Optimization design of conical reaction teeth of shear wave vibroseis vibration plate

The vibrator plate is the link between the vibroseis vehicle and the earth,as well as the core com-ponent of the vibrator vehicle.In this paper,the coupling effect between the vibrator plate and the earth is an-alyzed from two aspects of reaction tooth arrangement and reaction tooth conical angle,and three groups of experimental models are optimized and designed.The model construction and numerical analysis of the shear wave vibroseis vibrator plate are carried out with ANSYS software.The motion law between the vibration plate and the earth at work was studied,the strain energy of the three experimental models in operation,the maximum displacement of particle at the same position and other reference indices were compared and ana-lyzed,with 28 conical reaction teeth were arranged on both sides.The coupling effect between the vibration plate and the earth was best when the tooth angle was 60°.Compared with the toothless vibration plate,the energy efficiency is improved by about 20%,and the coupling effect between the vibrator plate and the earth is effectively enhanced.It is found that the coupling effect is enhanced through increasing the number of reac-tion teeth of the vibration plate by increasing the coupling area between the vibration plate and the earth.

Exact solution for thermal vibration of multi-directional functionally graded porous plates submerged in fluid medium

An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties of MFG porous plates change according to the length,width,and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology.Especially,new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work.Applying Hamilton's principle and the refined higher-order shear deformation plate theory,the governing equation of motion of an MFG porous rectangular plate in a fluid medium(the fluid-plate system)is obtained.The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass.The GalerkinVlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium.The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature.The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail.These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium.Thereby,they offer appropriate operational approaches for the structure when employed in various mediums.

Finite element analysis of functionally graded sandwich plates with porosity via a new hyperbolic shear deformation theory

This study focusses on establishing the finite element model based on a new hyperbolic sheareformation theory to investigate the static bending,free vibration,and buckling of the functionally graded sandwich plates with porosity.The novel sandwich plate consists of one homogenous ceramic core and two different functionally graded face sheets which can be widely applied in many fields of engineering and defence technology.The discrete governing equations of motion are carried out via Hamilton’s principle and finite element method.The computation program is coded in MATLAB software and used to study the mechanical behavior of the functionally graded sandwich plate with porosity.The present finite element algorithm can be employed to study the plates with arbitrary shape and boundary conditions.The obtained results are compared with available results in the literature to confirm the reliability of the present algorithm.Also,a comprehensive investigation of the effects of several parameters on the bending,free vibration,and buckling response of functionally graded sandwich plates is presented.The numerical results shows that the distribution of porosity plays significant role on the mechanical behavior of the functionally graded sandwich plates。

Dynamic Stability of Viscoelastic Plates with Finite Deformation and Shear Effects

Based on Reddy's theory of plates with higher order shear deformations and the Boltzmann superposition principles, the governing equations were established for dynamic stability of viscoelastic plates with finite deformations taking account of shear effects. The Galerkin method was applied to simplify the set of equations. The numerical methods in nonlinear dynamics were used to solve the simplified system. It could be seen that there are plenty of dynamic properties for this kind of viscoelastic plates under transverse harmonic loads. The influences of the transverse shear deformations and material parameter on the dynamic behavior of nonlinear viscoelastic plates were investigated.

Analysis and seismic tests of composite shear walls with CFST columns and steel plate deep beams

A composite shear wall concept based on concrete filled steel tube （CFST） columns and steel plate （SP） deep beams is proposed and examined in this study. The new wall is composed of three different energy dissipation elements： CFST columns; SP deep beams; and reinforced concrete （RC） strips. The RC strips are intended to allow the core structural elements - the CFST columns and SP deep beams - to work as a single structure to consume energy. Six specimens of different configurations were tested under cyclic loading. The resulting data are analyzed herein. In addition, numerical simulations of the stress and damage processes for each specimen were carried out, and simulations were completed for a range of location and span-height ratio variations for the SP beams. The simulations show good agreement with the test results. The core structure exhibits a ductile yielding mechanism characteristic of strong column-weak beam structures, hysteretic curves are plump and the composite shear wall exhibits several seismic defense lines. The deformation of the shear wall specimens with encased CFST column and SP deep beam design appears to be closer to that of entire shear walls. Establishing optimal design parameters for the configuration of SP deep beams is pivotal to the best seismic behavior of the wall. The new composite shear wall is therefore suitable for use in the seismic design of building structures.

