Boundary Conditions Of Plate Research Articles

Experimental research on the axial compressive performance of brick masonry walls strengthened with a steel plate frame considering initial load

Initial load means the load, including dead or/and live load, applied on brick masonry walls before being strengthened, which can influence the strengthening effect. However, research on the strengthening of brick masonry walls particularly considering the effect of initial load is insufficient. Steel is widely utilised for brick masonry strengthening because of its simple construction procedure and flexible configuration. Hence, for advancing the application of steel plates in brick masonry strengthening engineering and studying the effect of initial load on strengthening, an experiment was performed to investigate the axial compressive performance of a steel plate frame (SPF) strengthening brick masonry wall considering initial load for various frame configurations. The experiment results indicated that the SPF effectively confined the brick masonry wall, and steel plate columns underwent local buckling failure under axial load; the load-bearing capacity of brick masonry walls increased by at least 10.62 % strengthened with double-sided single-span SPF, and it further improved by 18.75 % strengthened with double-sided double-span SPF when initial load ratio was less than 0.25. Initial load ratio considerably affected the axial collaborative performance of the brick masonry wall and SPF, and increasing initial load ratio resulted in poor axial collaborative performance, following which the load-bearing capacity of the strengthened masonry walls decreased. The load-bearing capacity of the strengthened walls was higher for an initial load ratio less than 0.25. Conversely, a rare strengthening effect was observed when the initial load ratio exceeded 0.7. Based on the simplification of steel plate boundary conditions and the buckling theory of struts, a formula for predicting the load-bearing capacity of brick masonry walls strengthened with an SPF considering initial load was derived, which showed acceptable accuracy in comparison with experimental values.

Limit Cycle Oscillation of Elastic Plate in Supersonic Flow

Fluid–structure interaction of an elastic plate with piezoelectric elements, turbulent freestream flow at Mach 2.5, and a pressurized cavity is investigated computationally and correlated with a recent experiment. The pressure field on the plate is measured using pressure-sensitive paint, and the structural response is observed using the measured voltage of a piezoelectric patch. The measurements show a dominant frequency of oscillation which indicates the likely onset of flutter and a postflutter limit cycle oscillation (LCO). A computational investigation is conducted to study the effects of static pressure differential, temperature differential, cavity pressure coupling, and plate boundary conditions on the linear flutter onset condition and the nonlinear postflutter LCO characteristics. Rivets that connect the plate to the supporting structure are modeled as local constraint in the in-plane direction, and their effect is investigated. Computations show that the coupling between the cavity acoustic and plate structural modes is necessary for flutter onset in the wind-tunnel conditions. Correlation between computed and measured aerodynamic pressure shows reasonable agreement in amplitude and frequency. Computational results are obtained using Piston Theory and also potential flow aerodynamics. Computed and measured pressure LCO mode shapes are extracted and correlated.

New analytical model for multi-layered composite plates with imperfect interfaces under thermomechanical loading

AbstractA new analytical model for thermoelastic responses of a multi-layered composite plate with imperfect interfaces is developed. The composite plate contains an arbitrary number of layers of dissimilar materials and is subjected to general mechanical loads (both distributed internally and applied on edges for each layer) and temperature changes, which can vary from layer to layer and along two in-plane directions. Each layer is regarded as a Kirchhoff plate, and each imperfect interface is described using a spring-layer interface model, which can capture discontinuities in the displacement and stress fields across the interface. Unlike existing models, the governing equations and boundary conditions are simultaneously derived for each layer by using a variational procedure based on the first and second laws of thermodynamics, which are then combined to obtain the global equilibrium equations and boundary conditions for the multi-layered composite plate. A general analytical solution is developed for a symmetrically loaded composite square plate with an arbitrary number of layers and imperfect interfaces by using a new approach that first determines the interfacial normal and shear stress components on one interface. Closed-form solutions for two- and three-layer composite square plates are obtained as examples by directly applying the general analytical solution. Numerical results for two-, three- and five-layer composite plates under different loading and boundary conditions predicted by the current model are provided, which compare well with those obtained from finite element simulations using COMSOL, thereby validating the newly developed analytical model.

