Rectangle Plate Research Articles

Numerical investigation of simply supported periodic rectangular plates with acoustic black hole wedge

In this paper, we propose the periodic rectangle plate with one-dimensional acoustic black hole (ABH) wedge under the simply supported condition. The vibration performances have been investigated by the semi-analytic method based on the levy solution method combined with WKB approximation, which is also validated by finite element method (FEM) simulation. For the rectangle ABH wedge, we derive the flexural wave dispersive relationship in plate, which also revealed the cut-on frequency. It can also be found that with the increase of periodic number, the vibration of plate structure can be reduced not only in the high frequency range where traditional ABH effect takes effect, but in low and middle frequency range the periodic ABH wedge can also show its advantage. Meanwhile, the damping coupling performance between the periodic ABH wedge and attached damping layers has also been investigated to enhance the vibration reduction. This novel kind ABH structure shows its potential in engineering applications.

A novel narrowband MEMS filter with extensional mode resonators

This work proposes a novel electrostatic mechanically coupled narrowband filter based on width extensional mode (WEM) resonators. Rectangle plate WEM resonators have the potential for high quality factor (Q) and low motional resistance. The rectangle plate was slotted to reduce thermoelastic loss and optimize mode shape coefficient of WEMs. The Q values of coupled WEM resonators exceed 80,000, enabling a narrow bandwidth filter. A 3λ/4-length coupling beam filter (CBF) was demonstrated. The 3λ/4 coupling beam filter has a center frequency of 79.79 MHz and a bandwidth of 0.024 %. The CBF exhibits an impressive 26.39 dB stopband rejection and 6.97 dB insertion loss with 5.13 dB passband ripple. The MEMS filters presented in this work hold significant potential for applications in wireless communication systems.

Research on Vibration Energy Harvester Based on Two-Dimensional Acoustic Black Hole

The wave energy focus effect of an acoustic black hole (ABH) is used for broadband vibration energy harvesting and boosts the harvested power. A vibration energy harvester based on two-dimensional ABH is proposed in this study, which consists of a rectangle plate with 2-D ABH and PZT film attached. The structure of ABH was designed and analyzed based on numerical simulation. The optimal parameters of the ABH were obtained, such as the power index, truncation thickness, cross-sectional length, and round table diameter, which were 3, 0.4 mm, 40 mm, and 24 mm, respectively. The quadratic velocity of the plate surface with ABH is up to 22.33 times that of a flat plate, and PZT film adheres to the corresponding positions of the ABH structure and plate structure, respectively. In the same condition, the average output power of a PZT with an ABH structure is higher than that of a flat plate under the same excitation-vibration condition.

Time Period Analysis of Orthotropic Skew Plate with 2-D Circular Thickness and 1-D Circular Density

In the present study, the time period of vibration of an orthotropic parallelogram plate with 2 − D (two-dimensional) circular thickness under the effect of 2 − D parabolic temperature is investigated for the first time. The different edge conditions are C C C C , C C C F , C F C F , C S C F , and S F S F boundary conditions, where C, S, and F stands for clamped, simply supported, and free edges of the plate, respectively. The variation in density of plate material is considered to be 1 − D (one-dimensional) circular. The Rayleigh–Ritz technique is used to solve the differential equation and evaluate the time period for the first two modes of vibration. A convergence study of an orthotropic parallelogram, rectangle plate, and square plate for modes of frequency at various edge conditions is also carried out. The authors performed a comparative analysis of the time period and modes of frequency of orthotropic parallelogram, rectangle plate, and isotropic square plate with the available published results at various edge conditions. The main conclusion which we made from this study is that by choosing the above-mentioned plate parameters, we obtained fewer modes of frequency in comparison to other variations mentioned in the literature. Also, the study suggests that the variation in modes of frequency is less in comparison to other variations.

