In-plane Displacement Research Articles

Investigation of Wave Propagation Behavior of Partially Two-Layered Plates

Abstract In this study, the acoustic emission characteristics of a rectangular plate with a partially covered free damping viscoelastic layer excited by an acoustic source (Hsu-Nielsen) has been investigated. A partially covered plate configuration consisting of a base plate (aluminum) and free damping layer (polyethylene) is considered. An acoustic emission source generated different acoustic modes, which caused the plate to have in-plane and out-plane displacements. These plate displacements will be captured by acoustic sensors. To obtain the general form of plate displacements theoretically, Von Karman theory and a Kelvin-Voigt model were used and the equations of motion were derived using Galerkin’s method. The effects of nonlinear terms of the strain-displacement relation on wave propagation characteristics of plates were investigated. The main frequency ranges of signals and the propagation speed of acoustic modes and their attenuation are very important for source locating. These parameters depend on the acoustic source and transmitted medium. So, theoretically predicting the main frequency range of signals because of the acoustic source and propagation characteristics of different acoustic modes has an important role in an acoustic source–locating algorithm. For this purpose, acoustic emission experiments were carried out using two R15α sensors. Frequency domains of theoretical and experimental results were analyzed. A comparison of the obtained results showed good agreement between the experimental and theoretical Lamb velocities and main frequency ranges.

Dynamic response of functionally graded plates with a porous middle layer under time-dependent load

A dynamic analytical solution for a simply supported, rectangular functionally graded plate with a porous middle layer under time-dependent load based on a refined third-order shear deformation theory with a cubic variation of in-plane displacements according to the thickness and linear/quadratic transverse displacement is presented. The solution achieved in the trigonometric series form and rests on the Green's function method. Two porosity types and their influence on material properties, and mechanical behavior are considered. The network of pores is assumed to be empty or filled with low-pressure air, and the material properties are calculated using the power-law distribution idealization. Numerical calculations have been carried out to demonstrate the accuracy of the kinematic model for the dynamic problem, the effect of porosity, thickness of porous layers, power-law index, and type of loading on the dynamic response of an imperfect functionally graded material plate.

Effect of Fiber Optic Plate on Centroid Locating Accuracy of Monocentric Imager

We propose a method for obtaining the centroid locating accuracy (CLA) of a monocentric imager with a fiber optic plate (FOP) as a relay image transmission element in order to reduce the loss of CLA due to the addition of FOP. We constructed a two-stage image transmission coupling model of spherical focal surface (FOP) image sensor. By analyzing the influences of FOP parameters, including the fill factor and the fiber diameter, and FOP in-plane displacements, including rotation and translation on CLA, the loss of the lowest CLA that the monocentric imager can withstand caused by the addition of the FOP was reduced by 20%.

Analysis of a curved Timoshenko nano-beam with flexoelectricity

A Timoshenko beam model is applied for the analysis of the flexoelectric effect for a curved nano-beam. This theory transforms the beam to a 1-d problem along the beam axis. The electric intensity vector for the open-circuit condition can be expressed by mechanical quantities, namely strains and strain gradients. The variational principle is applied to derive the system of ordinary differential equations (ODEs) for the beam deflection, cross-section rotation, and in-plane displacement. A numerical solution based on the Taylor series expansion with Cartesian coordinate along the beam is proposed for the system of ODEs. A convergence analysis with respect to the number of terms in the Taylor series expansion is performed. Numerical results for the beam deflection, rotation, in-plane displacement, and induced electric intensity vector are presented for various flexoelectric coefficients and the beam curvature.

Determination of displacements on built-up steel beams during experiments by image processing

In this study, an image processing technique is developed for measuring the displacements during flexural loading experiments of structural beams as an alternative to measurements by traditional gauging devices. In this context, four-point bending tests were carried out on three built-up (welded) steel beams, one of them without stiffening plates and the others with stiffening plates. In the experiments, while the load-deflection values in each loading step were taken using load cells and LVDTs, a video recording of the experiments was simultaneously taken. The load-deflection curves were comparatively constructed using both the values measured with LDVTs and the data obtained by image processing. In order to match the data obtained using the point flow method of image processing technique to the gauged measurements, the scale coefficients in pixel / mm unit were calculated. The mean absolute error (MAE) and root mean square error RMSE error values were computed to determine the efficacy of the scale coefficients. The MAE and RMSE values for the beam without the stiffening plates turned out to be 3.42 and 4.52, while they were 1.29 and 1.82 for the beams with the stiffening plates. According to these results, the higher the lateral torsional buckling, the more difficult it is to determine the verification coefficient. The accuracy of the image processing method developed herein for determination of in-plane displacements can be further improved easily for experiments involving out-of-plane displacements due to local buckling also if the recordings of more cameras from different angles are included in the analyses.

Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride

The quantum anomalous Hall (QAH) effect is sometimes observed in twisted bilayer graphene (tBG) when it is nearly aligned with an encapsulating hexagonal boron nitride (hBN) layer. We propose that the appearance or absence of the QAH effect in individual devices could be related to commensurability between the graphene/graphene and graphene/hBN moir\'e patterns. We identify a series of points in the $(\theta_{\rm GG},\theta_{\rm GBN})$ twist-angle space at which the two moir\'e patterns are commensurate, allowing moir\'e band theory to be applied, and show that the band Chern numbers are in this case sensitive to a rigid in-plane hBN displacement. Given this property, we argue that the QAH effect is likely only when i) the $(\theta_{\rm GG},\theta_{\rm GBN})$ twist-angle-pair is close enough to a commensurate point that the two moir\'e patterns yield a supermoir\'e pattern with a sufficiently long length scale, and ii) the supermoir\'e has a percolating topologically non-trivial QAH phase. For twist angles far from commensurability, the hBN layer acts as a source of disorder that can destroy the QAH effect. Our proposal can explain a number of current experimental observations. Further experimental studies that can test this proposal more directly are suggested.

Large deformation behavior of functionally graded porous curved beams in thermal environment

The in-plane thermoelastic response of curved beams made of porous materials with different types of functionally graded (FG) porosity is studied in this research contribution. Nonlinear governing equations are derived based on the first-order shear deformation theory along with the nonlinear Green strains. The nonlinear governing equations are solved by the aid of the Rayleigh–Ritz method along with the Newton–Raphson method. The modified rule-of-mixture is employed to derive the material properties of imperfect FG porous curved beams. Comprehensive parametric studies are conducted to explore the effects of volume fraction and various dispersion patterns of porosities, temperature field, and arch geometry as well as boundary conditions on the nonlinear equilibrium path and stability behavior of the FG porous curved beams. Results reveal that dispersion and volume fraction of porosities have a significant effect on the thermal stability path, maximum stress, and bending moment at the crown of the curved beams. Moreover, the influence of porosity dispersion and structural geometry on the central radial and in-plane displacement of the curved beams is evaluated. Results show that various boundary conditions make a considerable difference in the central radial displacements of the curved beams with the same porosity dispersion. Due to the absence of similar results in the specialized literature, this paper is likely to provide pertinent results that are instrumental toward a reliable design of FG porous curved beams in thermal environment.

Subpixel sampling moiré method for in-plane displacement measurement considering the symmetric errors induced by interpolation.

Sampling moiré method (SMM) is a highly accurate vision-based deformation measurement method, whose measurement error is minimized when an integer that is closest to the grating pitch is selected as the sampling pitch. We propose a subpixel SMM by applying subpixel interpolation operation before the downsampling in traditional SMM; the sampling pitch was selected as a noninteger nearest to the grating pitch in the subpixel resolution image. Meanwhile, the average filter method was used to eliminate the symmetric error cause by interpolation. As a result, the period of moiré fringe was enlarged greatly, and the measurement accuracy was also increased. To investigate the efficiency of the subpixel SMM, a computer simulation was applied to analyze the accuracy of the subpixel SMM. Then a simple tensile experiment was conducted to validate the efficiency of this method, and the result of the subpixel SMM accorded well with the fiber Bragg grating. In summary, the proposed novel subpixel SMM is capable of being used for high accuracy in-plane deformation measuring.

Electrothermal micro tweezer for biomedical applications

This paper presents design, simulation and results analysis for a novel micro tweezer. The principal element in the proposed device is a double U-beam electrothermal actuator. Using FEM tool, Poly-Silicon material is applied to the device structure and analysed for both in-plane and out of plane displacement for respective range of actuation potential. The micro tweezer holder mouth provided a maximum in-plane displacement of ∼48µm at 4.5V actuation voltage. Comparatively negligible out of plane displacement exhibited by the device during simulation. The proposed micro tweezer is designed for the micromanipulation of biological cells in a better way.