Exact thickness-shear resonance frequency of electroded piezoelectric crystal plates

The determination of the precise thickness-shear frequency of electroded crystal plates has practical importance in quartz crystal resonator design and fabrication, especially when the high fundamental thickness-shear frequency has reduced the crystal plate thickness to such a degree that proper consideration of the effect of electrodes is very important. The electrodes effect as mass loading in the estimation of the resonance frequency has to be modified to consider the stiffness of electrodes, as the relative strength is increasingly noticeable. By following a known procedure in the determination of the thickness-shear frequency of an infinite AT-cut crystal plate, frequency equations of crystal plate without and with piezoelectric effect are obtained in terms of elastic constants and the electrode material density. After solving these equations for the usual design parameters of crystal resonators, the design process can be optimized to pinpoint the precise configuration to avoid time-consuming trial and reduction steps. Since these equations and solutions are presented for widely used materials and parameters, they can be easily integrated into the existing crystal resonator design and manufacturing processes.

Excitation and Detection of Shear Horizontal Waves with Electromagnetic Acoustic Transducers for Nondestructive Testing of Plates

The fundamental shear horizontal（SH0） wave has several unique features that are attractive for long-range nondestructive testing（NDT）. By a careful design of the geometric configuration, electromagnetic acoustic transducers（EMATs） have the capability to generate a wide range of guided wave modes, such as Lamb waves and shear-horizontal（SH） waves in plates. However, the performance of EMATs is influenced by their parameters. To evaluate the performance of periodic permanent magnet（PPM） EMATs, a distributed-line-source model is developed to calculate the angular acoustic field cross-section in the far-field. Numerical analysis is conducted to investigate the performance of such EMATs with different geometric parameters, such as period and number of magnet arrays, and inner and outer coil widths. Such parameters have a great influence on the directivity of the generated SH0 waves that arises mainly in the amplitude and width of both main and side lobes. According to the numerical analysis, these parameters are optimized to obtain better directivity. Optimized PPM EMATs are designed and used for NDT of strip plates. Experimental results show that the lateral boundary of the strip plate has no perceivable influence on SHO-wave propagation, thus validating their used in NDT. The proposed model predicts the radiation pattern ofPPM EMATs, and can be used for their parameter optimization.

Influence of Hartmann Number on Convective Flow of Maxwell Fluid between Two Hot Parallel Plates through Porous Medium Subject to Arbitrary Shear Stress at the Boundary

Natural convection flow of unsteady Maxwell fluid with the effects of constant magnetic force in the course of a porous media is investigated in this research work. Fluid motion between a channel of parallel plates is tempted by time dependent shear stress applied on one plate. The governing partial differential equations of a model under consideration are transformed into ordinary differential equations by Laplace transform method and then solved for temperature and velocity fields. The obtained results for temperature fields are expressed in terms of complementary error function. The influences of involved parameters likes Hartmann number, Grashf number, Prandlt number and porosity parameter, on temperature and velocity profiles are shown graphically. There is no such result regarding Maxwell fluid in the existing literature.

Seismic performance evaluation of steel frame-steel plate shear walls system based on the capacity spectrum method

This paper presents some methods that the standard acceleration design response spectra derived from the present China code for seismic design of buildings are transformed into the seismic demand spectra, and that the base shear force-roof displacement curve of structure is converted to the capacity spectrum of an equivalent single-degree-of-freedom (SDOF) system. The capacity spectrum method (CSM) is programmed by means of MATLAB7.0 computer language. A dual lateral force resisting system of 10-story steel frame-steel plate shear walls (SPSW) is designed according to the corresponding China design codes. The base shear force-roof displacement curve of structure subjected to the monotonic increasing lateral inverse triangular load is obtained by applying the equivalent strip model to stimulate SPSW and by using the finite element analysis software SAP2000 to make Pushover analysis. The seismic performance of this dual system subjected to three different conditions, i.e. the 8-intensity frequently occurred earthquake, fortification earthquake and seldom occurred earthquake, is evaluated by CSM program. The excessive safety of steel frame-SPSW system designed according to the present China design codes is pointed out and a new design method is suggested.