Thermal Vibration of Rectangle Plate with Two-Dimensional Circular Thickness Effect

Frequencies comprising two-dimensional circular thickness impacts are computed for the first time, for clamped rectangle plate under nonhomogeneity and temperature field. The study also comprises the two-dimensional temperature and one-dimensional density effect, on frequencies computation, utilizing the Rayleigh–Ritz technique. The objective of the study is to reduce the frequencies of the plate as well as to provide the effect of various plate parameters on frequencies. Numerical illustration and comparative study of the frequencies with other available results well authenticate the objective of the study. A comparison of frequency modes done for the clamped rectangle and square plate corresponding to tapering and aspect ratio and nonhomogeneity concludes that frequency obtained for the present study is very less in comparison with other studies done. A convergence study of the obtained results is also presented with the help of figures. The convergence study done concludes that rate of convergence in case of circular variation is faster than the other variations.

Time Period of Thermal-Induced Vibration of Skew Plate with Two-Dimensional Circular Thickness

In this study, two-dimensional circular thickness effects on time period of skew plate made with nonhomogeneous material properties are computed in variable temperature environment. Clamped C , simply supported S , and free-edge F conditions are the various combinations considered in this work. One-dimensional circular density and two-dimensional parabolic temperature variation on the plate are considered due to the nonhomogeneous nature of the material and variable temperature environment. Rayleigh–Ritz method is used to compute the time period for the first two modes of vibration. A convergence study of frequency modes of skew plate on various edge conditions has also been performed. The present work has been compared with the frequency modes of parallelogram and rectangle plate on various edge conditions. The objective of the study is to present a numerical data of time period as well as to show how one can control the frequencies of plate by taking an appropriate variation in plate parameters.

A diffusion Monte Carlo method for charge density on a conducting surface at non-constant potentials

Abstract We develop a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials. In the previous researches, last-passage Monte Carlo algorithms on conducting surfaces with a constant potential have been developed for charge density at a specific point or on a finite region and a hybrid BIE-WOS algorithm for charge density on a conducting surface at non-constant potentials. In the hybrid BIE-WOS algorithm, they used a deterministic method for the contribution from the lower non-constant potential surface. In this paper, we modify the hybrid BIE-WOS algorithm to a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials, where we can avoid the singularities on the non-constant potential surface very naturally. We demonstrate the last-passage Monte Carlo algorithm for charge densities on a circular disk and the four rectangle plates with a simple voltage distribution, and update the corner singularities on the unit square plate and cube.

The effect of layer orientation angle and its increasing on mechanical properties of laminated material: A numerical study

The mechanical properties of a laminated material due to different layer orientation angle and pattern of layers are simulated using the finite element method. The aim of this paper is to determine the effect of the different layer orientation angles and patterns on the mechanical properties of laminated material. Stainless steel laminated with epoxy carbon is used in this study. The model is a rectangle plate with 150 mm in length, 80 mm in width, and 4 mm in thickness. Linear static finite element analyses with 0,63 MPa normal force is applied to the three various models with different layer orientation angles and patterns. The results show that different layer orientation angles and numbers affect the mechanical properties of the material.

Experimental study of crack propagation and failure around a horseshoe tunnel during nearby blasting

To investigate the effects of nearby blasting on a horseshoe tunnel and to analyze dynamic response and crack growth with different loading directions, five laboratory experiments were performed using granite specimens of a rectangle plate containing a blast hole and horseshoe tunnel structure. HS photography and digital image correlation (DIC) methods were used to visualize the highly transient process of crack propagation in the surrounding rocks when the sidewall, spandrel, vault, corner, and bottom floor were selected as the front blasting faces. According to the experimental results, the shock wave attenuated to stress wave when the wave arrived at the front blasting face of the tunnel, and the radial fracturing played a significant role around the tunnel. The radial cracks originated from the borehole and merged with the cracks which from the tunnel. The central damage area between the borehole and the tunnel were similar for different loading directions. The initial stress wave became weak when it arrived at the tunnel back blasting face, the combined action of the reflected and diffracted stress waves played an important role in the crack growth. The side cracks were more easily generated in the orthogonal corner, and their growth was strongly influenced by the loading direction. Therefore, the reinforcement of the existing tunnel was valuable along the connection direction and corners.