Growth and Atomically Resolved Polarization Mapping of Ferroelectric Bi2WO6 Thin Films

Aurivillius ferroelectric $Bi_2WO_6$ (BWO) encompasses a broad range of functionalities, including robust fatigue-free ferroelectricity, high photocatalytic activity, and ionic conductivity. Despite these promising characteristics, an in-depth study on the growth of BWO thin films and ferroelectric characterization, especially at the atomic scale, is still lacking. Here, we report pulsed laser deposition (PLD) of BWO thin films on (001) $SrTiO_3$ substrates and characterization of ferroelectricity using the scanning transmission electron microscopy (STEM) and piezoresponse force microscopy (PFM) techniques. We show that the background oxygen gas pressure used during PLD growth mainly determines the phase stability of BWO films, whereas the influence of growth temperature is comparatively minor. Atomically resolved STEM study of a fully strained BWO film revealed collective in-plane polar off-centering displacement of W atoms. We estimated the spontaneous polarization value based on polar displacement mapping to be about 54 $\pm$ 4 ${\mu}C cm^{-2}$, which is in good agreement with the bulk polarization value. Furthermore, we found that pristine film is composed of type-I and type-II domains, with mutually orthogonal polar axes. Complementary PFM measurements further elucidated that the coexisting type-I and type-II domains formed a multidomain state that consisted of 90$\deg$ domain walls (DWs) alongside multiple head-to-head and tail-to-tail 180$\deg$ DWs. Application of an electrical bias led to in-plane 180$\deg$ polarization switching and 90$\deg$ polarization rotation, highlighting a unique aspect of domain switching, which is immune to substrate-induced strain.

Extracting plastic properties from in-plane displacement data of spherical indentation imprint

This study proposes a method for evaluating elastic limit and strain hardening exponent by a single spherical indentation test. The method extracts the plastic properties from radial displacement fields and vertical profile of a residual imprint. Based on finite element (FE) and regression analyses, an evaluation algorithm is developed by relating the imprint data with plastic properties. Digital image correlation (DIC) method is used for measurements of the radial displacement fields. The errors of the properties determined with our method were less than 12 % for elastic limit stress, 0.6 for strain hardening exponent compared with those from tensile tests. The sensitivity of the inverse analysis algorithm is also shown to be acceptable.

Application of Digital Image Correlation (DIC) Technique for Semi Interlocking Masonry (SIM) Panels under Large Cyclic In-Plane Shear Displacement

Semi interlocking masonry (SIM) is an innovative masonry building system which is being developed in the Centre for Infrastructure Performance and Reliability at The University of Newcastle, Australia. It utilizes a special method of interlocking of mortar-less engineered masonry panels made of semi-interlocking masonry (SIM) units which possess significant energy dissipation capacity due to friction on sliding bed joints between units of the panel during a seismic event. This special method of interlocking SIM bricks allows relative sliding of unit courses in-plane of a wall and prevents out-of-plane relative movement of units. Because all bed joints in a SIM panel are sliding joints, SIM panels can withstand large in-plane displacements without damage. To test SIM panels, a special steel frame with pin connections at each corner was designed and built. The arrangement with pin connections allows application of in-plane shear distortion to the panel of up to 120 mm. The study presented herein focused on the experimental investigation of displacement capacities of three different types of panels (panel with open gap between the steel frame and top of the panel, panel with foam in the gap, panel with grout in the gap) with two types of SIM units. The paper expands significantly from the previously published conference paper and examines the behavior of SIM panels subject to 100 mm (5% storey drift) cyclic in-plane lateral displacement on six SIM panels. The horizontal and vertical movement of SIM units were recorded using Digital Image Correlation (DIC) every 10 s over approximately 8 h of testing. This study reveals that the DIC displacement outputs show good agreement with displacements measured using traditional instrumentation, even at large displacements (up to 100 mm). The structural performance of the SIM panels is also analyzed and potential joint opening widths are quantified under large displacement by plotting the outputs from DIC results.

A Contactless Laser Doppler Strain Sensor for Fatigue Testing with Resonance-Testing Machine.

In this article, a non-contact laser Doppler strain sensor designed for fatigue testing with the resonance-testing machine is presented. The compact sensor measures in-plane displacements simultaneously from two adjacent points using the principle of in-plane, laser-Doppler vibrometry. The strain is computed from the relative displacements divided by the distance between these two points. The optical design, the mathematical model for estimating noise-limited resolution, the simulation results of this model, and the first measurement results are presented. The comparison of the measurement results of our sensor with the results of a conventional strain gauge shows that our design meets the measurement requirements. The maximum strain deviation compared to conventional strain gauges of the laser-Doppler extensometer is below in all performed experiments.

Revisiting imperfect interface laws for two-dimensional elastodynamics.

