Circular Plate Research Articles

A behavioral nonlinear modeling implementation for MEMS capacitive microphones

We are highlighting the behavioral nonlinear system-level modeling approach for MEMS capacitive microphones. The combination of finite element modeling and large signal nonlinear circuit modeling provides a strong capability to predict electroacoustical performance for capacitive transductions. Circuit simulation tools such as Cadence Virtuoso have emerged as powerful aids in designing behavioral models in both linear and nonlinear regimes. Typical small signal lumped element models fail to capture the MEMS behavior which changes over pressure and electrical bias conditions. The models described herein capture diaphragm displacement and capacitance change over large pressure ranges for a simply supported circular plate. This can be coupled with the electrostatic force, due to the applied bias voltage, and converted back to pressure, thereby realizing a feedback loop in the circuit model. The nonlinear model capability is extended to predict capacitance-bias behavior and estimate pull-in of the MEMS device. The microphone sensitivity, signal-to-noise ratio, and harmonic distortions are accurately predicted using the nonlinear large signal model when compared to measured microphone data.

Comparison of the Effects of Cinnamic Acid and Silver Sulfadiazine on Deep Second-degree Burns in Rabbits

Background: Burns are wounds caused by thermal, chemical, electrical, or radiation injuries. They are complex wounds that are difficult to heal and are associated with thousands of deaths each year. Cinnamic acid (CA) is a natural organic compound found in plants, fruits, vegetables, and honey. CA possesses antimicrobial, anti-inflammatory, antioxidant, and wound healing properties. Objectives: The aim of this study was to compare the healing effects of CA with silver sulfadiazine (SSD), a standard topical agent for burn treatment, on deep second-degree burns. Methods: This experimental study compared the healing effects of CA and SSD on second-degree burns. Fifteen New Zealand white rabbits weighing 2 to 2.3 kg were divided into 5 equal groups. Deep second-degree burn wounds were created on the backs of the rabbits by contacting a heated circular metal plate. The first group was treated with SSD 1% cream, the second, third, and fourth groups were treated with prepared ointments containing 0.1%, 0.5%, and 1% w/w of CA in Eucerin, respectively. The fifth group was treated with Eucerin alone. Wound healing effects were assessed by measuring the rate of wound contraction and the amount of collagen in tissue specimens obtained from different groups. Additionally, histopathological studies were performed on tissue samples. Results: The results showed that CA was significantly more effective than SSD in burn wound healing. Cinnamic acid ointments significantly increased the rate of wound contraction (P < 0.05) and tissue collagen content (P < 0.001) compared to SSD and Eucerin. Conclusions: Our findings suggest that topical CA possesses burn wound healing properties and could be used as an effective topical agent for the treatment of burns.

Hydraulic characterization and start-up of a novel circulating flow bio-carriers

High-quality biofilm carriers are crucial for the formation of biofilm, but problems such as slow biofilm growth on the carrier surface have been troubling a large number of researchers. The addition of a carrier changes the flow state in the reactor, which in turn affects the microbial attachment and the quantity of microorganisms. Also, aerobic microorganisms need to use dissolved oxygen in the water to remove water pollutants. In this paper, a novel recirculating flow carrier with a hollow cylinder structure is proposed, with a certain number of hollow inverted circular plates placed at equal distances inside. In this paper, the hydraulic residence time, aeration volume, and the spacing of the inflow plates of the recirculating flow biofilm carrier, which are three important factors affecting the hydraulic characteristics of the reactor, are first investigated. At the same time, it was compared with the common combined carrier to find the optimal operating conditions for the hydraulic characteristics. Secondly, a reactor start-up study was carried out to confirm that the new recirculating flow biofilm carrier could accelerate the biofilm growth by changing the hydraulic characteristics. The results showed that under the same conditions, the hydraulic properties of the reactor were better with the addition of the recirculating flow carrier, with an effective volume ratio of 98% and a significant reduction in short flows and dead zones. The stabilized removal of COD, NH3-N, and TN in the reactor with the addition of the recirculating flow carrier reached about 94%, 99%, and 91% respectively, at the beginning of the 15th day, which effectively proved the feasibility of the recirculating flow carrier.

Exploration of Resonant Modes for Circular and Polygonal Chladni Plates.

In general, sound waves propagate radially outwards from a point source. These waves will continue in the same direction, decreasing in intensity, unless a boundary condition is met. To arrive at a universal understanding of the relation between frequency and wave propagation within spatial boundaries, we explore the maximum entropy states that are realized as resonant modes. For both circular and polygonal Chladni plates, a model is presented that successfully recreates the nodal line patterns to a first approximation. We discuss the benefits of such a model and the future work necessary to develop the model to its full predictive ability.