Calibrating the Discrete Boundary Conditions of a Dynamic Simulation: A Combinatorial Approximate Bayesian Computation Sequential Monte Carlo (ABC-SMC) Approach.

This paper presents a novel adaptation of the conventional approximate Bayesian computation sequential Monte Carlo (ABC-SMC) sampling algorithm for parameter estimation in the presence of uncertainties, coined combinatorial ABC-SMC. Inference of this type is used in situations where there does not exist a closed form of the associated likelihood function, which is replaced by a simulating model capable of producing artificial data. In the literature, conventional ABC-SMC is utilised to perform inference on continuous parameters. The novel scheme presented here has been developed to perform inference on parameters that are high-dimensional binary, rather than continuous. By altering the form of the proposal distribution from which to sample candidates in subsequent iterations (referred to as waves), high-dimensional binary variables may be targeted and inferred by the scheme. The efficacy of the proposed scheme is demonstrated through application to vibration data obtained in a structural dynamics experiment on a fibre-optic sensor simulated as a finite plate with uncertain boundary conditions at its edges. Results indicate that the method provides sound inference on the plate boundary conditions, which is validated through subsequent application of the method to multiple vibration datasets. Comparisons between appropriate forms of the metric function used in the scheme are also developed to highlight the effect of this element in the schemes convergence.

Investigation of the Zero-Frequency Component of Nonlinear Lamb Waves in a Symmetrical Undulated Plate.

When an ultrasonic pulse propagates in a thin plate, nonlinear Lamb waves with higher harmonics and a zero-frequency component (ZFC) will be generated because of the nonlinearity of materials. The ZFC, also known as the static displacement or static component, has its unique application on the evaluation of early-stage damages in the elastic symmetrical undulated plate. In this study, analysis of the excitation mechanism of the ZFC and the second harmonic component (SHC) was theoretically and numerically investigated, and the material early-stage damage of a symmetrical undulated was characterized by studying the propagation of nonlinear Lamb waves. Both the ZFC and SHC can be effectively employed in monitoring the material damages of the undulated plate in its early stage. However, several factors must be considered for the propagation of the SHC in an undulated plate because of the geometric curvature and interference between the second harmonics during propagation, preventing efficient application of this technique. If the fundamental wave can propagate in the plate regardless of the plate boundary conditions, an accumulative effect always exists for the ZFC in a thin plate, indicating that the ZFC is independent of the structural geometry. This study reveals that the ZFC-based inspection technique is more efficient and powerful in characterizing the damages of a symmetrical undulated plate in the early stage of service compared to the second harmonic method.

Thermomechanical bending of functionally graded carbon nanotubes reinforced composite plate by meshless method

AbstractFunctionally graded (FG) carbon nanotubes (CNTs) reinforced composite possessing continuously varied material properties have received extensive concern in the area of aviation, automotive, military, and spaceflight. The nonlinear bending of FG CNT composite is performed by developing a novel meshless model on the base of Smoothed Particle Hydrodynamics (SPH) method. The equivalent temperature relative material properties of composite is established in the light of the extended rule of mixture model. Different gradient dispersions of CNTs are taken into account and modeled. The governing equations are explored using the Mindlin theory and discretized though a symmetric SPH method with high prediction ability. The developed model is verified by analyzed several examples and compared to the solution obtained in literature. Influences of CNT dispersion, content, plate aspect ratio, boundary conditions and lamination angle on the bending response are elaborated. The present study provides an alternative potential method to solve the mechanical performances of FG CNT composites based on the meshless SPH formulation.Highlights Thermo‐mechanics of FG‐CNTRC is firstly solved by SPH method. The model is verified by solving the benchmarks in literature. Nonlinear bending behaviors of FG‐CNTRC are demonstrated. The minimum deflection take place in FG‐X type composite. For laminate plate, the smallest deformation occurs in 0° CNTRC.

Parametric Analysis of Free Vibration of Functionally Graded Porous Sandwich Rectangular Plates Resting on Elastic Foundation.

