materials with a coupling resonator

Shear-mode piezoelectric materials have been widely used to shunt the damping of vibrations where utilizing surface or interface shear stresses. The thick-shear mode （TSM） elastic constant and the mechanical loss factor can change correspondingly when piezoelectric materials are shunted to different electrical circuits. This phenomenon makes it possible to control the performance of a shear-mode piezoelectric damping system through designing the shunt circuit. However, due to the difficulties in directly measuring the TSM elastic constant and the mechanical loss factor of piezoelectric materials, the relationships between those parameters and the shunt circuits have rarely been investigated. In this paper, a coupling TSM electro-mechanical resonant system is proposed to indirectly measure the variations of the TSM elastic constant and the mechanical loss factor of piezoelectric materials. The main idea is to transform the variations of the TSM elastic constant and the mechanical loss factor into the changes of the easily observed resonant frequency and electrical quality factor of the coupling electro-mechanical resonator. Based on this model, the formular relationships are set up theoretically with Mason equivalent circuit method and they are validated with finite element （FE） analyses. Finally, a prototype of the coupling electro-mechanical resonator is fabricated with two shear-mode PZT5A plates to investigate the TSM elastic constants and the mechanical loss factors of different circuit-shunted cases of the piezoelectric plate. Both the resonant frequency shifts and the bandwidth changes observed in experiments are in good consistence with the theoretical and FE analyses under the same shunt conditions. The proposed coupling resonator and the obtained relationships are validated with but not limited to PZT5A.

基于材料应变的新型装配式剪力墙变形指标限值

为研究新型装配式剪力墙的抗震性能及其变形指标限值,基于课题组所做新型装配式剪力墙抗震性能试验,采用析因法,共设计216个不同剪跨比、轴压比、边缘构件纵筋配筋率等新型装配式剪力墙模型,完成相应的单推性能研究;基于有限元破坏形态识别,将构件破坏形态划分为弯曲破坏、弯剪破坏和剪切破坏3类,提出墙体破坏形态划分准则。参考GB 50011—2010《建筑抗震设计规范》,对弯曲破坏和弯剪破坏划分6个性能状态,对剪切破坏划分两个性能状态,基于构件极限状态下混凝土、钢筋应变和承载力,确定墙体性能状态判定准则。通过线性回归分别得到弯曲破坏、弯剪破坏和剪切破坏形态下构件各塑性位移角限值的回归方程,并提出各破坏形态下具有90%保证率的构件变形指标限值标准,为基于性能的新型装配式剪力墙抗震设计提供参考。