Avalanche scaling law for heterogeneous interfacial fracture

A new approach is proposed to study the statistical law of avalanches due to the fracture of a heterogeneous interface. Firstly, a discrete interface is considered as a bundle of fibers clamped with two elastic circular plates, fiber strength being either a random variable or a stochastic field. Based on the theory of solid mechanics, equations governing the dynamic fracture process of fibers under tension are exactly derived and solved. The statistical law of fracture avalanches is accurately obtained. By tuning parameters, the model covers the whole scheme of stress-transfer mechanism due to fiber breaking from local load sharing to equal load sharing. Results show that the distribution of avalanche size of interfacial fracture follows a power-law relation, with the power exponent in the range [1.5,2.5], depending on both disorders of interface and stiffness of plates. Particularly, the exponent monotonically increases with plate stiffness to the value 2.5, a universal constant obtained by Hemmer and Hansen (1992). Then, the fracture of a laminated interface is analyzed. By discretizing the interface to a set of prismatic elements, the problem reduces to that of a discrete interface. Similar statistical behaviors are also observed. Furthermore, the temporal variation of avalanche scaling law is investigated. It is shown that in the vicinity of collapse point, the exponent of each time window is smaller than the exponent evaluated with the whole time series of event, probably a precursor for imminent catastrophic failure of interface.

An efficient shear and bending‐locking‐free quadrilateral plate element using a modified Hellinger‐Reissner functional and the Bergan free formulation

AbstractThis paper presents a general variational principle as theoretical support for creating a simple and efficient quadrilateral plate finite element called BKWA, having only a single displacement and two rotations at corner nodes according to the Reissner‐Mindlin plate theory. The functional is a modified Hellinger‐Reissner in terms of the kinematic variables and independent transverse shear strains. Hence, we consider quadratic rotations, as in DKQ, and linear independent shear strains with constant tangential components on sides, as in MITC4. The quadratic rotation contributions and the mixed shear strain components are wiped out by static condensation. To adequately satisfy the constant curvature patch tests, we also consider the orthogonality conditions between the linear and quadratic bending modes, as in the Bergan free formulation, to avoid ‘spurious bending energy’ for thick plates (also called bending locking). The paper contains comprehensive patch tests and convergence tests with regular and irregular meshes (displacements, internal forces, and strain energy) of circular and square plates. The element is compared with other existing elements (MITC4, DKMQ). It is concluded that BKWA is an efficient element regarding several criteria.

Thermal hydraulic performance of a tubular heat exchanger with in‐line perforated baffle with shutter type saw tooth turbulator

AbstractThis experimental investigation aimed to analyze the impact of a unique design of swirl generator airflow on the performance of a tubular heat exchanger operating with axial flow. To conduct the experiment, we utilized a custom‐built apparatus containing eight sawtooth air deflectors with differing space height ratios (e/h). These deflectors were oriented in a uniform manner (shutter type) and positioned at various inclination angles. Circular baffle plates, housing these deflectors, were equidistantly spaced at different pitch ratios. The arrangement of tubes within the heat exchanger remained constant throughout the study, while the Reynolds number ranged from 16,000 to 30,000. In addition, a consistent heat flux condition was maintained on the surface of the tubes. The research outcomes indicated that incorporating a deflector baffle plate with an inclination angle of 30°, an e/h ratio of 0.4, and a pitch ratio of 1.2 led to an average increase of 1.36 in the thermal enhancement factor when compared to a heat exchanger lacking a baffle plate, tested under similar conditions.

Analysis of vibration and noise reduction performance of 3D flower-shaped resonance structure with low-frequency bandgap

In this paper, two single-phase acoustic metamaterials that can produce localized resonance effects are proposed. Dispersion curves and vibrational modes of each structure are plotted using finite element software, and the bandgap properties and bandgap opening mechanism of these structures are explored by comparing the energy band structures and vibrational forms. Then the topological optimization of the flower-shaped structure was performed to obtain two new structures with bandgaps having lower onset frequencies. Finally, the accuracy of the frequency range corresponding to the bandgap is verified by transmission curves and stress cloud diagrams, and the vibration attenuation ability of several structures is analyzed. The results show that each new structure has excellent bandgap properties and vibration attenuation performance due to the local resonance effect, and the topology optimization method of adding spheres to the circular plate has a very good improvement of bandgap properties at low frequencies. This paper provides a means for structure optimization of single-phase material phononic crystals, a method for analyzing the vibration and noise reduction properties of the structures, and several three-dimensional phononic crystals with potential for practical applications.