Based on the three-dimensional elasticity theory, the free vibration of functionally graded porous (FGP) sandwich rectangular plates is studied, and a unified solution for free vibration of the plates is proposed in this study. The arbitrary boundary conditions of FGP sandwich rectangular plates are simulated by using the Rayleigh-Ritz method combined with artificial spring theory. The calculation performances of the unified solution for FGP sandwich rectangular plates such as convergence speed and computational efficiency are compared extensively under different displacement functions. In addition, three kinds of elastic foundation (Winkler/Pasternak/Kerr foundations) and three porosity distributions are considered. Some benchmark results and accurate values for the free vibration of FGP sandwich rectangular plates resting on elastic foundations are given. Finally, the effects of diverse structural parameters, elastic foundations with different parameters, and boundary conditions on the free vibration of the FGP sandwich rectangular plates are analyzed.

A deviatoric couple stress Mindlin plate model and its degeneration

Based on the classical couple stress theory, the deviatoric couple stress theory (DCST), where both couple stress and curvature tensors are traceless, is developed. The deviatoric couple stress Mindlin plate is established based on a new hypothesis of the vanishing curvature of the transverse normal, and the governing equations and associated boundary conditions of the simplified size-dependent Mindlin plate are respectively derived by the principle of virtual work. In the absence of couple stresses, a simplified Mindlin plate model between the classical Kirchhoff plate model and classical Mindlin plate model is derived. To illustrate the simplified DCST-based Mindlin plate model, the static bending and free vibration of rectangular plates are studied. The dependence of the length scale parameter and curvature ratio on the deflection, rotation and natural frequency is analyzed. The numerical results show that the consideration of couple stresses and curvatures hardens the stiffness of the microstructure, resulting in a decrease in its deflection and rotation compared with that of the macroscopic structure under the same conditions, while the natural frequency increases, which is consistent with the size effect observed in experiments.

On the boundary conditions for a thin circular plate conjugated to a massive body

The problem of deformation under the action of uniform pressure of a circular plate coupled with a massive base is considered, while the condition for the coupling of the plate with the base is modeled using boundary conditions of the generalized elastic embedding type, i.e. the relationship between the bending moment and forces at the edge of the plate with displacements and rotation angles through the compliance matrix. The main goal of the work is to study the influence of the elasticity of the embedding on the elastic response of the plate. The solution to the problem was obtained in the formulation of the linear theory of plates, the theory of membranes in the approximation of homogeneity of longitudinal forces, and the Foppl — von Karman theory, also in the approximation of the assumption of homogeneity of longitudinal forces. The values of the coefficients of the compliance matrix were obtained using the finite element method for the auxiliary problem and compared with the values of the coefficients obtained for related problems by analytical methods. Numerical results were obtained for an aluminum wafer on a silicon base. The obtained solution was compared with the solution obtained for the rigid embedment condition for all three models used. It is shown that in the case of large deflections (several plate thicknesses), taking into account the compliance of the embedment becomes essential.

Impact of Backing Plate and Thermal Boundary Conditions for High-Speed Friction Stir Welding of 25-mm Thick Aluminum Alloy 7175-T79

Impact of Backing Plate and Thermal Boundary Conditions for High-Speed Friction Stir Welding of 25-mm Thick Aluminum Alloy 7175-T79

Computational investigation of magnetohydrodynamic convective flow in a trapezoidal cavity with multiple obstacles via finite element analysis