We study the interaction of in-plane elastic waves with imperfect interfaces composed of a periodic array of voids or cracks. An effective model is derived from high-order asymptotic analysis based on two-scale homogenization and matched asymptotic technique. In two-dimensional elasticity, we obtain jump conditions set on the in-plane displacements and normal stresses; the jumps involve in addition effective parameters provided by static, elementary problems being the equivalents of the cell problems in classical two-scale homogenization. The derivation of the model is conducted in the transient regime and its stability is guarantied by the positiveness of the effective interfacial energy. Spring models are envisioned as particular cases. It is shown that massless-spring models are recovered in the limit of small void thicknesses and collinear cracks. By contrast, the use of mass-spring model is justified at normal incidence, otherwise unjustified. We provide quantitative validations of our model and comparison with spring models by means of comparison with direct numerical calculations in the harmonic regime.

Deformation studies of cylindrical nanostructured silica aerogels by using phase shifting digital holographic interferometry

In this paper, we have studied the deformation of cylindrical nanostructured silica aerogels prepared with methyltrimithoxysilane (MTMS) precursor. Two beam phase-shifting digital holographic interferometry (PSDHI) is applied along with a two-beam illumination technique to study in-plane displacements. To obtain the aerogels with different densities, the MeOH/MTMS molar ratio was systematically increased from the value 20 to 26. The cylindrical aerogels are loaded with various loads from the top surface. Phase shifted holograms of silica aerogels with varying densities, with and without deformation, are recorded with two beam illumination by CCD camera. Fresnel Diffraction integral is used to reconstruct the complex amplitude of aerogel samples. For in-plane displacements, phase distribution in deformed aerogels is determined by measuring the change in the two-phase distributions. The patterns corresponding to the phase distribution of aerogels for different loads and densities are recorded. It has been observed that the deformation of silica aerogels reduces by the value 0.02058 cm to 0.0017 cm, with an increase in bulk density 0.01742 gm/cc to 0.1952 gm/cc. The elastic behavior of aerogels has been explained under various loads by considering the phase distribution patterns and condensation reaction.

Doping controlled Fano resonance in bilayer 1T'-ReS2: Raman experiments and first-principles theoretical analysis.

In the bilayer ReS2 channel of a field-effect transistor (FET), we demonstrate using Raman spectroscopy that electron doping (n) results in softening of frequency and broadening of linewidth for the in-plane vibrational modes, leaving the out-of-plane vibrational modes unaffected. The largest change is observed for the in-plane Raman mode at ∼151 cm-1, which also shows doping induced Fano resonance with the Fano parameter 1/q = -0.17 at a doping concentration of ∼3.7 × 1013 cm-2. A quantitative understanding of our results is provided by first-principles density functional theory (DFT), showing that the electron-phonon coupling (EPC) of in-plane modes is stronger than that of out-of-plane modes, and its variation with doping is independent of the layer stacking. The origin of large EPC is traced to 1T to 1T' structural phase transition of ReS2 involving in-plane displacement of atoms whose instability is driven by the nested Fermi surface of the 1T structure. Results are compared with those of the isostructural trilayer ReSe2.

Nonlinear forced vibration of in-plane bi-directional functionally graded materials rectangular plate with global and localized geometrical imperfections

This research aims to investigate the nonlinear vibration of the in-plane bi-directional functionally graded (BDFG) plate with global and localized geometrical imperfection subjected to a transverse harmonic excitation. The material properties of plate are varying along two in-plane directions. The global and localized geometrical imperfections are simulated in the form of products of trigonometric and hyperbolic functions. Based on the von Kármán’s nonlinear plate theory, coupled nonlinear partial differential equations governing in-plane and transverse displacements of BDFG plate are derived employing Hamilton’s principle. The continuous nonlinear model of imperfect BDFG plate is discretized using the Galerkin scheme, resulting in the reduced order model. The pseudo-arclength continuation technique is employed to trace the periodic motion of plate and construct frequency-/force-response curves. Dynamic responses are solved using numerical integration. Numerical results of ceramic-metal BDFG plates are presented to examine the effects of system parameters, e.g. functional gradient parameters, external excitation parameters and damping coefficients. Particularly, influences of global and localized geometrical imperfections are highlighted. Results show that the variation of gradient parameter and the existence of geometrical imperfection change the nonlinearity of resonant response. Cyclic-fold, period doubling and torus bifurcations of the periodic solution are detected as excitation parameters varying. Periodic, quasi-periodic and chaotic motions of plate are also explored.