Effect of the heave plate's diameter on the transitional motions of a straked marine circular cylinder under different marine conditions

This numerical study investigated the influence of the heave plate's diameter on the amplitude of the transitional motions of a marine circular cylinder (MCC) with a low aspect ratio under the marine current and regular waves. Due to the experimental model of the straked MCC, different diameters of the circular heave plate were chosen to be installed at the keel of the 3-straked MCC. In this numerical study, the diameter of the heave plate varied from 1.2 to 1.6 DMCC, while other parameters, such as reduced velocity (VR), Reynolds (Re) number, and Froude number, were kept constant. In this study, the transitional motions, including surge, sway, and heave, were analyzed. The results showed that increasing the heave plate's diameter decreased the amplitude of the transitional motions in both marine current and regular waves. Also, the finding revealed that the heave plate not only reduced the amplitude of the heave motion but also decreased the amplitude of surge and sway motions. Moreover, the outcomes indicated that the heave plate's diameter increased by approximately 20%–40% more than the MCC's diameter. This caused the smaller amplitude of the transitional motions under both marine currents and regular waves.

Demonstration of nonlinear tuning curve vibration response using a homemade analog sweep spectrum analyzer

A super-heterodyne sweep spectrum analyzer has been designed (using analog circuitry), built and tested to cover the 5 to 1000 Hz range. The analyzer employs a linear ramp voltage versus time, driving a voltage-controlled oscillator VCO that generates a sweep from 32.768 kHz to 33.768 kHz in 70 s. An analog AD734 multiplies the VCO signal by a sinusoidal signal (generated by a watch crystal 32.768 kHz oscillator). The “mixer” signal is low-pass filtered and amplified to generate a 5-1000 Hz swept tone using a 2-in. speaker. The accelerometer (mounted on a thin circular clamped acrylic plate) vibration response involves multiplying this signal by the VCO, then filtering this “mixer” signal using a 4-stage watch crystal ladder filter with a 1 Hz bandwidth. This signal is squared and low-pass filtered to generate the time (converted to frequency) vs. mean-squared voltage response on an oscilloscope. In the demonstration, 300 g of 6 mm diameter glass beads are supported by the 11.4 cm diam, 3.2 mm thick plate and upper rigid cylindrical wall column. The nonlinear tuning curve vibration response is recorded for various incremental drive amplitudes to demonstrate that the tuning curve resonant frequency significantly decreases with increasing drive amplitude.

AXISYMMETRIC DYNAMIC BEHAVIOUR OF THIN OBLATE SHELLS

This paper presents a theoretical investigation of the axisymmetric free vibrations of an isotropic thin oblate spheroid shell. The analysis depends on the Rayliegh – Ritz's method. The non – shallow shell theory is used for the analysis. The analysis based on considering the oblate spheroid as a continuous system constructed from two spherical shell elements matched at the continuous boundaries.Throughout the results, it is shown that when the eccentricity reaches zero, an exact thin sphere solution is emerged and when the eccentricity equals one an exact thin circular plate solution is emerged. Therefore, the eccentricity of an oblate shell at medium value lies between these two values.It was found that the Rayleigh – Ritz's method is suitable for all eccentricities, while the literature showed that the Rayleigh's method is suitable for eccentricities less than 0.6.

Incompatible Deformations in Hyperelastic Plates

The design of thin-walled structures is commonly based on the solutions of linear boundary-value problems, formulated within well-developed theories for elastic plates and shells. However, in modern appliances, especially in MEMS design, it is necessary to take into account non-linear mechanical effects that become decisive for flexible elements. Among the substantial non-linear effects that significantly change the deformation properties of thin plates are the effects of residual stresses caused by the incompatibility of deformations, which inevitably arise during the manufacture of ultrathin elements. The development of new methods of mathematical modeling of residual stresses and incompatible finite deformations in plates is the subject of this paper. To this end, the local unloading hypothesis is used. This makes it possible to define smooth fields of local deformations (inverse implant field) for the mathematical formalization of incompatibility. The main outcomes are field equations, natural boundary conditions and conservation laws, derived from the least action principle and variational symmetries taking account of the implant field. The derivations are carried out in the framework of elasticity theory for simple materials and, in addition, within Cosserat’s theory of a two-dimensional continuum. As illustrative examples, the distributions of incompatible deformations in a circular plate are considered.