The present research deals with magnetohydrodynamic (MHD) natural convection within a trapezoidal cavity under the influence of inner solid obstacles of different shapes. The cavity includes two horizontal plates and two heated circular cylinders and is subjected to a uniform horizontal magnetic field. The walls of the domain can either be heated or cooled isothermally. The finite element method is used to solve the Oberbeck-Boussinesq equations that govern the fluid flow and heat transfer process. Three different thermal conditions are considered for the horizontal plates: isothermal heating, isothermal cooling, and adiabatic. The investigation explores the impact of varying Rayleigh numbers (Ra = 104–106), Hartmann numbers (Ha = 0–100), and thermal boundary conditions for inner horizontal plates on the flow patterns and heat transfer efficiency. The results indicate that as the Rayleigh number rises and the magnetic field strength diminishes, a noticeable improvement in heat transfer is observed, particularly in cases where the horizontal plates are subjected to cooling. Conversely, the heated inner horizontal plates exhibit less effective energy transport across the considered three configurations. It should be noted that the heat transfer rate for Ra = 106 can be increased more than 5 % when cooled ones will replace the heated inner plates. Whilst a transition between the adiabatic inner plates to cooled ones allows improving the average Nusselt number at the bottom heated wall at about 3 %. Moreover, the convective flow intensity can be described using the kinetic energy, where a growth of the magnetic field strength from 0 till 100 for Ra = 105 decreases the total kinetic energy at 76 times for heated plates, at 100 times for cooled plates and at 92 times for adiabatic plates.

Comparison of geodetic slip-deficit and geologic fault slip rates reveals that variability of elastic strain accumulation and release rates on strike-slip faults is controlled by the relative structural complexity of plate-boundary fault systems

Comparison of geodetic slip-deficit rates with geologic fault slip rates on major strike-slip faults reveals marked differences in patterns of elastic strain accumulation on tectonically isolated faults relative to faults that are embedded within more complex plate-boundary fault systems. Specifically, we show that faults that extend through tectonically complex systems characterized by multiple, mechanically complementary faults (that is, different faults that are all accommodating the same deformation field), which we refer to as high-Coefficient of Complexity (or high-CoCo) faults, exhibit ratios between geodetic and geologic rates that vary and that depend on the displacement scales over which the geologic slip rates are averaged. This indicates that elastic strain accumulation rates on these faults change significantly through time, which in turn suggests that the rates of ductile shear beneath the seismogenic portion of faults also vary through time. This is consistent with models in which mechanically complementary faults trade off slip in time and space in response to varying mechanical and stress conditions on the different component faults. In marked contrast, structurally isolated (or low-CoCo) faults exhibit geologic slip rates that are similar to geodetic slip-deficit rates, regardless of the displacement and time scales over which the slip rates are averaged. Such faults experience relatively constant geologic fault slip rates as well as constant strain accumulation rate (aside from brief, rapid post-seismic intervals). This suggests that low-CoCo faultsd "keep up" with the rate imposed by the relative plate-boundary condition, since they are the only structures in their respective plate-boundary zone that can effectively accommodate the imposed steady plate motion. We hypothesize that the discrepancies between the small-displacement average geologic slip rates and geodetic slip-deficit rates may provide a means of assessing a switch of modes for some high-CoCo faults, transitioning from a slow mode to a faster mode, or vice versa. If so, the differences between geologic slip rates and geodetic slip-deficit rates on high-CoCo faults may indicate changes in a fault's behavior that could be used to refine next-generation probabilistic seismic hazard assessments.

Observations of how boundary conditions affect estimates of Poisson's ratio from simulated mode shapes

This research extends a method for direct estimation of Poisson's ratio from mode shapes of plates with hinged-hinged boundary conditions to include combinations of clamped and free boundary conditions. Using finite element simulations, we observe the effects of boundary conditions on the estimate of Poisson's ratio using the combination of Time-Average Scanning Digital Holography and Cornu's method. First, we introduce the abstraction of the span-to-width ratio to an effective antinode region. This abstraction enables us to extend the direct estimation technique to plates with various boundary conditions. Second, for long and thin enough plates, the effects of boundary conditions become negligible and Cornu's method is sufficient for direct estimation of the true value of Poisson's ratio from an out-of-plane bending mode shape. We note that for many situations, the necessary plate dimensions could be a limitation. Therefore, as a third concept, we discuss the behavior of the direct estimate of Poisson's ratio with respect to each type of boundary condition. Ultimately, this research initiates a path forward for a common processing technique for making a direct estimate of Poisson's ratio across different types of opposing boundary conditions for thin plates.