Experimental Investigations on Crack Propagation Characteristics of Granite Rectangle Plate with a Crack (GRPC) under Different Blast Loading Rates

The experimental system of 3D digital image correlation (3D-DIC) is set up to eliminate a certain extent of out-of-plane motion for accurate measuring the full-field strain field during crack propagation, and the effect of blast loading rates of fracture behavior of granite rectangle plate with a crack (GRPC) is investigated. The experimental results indicated that the maximum values of the strain concentration zone do not fully represent the crack tip during the whole process of crack propagation. The axial strain threshold value tip (ASTVT) plotting with lines and coordinate contours corresponding with the actual crack at the shooting area can be used to describe the position of the crack. The axial strain 1.3% is more practical to obtain crack velocity and average crack velocity, and the average crack velocity decreases as the blast loading rates increase. Through observing the relationship between crack width and time, it can be found that there are three stages, and the crack width increases as the blast loading rates increase.

Synthesis of diepoxycyclohexylethyl tetramethyldisiloxane and its application to stereolithography 3D printing

Purpose The purpose of this study is to synthesize a new kind of a cationic-type UV-curing prepolymer diepoxycyclohexylethyl tetramethyldisiloxane, which is used to replace the current prepolymers’ common cycloaliphatic epoxy resins to prepare a novel 3D printing stereolithography material. Design/methodology/approach Diepoxycyclohexylethyl tetramethyldisiloxane was characterized and analyzed by FT-IR and 1HMR. Diepoxycyclohexylethyl tetramethyldisiloxane was compounded with a polycaprolactone polyol, some acrylates and photoinitiators to prepare a novel 3D printing stereolithography resin (3DPSLR11). Optical properties of 3DPSLR11 were investigated by HRPL-150A stereolithography apparatus and INITELLI-RAY400 UV-curing system. Tensile mechanical properties of printed 3DPSLR11 specimens were tested by WDW-50-type universal testing machine, and the glass transition temperature (Tg) was determined by DMA. Rectangle plates and double-cantilever parts were fabricated by using the stereolithography apparatus with 3DPSLR11 as the printing material, and the dimension shrinkage factors and the curl factors of the parts were investigated. Findings The experimental results showed that the critical exposure (Ec) of the 3D printing 3DPSLR11 was 11.6 mJ/cm2, its penetration depth (Dp) was 0.18 mm, the tensile strength of the cured 3DPSLR11 was 40.1 MPa, the tensile modulus was 1,741.4 MPa, the elongation at break was 15.3%, Tg was 113°C, the dimension shrinkage factor was less than 0.85% and the curl factor was less than 8.00%. Originality/value In this work, a novel 3D printing 3DPSLR11 was prepared with diepoxycyclohexylethyl tetramethyldisiloxane as a main prepolymer. The novel 3DPSLR11 possessed excellent photosensitivity, and its cured products had good mechanical and thermal properties. The accuracy and resolution of the fabricated parts were high with 3DPSLR11 for stereolithography in 3D printing, which showed that 3DPSLR11 has potential application value as 3D printing material.

Study on Transient Thermal Response for Functionally Graded Materials Based on Peridynamic Theory

The transient heat conduction formula of functionally graded materials (FGMs) is presented based on peridynamics (PD). The simplified micro-heat conductivity model for FGMs is proposed and the numerical discretization and the peridynamic numerical formation are also illustrated. A FORTRAN program is coded to implement calculations. The accuracy of the program is verified by comparing the FEM and analytical results with PD solution. The FGM rectangle plate composed by titanium alloy coating zirconium oxide is performed to calculate temperature fields. The effects of material gradient, porosity and temperature load on thermal response are studied. It is shown that the ceramic proportion of FGMs is increased with an increasing material shape parameter and the thermal shielding performance of FGMs is also improved. The effect of the porosity on thermal response is more and more significant with the increasing time step. The increasing temperature load only affects the temperature response of FGM ceramic area. The thickness of temperature distribution area is increased with the increasing of heat conduction time.