KRMN-TYPE EQUATIONS FOR A HIGHER-ORDER SHEARDEFORMATION PLATE THEORY AND ITS USE IN THE THERMAL POSTBUCKLING ANALYSIS

arman-type nonlinear large deflection equations are derived occnrding to theReddy's higher-order shear deformation plate theory and used in the thermal postbuckling analysis The effects of initial geometric imperfections of the plate areincluded in the present study which also includes th thermal effects.Simply supported,symmetric cross-ply laminated plates subjected to uniform or nomuniform parabolictemperature distribution are considered. The analysis uses a mixed GalerkinGolerkinperlurbation technique to determine thermal buckling louds and postbucklingequilibrium paths.The effects played by transverse shear deformation plate aspeclraio, total number of plies thermal load ratio and initial geometric imperfections arealso studied.

ON THE REFINED FIRST-ORDER SHEAR DEFORMATION PLATE THEORY OF KARMAN TYPE

A new refined first-order shear-deformation plate theory of the Karman type is presented for engineering applications and a new version of the generalized Karman large deflection equations with deflection and stress functions as two unknown variables is formulated for nonlinear analysis of shear-deformable plates of composite material and construction, based on the Mindlin/Reissner theory. In this refined plate theory two rotations that are constrained out in the formulation ate imposed upon overall displacements of the plates in an implicit role. Linear and nonlinear investigations may be mode by the engineering theory to a class of shear-deformation plates such as moderately thick composite plates, orthotropic sandwich plates, densely stiffened plates, and laminated shear-deformable plates. Reduced forms of the generalized Karman equations are derived consequently, which are found identical to those existe in the literature.

SHEAR EFFECTS ON LARGE AMPLITUDE FORCED VIBRATIONOF SYMMETRICALLY LAMINATED RECTILINEARLYORTHOTROPIC CIRCULAR PLATES

In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed. The analytical solution for the relationship between forcing frequency and amplitude of vibration is obtained by Galerkin's method. Finally, the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period for nonlinear free vibration of the plate.

Elastic-plastic analytical solution for centric crack loaded by two pairs of point shear forces in finite plate

The near crack line analysis method was used to investigate a centric crack loaded by two pairs of point shear forces in a finite plate, and the analytical solution was obtained. The solution includes the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near the crack line, the variations of the length of the plastic zone along the crack line with an external load, and the bearing capacity of a finite plate with a centric crack loaded by two pairs of point shear forces. The results are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions are taken.

Analysis of strain variation in cross shear zone of plate during snake hot rolling

In order to study the distribution of equivalent and shear strain of aluminum alloy plate during snake hot rolling, several coupled thermo-mechanical finite element models(FEM) are established. Effects of speed ratio and offset distance on strain distribution of the plate are analyzed. The length of cross shear zone is defined to have a better understanding of the deformation characteristic in cross shear zone, which is the essential difference from symmetrical rolling in deformation zone. The results show that the equivalent strain and shear strain of lower part both increase with the increase of speed ratio, while the upper part decreases; the equivalent strain through the whole thickness decreases with ascending offset distance, while the shear strain of lower part increases. The length of cross shear zone quickly increases with ascending speed ratio and slightly decreases with ascending offset distance. The "positive" and "negative" cross shear zones are formed with the increase of speed ratio and offset distance, respectively. The value of the sensitivity coefficient of speed ratio is an order of magnitude bigger than the offset distance. However, the shear strain at center point increases with the ascending speed ratio and offset distance for different mechanism. As speed ratio increases, the asymmetry of the distribution of equivalent is becoming larger and the shear strain is generated in the same direction in cross shear zone. The FEM results agree well with experimental results.