Buckling analysis of rectangular plates with rotationally restrained edges subjected to linearly varying in-plane loading

This study addresses a comprehensive procedure for the buckling behavior of rectangular plates with rotationally restrained edges. They are subjected to uniaxial in-plane load that varies linearly from compression to bending. The load is applied to opposite edges with variable boundary conditions, ranging from simply supported to clamped. The other edges can also be free, guided, or between them. For the first time, the generalized integral transform technique (GITT) is applied to the buckling equation of such a plate. The integral kernel perfectly satisfies the plate boundary conditions and its constituent terms are limited to the approximate range of ±1 which prevents the numerical instability. The transformed equation is a set of linear algebraic equations which establish an eigenvalue problem. The plate buckling coefficient, and corresponding mode shape (contours of the buckled plate, the number of half-waves in each direction, etc.) are presented according to variations of the edge relative stiffness as well as the plate aspect ratio, the loading shape, and Poisson's ratio. The latter parameter has a significant effect on the buckling behavior when at least one of the edges is free, guided, or between them. This portion is developed for auxetic materials (negative Poisson's ratios), and it was concluded that the minimum buckling load mostly occurs as the Poisson's ratio tends to zero.

Acoustic Characteristics of a Plate Silencer with a Flexible Back Cavity Under Arbitrary Boundary Conditions

The flexible back cavity (FBC) plate silencer is composed of an FBC and a flexible inner plate. Through the coupling of the sound field with the flexible inner and outer plates, the transmitted sound energy of the downstream is reduced, and it has a good broadband muffling effect at low frequencies. In order to obtain the transmission loss (TL) of the FBC plate silencer under arbitrary boundary conditions, this paper establishes the acoustic-vibration coupling model of the FBC plate silencer based on the energy principle. Translational restraints and rotational restraints are used to simulate the arbitrary boundary conditions of the flexible plate, and then the influence of the boundary conditions of the flexible plate on the TL is analyzed. The results show that the results of the proposed method are in good agreement with the finite element method (FEM) results. The structural boundary restraint has a significant influence on the acoustic characteristics of the system, and the rotational restraints suppress the muffling effect. By appropriately releasing the translational restraints, a better low-frequency broadband muffling effect can be achieved, with the minimum muffling frequency reduced by 44.8% and the muffling bandwidth broadened by 57.4%.

DETERMINATION AND ANALYSIS OF THE TEMPERATURE FIELD IN A THREE-LAYER ISOTROPIC PLATE WITH A GIVENINITIAL TEMPERATURE DISTRIBUTION

An approximate system of two-dimensional heat conduction equations for a multilayer isotropic plate is written down. Boundary conditions for a rectangular plate of finite dimensions are formulated. A general solution of the non-stationary heat conduction problem for this plate was found using integral Fourier transforms in spatial variables and Laplace transform in time.On the basis of the obtained general solutions, the solution of the thermal conductivity problem for a three-layer plate, which at the initial moment of time is heated by a temperature field linear in its thickness, which is uniformly distributed over the surface of the plate in a rectangular region, was analyzed.The numerical analysis of the temperature field was performed for a three-layer plate, the middle layer of which is made of metal, and the outer layers are made of ceramics.

An efficient Legendre-Galerkin approximation for the fourth-order equation with singular potential and SSP boundary condition

Abstract In this article, we develop an efficient Legendre-Galerkin approximation based on a reduced-dimension scheme for the fourth-order equation with singular potential and simply supported plate (SSP) boundary conditions in a circular domain. First, we deduce the equivalent reduced-dimension scheme and essential pole condition associated with the original problem, based on which a class of weighted Sobolev spaces are defined and a weak formulation and its discrete scheme are also established for each reduced one-dimensional problem. Second, the existence and uniqueness of the weak solution and the approximation solutions are given using the Lax-Milgram theorem. Then, we construct a class of projection operators, give their approximation properties, and then prove the error estimates of the approximation solutions. In addition, we construct a set of effective basis functions in approximate space using orthogonal property of Legendre polynomials and derive the equivalent matrix form of the discrete scheme. Finally, a large number of numerical examples are performed, and the numerical results illustrate the validity and high accuracy of our algorithm.