Measuring method of dynamic fracture toughness of mode I crack under blasting using a rectangle specimen with a crack and edge notches

In order to study fracture toughness of mode I crack under blast load, a new specimen of a rectangle plate with a crack and edge notches (RPCEN) was proposed in this study. The PMMA was selected to prepare the RPCEN specimens. The testing system consists of a dynamic strain amplifier, an oscilloscope, a constant source, strain gauges and crack propagation gauges. The strain gauges and crack propagation gauges (CPGs) were used to measure the blast load and crack propagation speed, respectively. The scanning electron microscope was applied in studying the property of fracture surface. The explicit dynamic software AUTODYN was applied in simulating crack dynamic propagation behavior. The JWL equation of state (EOS) was applied to the explosive detonation products, and a linear EOS was used to describe the relationship between pressure and density of PMMA. A modified principle stress failure criterion was employed to assess the material state. The experimental-numerical method was used to determine the dynamic initiation and propagation toughness of the PMMA. The dynamic stress intensity factors (DSIFs) were calculated by the finite element code ABAQUS. The experimental and numerical results show that: (1) The RPCEN specimen proposed in this paper has the function to minimize the reflected tensile stress waves; (2) During crack propagation the fracture surface roughness and the nucleation rate increase with crack propagation speed; (3) Crack propagation speed is not a constant, and propagation toughness is related to the crack propagation speed.

Preparation of a Novel Cationic Photosensitive Resin (3D-SLR01) for Stereolithography 3D Printing and Determination of Its Some Properties

A novel cationic photosensitive resin (3DSLR-01) for stereolithography 3D printing was prepared with 3,4-epoxycyclohexylmethyl-3',4'-epoxycyclohexane carboxylate (2021P), 1,4-cyclohexanedimethanol glycidyl ether (JX-026), diglycidyl 4,5-epoxycyclohexane-1,2-dicarboxylate (S-186), polycaprolactone polyol(Polyol-0305), novolac epoxy resin(F-51), bis(3-ethyl-3-oxetanylmethyl) ether (S-221) and a mixture of triarylsulfonium hexafluoroantimonate salts solution (UVI-6976). The properties of the photosensitive resin and its UV-cured films were investigated by some instruments and equipment. The experimental results show that the critical exposure (Ec) of the photosensitive resin is 16.3 mJ/cm2, the penetration depth (Dp) is 0.14 mm, and the optical property of the photosensitive resin is excellent. Rectangle plates were printed by using a stereolithography apparatus (HRPL-150A) with the photosensitive resin as the manufacturing material, and the shrinkage rates of the plates were less than 0.60%, which showed that the accuracy of the manufactured plates was very high.

Vibration of rectangle plate with variable density and Poisson’s ratio

The effect of variation in density and Poisson’s ratio is examined, on the vibration of rectangle plate with linear variable thickness. Bi parabolic temperature effect on the plate is also studied and vibrational modes of rectangular plate is calculated by using Rayleigh Ritz method. Authors also compared the present finding with the published results.

Mild Hydrothermal Crystallization of Heavy Rare-Earth Chromite RECrO3 (RE = Er, Tm, Yb, Lu) Perovskites and Magnetic Properties.