Converging Parallel Plate Flow Chambers for Studies on the Effect of the Spatial Gradient of Wall Shear Stress on Endothelial Cells

Many in vitro studies focus on effects of wall shear stress (WSS) and wall shear stress gradient (WSSG) on endothelial cells, which are linked to the initiation and progression of atherosclerosis in the arterial system. Limitation in available flow chambers with a constant WSSG in the testing region makes it difficult to quantify cellular responses to WSSG. The current study proposes and characterizes a type of converging parallel plate flow chamber (PPFC) featuring a constant gradient of WSS. A simple formula was derived for the curvature of side walls, which relates WSSG to flow rate (Q), height of the PPFC (h), length of the convergent section (L), its widths at the entrance (w0) and exit (w1). CFD simulation of flow in the chamber is carried out. Constant WSSG is observed in most regions of the top and bottom plates except those in close proximity of side walls. A change in Q or h induces equally proportional changes in WSS and WSSG whereas an alteration in the ratio between w0 and w1 results in a more significant change in WSSG than that in WSS. The current design makes possible an easy quantification of WSSG on endothelial cells in the flow chamber.

Von Misses Pure Shear in Kirchhoff’s Plate Buckling

The pure shear strength for the all-simply supported plate has not yet been found;what is described as pure shear in that plate, is, in fact, a pure-shear solution for another plate clamped on the “Y-Y” and simply supported on the long side, X-X. A new solution for the simply supported case is presented here and is found to be only 60-percent of the currently believed results. Comparative results are presented for the all-clamped plate which exhibits great accuracy. The von Misses yield relation is adopted and through incremental deflection-rating the effective shear curvature is targeted in aspect-ratios. For a set of boundary conditions the Kirchhoff’s plate capacity is finite and invariant for bending, buckling in axial and pure-shear and in vibration.

Lateral load-carrying capacity analyses of composite shear walls with double steel plates and filled concrete with binding bars

A method is developed to predict the lateral load-carrying capacity of composite shear walls with double steel plates and filled concrete with binding bars(SCBs). Nonlinear finite element models of SCBs were established by using the finite element tool, Abaqus. Tie constraints were used to connect the binding bars and the steel plates. Surface-to-surface contact provided by the Abaqus was used to simulate the interaction between the steel plate and the core concrete. The established models could predict the lateral load-carrying capacity of SCBs with a reasonable degree of accuracy. A calculation method was developed by superposition principle to predict the lateral load-carrying capacity of SCBs for the engineering application. The concrete confined by steel plates and binding bars is under multi-axial compression; therefore, its shear strength was calculated by using the Guo-Wang concrete failure criterion. The shear strength of the steel plates of SCBs was calculated by using the von Mises yielding criterion without considering buckling. Results of the developed method are in good agreement with the testing and finite element results.

Bending and stress analysis of polymeric composite plates reinforced with functionally graded graphene platelets based on sinusoidal shear-deformation plate theory

The bending and stress analysis of a functionally graded polymer composite plate reinforced with graphene platelets are studied in this paper.The governing equations are derived by using principle of virtual work for a plate which is rested on Pasternak’s foundation.Sinusoidal shear deformation theory is used to describe displacement field.Four different distribution patterns are employed in our analysis.The analytical solution is presented for a functionally graded plate to investigate the influence of important parameters.The numerical results are presented to show the deflection and stress results of the problem for four employed patterns in terms of geometric parameters such as number of layers,weight fraction and two parameters of Pasternak’s foundation.

Three-Dimensional Scattering of an Incident Plane Shear Horizontal Guided Wave by a Partly through-Thickness Hole in a Plate

We investigate the three-dimensional （3D） scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate, in which the Lamb wave modes are also included due to the mode conversions by the scattering obstacle in the 3D problem. An analytical model is presented such that the wave fields are expanded in all of propagating and evanescent SH modes and Lamb modes, and the scattered far-fields of three fundamental guided wave modes are analyzed numerically for different sizes of the holes and frequencies. The numerical results are verified by comparing with those obtained by using the approximate Poisson/Mindlin plate model for small hole radius and low frequency. It is also found that the scattering patterns are different from those of the SO wave incidence. Our work is useful for quantitative evaluation of the plate-like structure by ultrasonic guided waves.

Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.