A fast Chebyshev spectral approach for vibroacoustic behavior analysis of heavy fluid-loaded baffled rectangular plates with general boundary conditions

A computationally efficient Chebyshev spectral approach is proposed to solve the vibroacoustic response of heavy fluid-loaded baffled rectangular plates. The governing equations for the displacements of motion in rectangular plates and the sound pressure in the Helmholtz integral are formulated using high-order, first-class Chebyshev polynomial expansions. This formulation is combined with Gauss-Chebyshev-Lobatto sampling. The quadruple integral encountered in solving the work done by the heavy fluid on the plate is reformulated into the configuration of a tensor product. The approach significantly reduces the computation time for solving the acoustic equations, bringing the vibration response of fluid-loaded plates closer to that of vacuum plates and limiting it to just a few seconds. The elastic boundary conditions of the rectangular plates are simulated using linear and rotational springs. Predictions of vibroacoustic behavior, including plate velocity, sound pressure, sound power, and radiation efficiency, are validated against literature results. The accuracy and efficiency of the Chebyshev spectral approach for the vibroacoustic coupling systems are demonstrated by the presence of exemplary agreements. Furthermore, this study investigates the effect of boundary conditions, geometric characteristics, and damping variables on the vibroacoustic behavior of rectangular plates.

Experimental Study on Multi Bubble Ice Breaking Under Layer Ice Boundary Conditions

Under certain conditions of bubble spacing and bubble to ice distance, the motion state and ice breaking effect of horizontal and vertical bubbles under ice plate boundary conditions were studied. Bubbles are generated through underwater discharge, and the generating device is placed horizontally or vertically below the ice plate, and the experimental phenomenon is observed through an ultra-high-speed camera. Firstly, the motion characteristics and ice breaking ability of two horizontal bubbles under an unperforated ice block were demonstrated. Then, the motion characteristics of two horizontal bubbles and two vertical bubbles under a porous ice block, the breaking effect of the ice block, and the water mound phenomenon on the free surface were observed. The experiment observed unique bubble behavior, including bubble fusion, bubble collapse, and oblique jet, as well as the influence of bubble-bubble and bubble-ice interactions on the morphology evolution and ice breaking effect of bubbles. The results indicate that the ice breaking effect of the interaction between bubbles and perforated ice plates is weaker than that of non-perforated ice plates, which may be more helpful for subsequent bubble ice breaking research.

Flywheel Vibration Isolation of Satellite Structure by Applying Structural Plates with Elastic Boundary Instead of Restrained Boundary

Flywheels play a critical role as core components in satellite attitude control systems. However, their high-speed rotation inevitably generates vibrations that have a detrimental impact on the in-orbit imaging capabilities of high-precision remote sensing payloads. This study focuses on the passive vibration isolation design of satellite flywheels. The flywheel-mounted structural plate and flywheel vibration isolation platform are considered as a whole system (termed a plate-isolator system). In this system, the structural plate is treated as an elastomer. By simplifying the plate-isolator system as a 2-degree-of-freedom vibration system, it becomes evident that obtaining an ideal vibration isolation effect through the optimization of the flywheel vibration isolation platform (FVIP) alone is difficult. In order to enhance the passive vibration isolation effect for satellite flywheels, this study introduces the concept of an elastic boundary applied to the flywheel-mounted structural plate, thus treating the elastic boundary as a design factor. Consequently, the plate-isolator system can be simplified as a 3-stage vibration isolation system. The optimization of the elastic boundary condition of the structural plate is performed using the kinetic model of the simplified 3-stage system. The vibration isolation effect of the plate-isolator system with an elastic boundary is further confirmed through finite element simulation. The calculation results demonstrate that, after establishing a reasonable elastic boundary for the satellite structural plate, the overall vibration/force transmission rate of the plate-isolator system becomes similar to that of a single-degree-of-freedom dynamic system. Finally, the proposed concept is validated through kinetic response analysis of a cube satellite. The results reveal that the vibration amplitude of the satellite’s top and side structural plates can be effectively lowered if the elastic boundary condition is set for the flywheel-mounted bottom structural plate.