Crystallization of perovskite structure chromites (ACrO3) in aqueous conditions is difficult owing to the amphoteric nature of the Cr3+ in the alkaline-mediated reaction conditions. This is especially true for the small metal cations at the A-site with large distortion angle of CrO6 octahedral and small Goldschmidt tolerance factors. Here, we performed a progressive dehydration crystallization strategy to synthesize four RECrO3 with the smallest radii of rare earth elements (Er, Tm, Yb, Lu) in mild hydrothermal conditions. Profile refinement of the high-resolution powder X-ray diffraction results indicated slightly longer unit cell parameters of a and c in our samples with a higher distorted angle of CrO6 octahedral units along ⟨010⟩ direction. All of the samples show rounded rectangle plate morphology with uniform distribution of particle sizes. These four RECrO3 crystals can only form in a very narrow mineralization temperature range, i.e., 260-280 °C and 4.45-6.24 M of KOH. HRTEM results indicated that the normal crystallographic direction is ⟨001⟩, and the lattice of steps at the edge of elliptic rounded crystal is consistent with the bulk, which demonstrated single crystalline nature of the as-obtained crystals. Room-temperature Raman and FT-IR spectra reveal a continuous symmetry mode shift-dependent on the radii of A-site rare-earth cations. Temperature-dependent magnetization curves of RECrO3 show typical antiferromagnetism to paramagnetism transition with Néel temperature of 93, 90, 86, and 83 K for ErCrO3, TmCrO3, YbCrO3, and LuCrO3, respectively. Samples of YbCrO3 and LuCrO3 show clear magnetization reversal and exchange bias phenomena below their Néel points. This paper indicates that the coupling of magnetic exchange in perovskite structure oxides could be tailorable in mild hydrothermal condition, towards the exploration of new magnetic and other physical properties.

Free vibration analysis of porous plates with porosity distributions in the thickness and in-plane directions using isogeometric approach

The main purpose of this paper is to study the free vibration of porous square plate, circular plate, and rectangle plate with a central circular hole in the framework of isogeometric analysis (IGA). Generally, the porosity distributions of plates are assumed to happen in the thickness direction. However, the graded distributions of porosity may occur through the in-plane direction of plates. Therefore, porosity distributions along both the thickness direction and in-plane direction are considered in this study. The displacement fields are described by the first order shear deformation theory (FSDT) and the exact geometric models are formulated wholly by non-uniform rational B-spline (NURBS) basis functions, which bear high-order continuity inherently. To ensure the versatility of IGA-FSDT, several numerical examples for isotropic and porous plates with different boundary conditions and various types of porosity distributions are presented. Moreover, some innovative results are presented and discussed, which can be the benchmark data for other algorithm researches. The effects of porosity coefficient, boundary conditions and geometric parameters on the free vibration of porous plates are investigated comprehensively.

Natural frequency of skew FGM plates using finite element method

In the present work aims the free vibration analysis of functionally graded material (FGM) skew plates. Kinematics equations are based on the first order shear deformation theory and a four noded rectangular element is used to mesh the plate geometry. Properties of FGM (Stainless steel and Alumina)material constituents of the plate are considered to be as position and assumed to vary along the thickness direction according to a simple power law. Rectangle plate displacement components are renovated into skew plate geometry by suitable transformation rule. The effects of power law index and boundary condition on natural frequency parameters of FGM skew plates are reported based on FOSD. The related results are discussed briefly. Results are generated for vibration analysis of the FGM skew plate, which may be implemented in the future research involving similar kind of problems.

A refined two‐dimensional theory for thermal bending of functionally graded plates with thickness normal strains

AbstractA refined theory is presented for the thermal response of composite functionally graded plates under thermo‐mechanical loads. The theory includes shear deformation and normal strain effects by assuming through‐the‐thickness linear in‐plane displacements and parabolic transverse displacement. A mixed variational approach is used to introduce stresses satisfying the loading conditions on the plate surfaces without employing any shear correction factor used in other theories of the same order. A thermal bending problem is solved for metal/ceramic rectangle plates. Some numerical results are compared with numerical results of 3D exact solutions. The importance of the normal strain effect for such problems is studied.

Determination of the modal parameters on the thin flat structures

This paper presents the investigation of modal parameters using the different approaches. The object of the examination is the simple structure such as flat rectangle plate is. Before starting the measurement, there have been calculated natural frequencies of the plate by analytical approach. Subsequently, the experiment part is performed. The appropriate measuring apparatus has to be applicated for the experimental analysis. First, there are evaluated modal parameters of the specimen, the so-called “frequency sweep” is used as the input signal for excitation. After that, the experimental harmonic analysis is performed according the obtained eigen frequencies from the modal analysis. In the final stage, the data from simulations and experimental measurement are compared.