Free vibration analysis of a laminated composite sandwich plate with compressible core placed at the bottom of a tank filled with fluid

The paper addresses the free vibration problem of a laminated composite sandwich plate with compressible core, placed at the bottom of a tank filled in with fluid. The analysis is performed based on the extended higher order sandwich plate theory (EHSAPT). First-order shear deformation theory (FSDT) is used for the face sheets. Cubic and quadratic polynomials are used to describe the in-plane and transverse displacements of the core, respectively. The fluid is assumed inviscid, incompressible, and irrotational. To obtain the kinetic energy of the fluid, its velocity potential is expressed by using the compatibility and boundary conditions. The governing differential equations and corresponding boundary conditions are derived from Hamilton’s principle. A single series expansion is considered with two-variable orthogonal polynomials as a set of admissible functions satisfying the boundary conditions. The natural frequencies of the coupled sandwich plate-fluid system are calculated by using the Rayleigh-Ritz method. Convergence of the adopted strategy is first investigated. Then, comparisons are conducted with previous results reported in the literature. Also, the effects are investigated of several parameters, such as the plate side-to-thickness ratio, the core-to-face sheets thickness ratio, the face sheet-to-core flexural modulus ratio, the height and aspect ratio of the tank.

Measurement of three-dimensional displacements by radial shearing interferometer

<sec> Moiré patterns formed by overlapping two circular gratings of slightly different pitches have been extensively used for measuring the two-dimensional (2D) and three-dimensional (3D) displacements. However, in the existing applications, Moiré patterns are analyzed based on geometric superposition, by which the 3D displacements cannot be instantaneously or simultaneously measured with a high accuracy. In this paper, radial shearing interferometry with double circular gratings of slightly different pitches is presented to realize the simultaneous measurement of 3D displacements. </sec><sec> The measurement is based on the principle that Moiré patterns produced by radial shearing interferometry are determined not only by the 2D in-plane displacements, but also by the out-of-plane displacement that brings about a phase shift between Moiré patterns of +1 and –1 diffraction orders. First, the production mechanism of Moiré patterns by radial shearing interferometry is studied based on the scalar diffraction theory and the intensity distribution of Moiré fringes of +1 and –1 orders is derived to establish the exact analytic relations between Moiré patterns and 3D displacements. Second, on the basis of spectrum characteristics of circular grating, a semicircular ring filter is proposed for spatial filtering to realize the simultaneous imaging of Moiré fringes of +1 and –1 orders. Then, the algorithm to quantitatively extract 3D displacements from Moiré patterns is proposed and demonstrated by numerical simulation. In the algorithm, Moiré patterns in the rectangular coordinate system are transformed into the polar coordinate system and skeletons are extracted to determine the feature points of the bright fringes. The in-plane displacements can be solved by feature points of +1 or –1 diffraction order, and the out-of-plane displacement can be computed by the feature points of +1 and –1 diffraction orders in the same bright fringe. Finally, experimental results prove that the maximum absolute error and mean error for in-plane displacements are 4.8 × 10<sup>–3</sup> mm and 2.0 × 10<sup>–4</sup> mm respectively, and 0.25 mm and 8.6 × 10<sup>–3</sup> mm for out-of-plane displacement. </sec><sec> In conclusion, by using the Moiré patterns of +1 and –1 diffraction orders imaged by radial shearing interferometer with double circular gratings of slightly different pitches, the 3D displacement can be simultaneously measured. The method has the advantages of simple device, high measurement accuracy, non-contact and instantaneous measurement, which provides an important guidance for practically measuring the 3D displacements. </sec>

Stress analysis of smart composite plate structures

In the present study, the electro-mechanical responses of smart laminated composite plates with piezoelectric materials are derived using a two-dimensional (2 D) displacement-based non-polynomial higher-order shear deformation theory. The kinematics of the mathematical model incorporates the deformation of laminates which account for the effects of transverse shear deformation and a non-linear variation of the in-plane displacements using inverse sine hyperbolic function of the thickness coordinate. The equilibrium equations are obtained using the minimization of energy principle known as the principle of minimum potential energy (PMPE) which is also based on a variational approach and the solutions are obtained using Navier’s solution technique for diaphragm supported smart laminated composite plates. The responses obtained in the form of deflection and stresses are compared with three dimensional (3 D) solutions and also with different polynomial and non-polynomial based higher-order theories in the literature. The transverse shear stresses are obtained using 3 D equilibrium equations of elasticity to enhance the accuracy of the present results. Various examples are numerically solved to establish the efficiency of the present model.