Active control of thermally induced vibrations of temperature-dependent FGM circular plate with piezoelectric sensor/actuator layers

This study investigates the novel application of active control methods in mitigating thermally induced vibrations of functionally graded material (FGM) circular plates subjected to thermal shock. The top surface of the FGM circular plate is exposed to rapid surface heating, resulting in thermally induced vibrations. To counteract these deflections, two piezoelectric layers, one functioning as a sensor and the other as an actuator, are strategically integrated into the plate opposite sides. This layered configuration effectively distances the direct rapid surface heating from piezoelectric layers. All thermos-electro-mechanical properties of the used materials are considered temperature-dependent. The research employs the Generalized differential quadrature element (GDQE) method and the Crank-Nicolson time marching procedure to solve the nonlinear Fourier-type heat conduction equations for the layered structure. After obtaining the transient temperature profile, the study calculates thermal moments, forces, and pyroelectric terms. These thermally induced effects are then integrated into the motion and electrostatic equations, which inherently exhibit nonlinearity due to the von Kármán large deformations theory. The plate displacements are approximated using the first-order shear deformation theory (FSDT) along the plate thickness, while a quadrature distribution is considered for approximating the electric potential within the piezoelectric layers. The highly coupled electro-mechanical equations are solved using the GDQ method and the Newmark approach, with the Newton-Raphson iterative scheme utilized to address nonlinearity. A significant contribution of this research lies in the exploration of three distinct active control strategies: proportional control, derivative control, and proportional-derivative control. The study thoroughly analyzes the impact of each control type on the plate response, considering various boundary conditions.

Mechanical behavior of nanocircular plates under coupled surface and nonlocal effects by using molecular dynamics simulations

The equations of control for a circular thin plate under simple support are obtained by coupling the surface effect and non-local effect using the equilibrium method. Molecular dynamics simulations were used to calculate the residual surface strain energies at different crystal orientations. Different crystal orientations of the same material would affect its surface energy and thus result in different mechanical behaviors. The effects of residual surface strain energy and non-local parameters on the mechanical behavior of circular thin plates were analyzed. The analysis reveals that the surface effect and non-local effect on the deflection of the nanoplates are significant. The surface effect parameter of tensile stress increases the deflection, while the opposite is true for the surface effect parameter of compressive stress, and the non-local parameter decreases the deflection. The influence of surface effect and non-local effect is significant for smaller thicknesses and weakens for larger thicknesses.

Bending and free vibration analysis of FG circular plates using a five unknown high order shear deformation theory

In this study, the bending and free vibrations of functionally graded material (FGM) circular plates are investigated using a new quadrilateral finite element based on a five-unknown high-order shear deformation theory. The proposed model accounts for a quadratic distribution of the transverse shear stress through the plate thickness and zero transverse shear stress at the top and bottom surfaces of the plate. The properties of the plate are changed through its thickness according to a power law in which the index varies from 0 value for a fully ceramic plate to infinity for a fully metallic plate. The concept of the physical neutral plane is introduced to avoid membrane-bending coupling. The total potential energy principle and the kinetic energy are used to derive the elementary rigidity and mass matrices. The performance and the convergence of the developed element are demonstrated through examples from the literature. Furthermore, the effect of various parameters, such as the power law index and the radius-to-thickness ratio, on the plate behavior is also considered.

Modeling and solving for vibration and buckling of circular functionally graded dielectric plates reinforced by graphene platelets considering complex conditions

The vibration and bucking behaviors of circular functionally graded (FG) dielectric plates reinforced by graphene platelets (GPL) under external electric fields are studied at the presence of many complex factors such as dielectric effect, pre-stress, gradient slope, imperfect bonding between GPL and matrix material, interface electron tunneling and Maxwell–Wagner-Sillars (MWS) polarization. Based on the effective medium theory and linear rule of mixtures, material properties of the GPL reinforced composites (GPLRC) are calculated. Dynamic differential equations of the circular FG-GPLRC dielectric plates are numerically solved by the differential quadrature method, and natural frequencies and critical loads are obtained. Trans-scale analyses for the influences of the volume fraction, geometric size, gradient distributed pattern and gradient slope on the percolation threshold, permittivity and the vibration or buckling characteristics are provided. Furthermore, variations of the natural frequencies and critical loads with electric field parameters, the pre-stress and thickness of the interphase layer are also discussed. Results show that the natural frequencies and critical loads of the plates can be changed artificially and effectively by adjusting the external electric field, pre-stress and the parameters of GPL. The larger the diameter to thickness ratio of GPL, the bigger the equivalent permittivity and the smaller the percolation threshold. When the volume fractions of GPL are less than the threshold, the mechanical properties dominate the vibration and buckling. However, when the volume fractions are bigger than the threshold, the electrical properties have significant influences. Therefore, higher macro mechanical properties can be obtained by changing the microstructure of the materials.

Analytical Solution of Ice–Rock-Model Stress Field and Stress Intensity Factors in Inhomogeneous Media

The stress distribution and fracture parameter calibration of ice–rock models are important aspects of studying rock properties at high altitudes and latitudes. However, progress in ice–rock modeling has been slow and singular, and it is limited due to the discrete nature of rocks and the applicability of fracture mechanics. In this study, a circular inhomogeneous ice–rock model is proposed for the first time, and a method is provided for calculating the stress field of the model under biaxial loading. A method for calculating the single-crack stress intensity factor of the model subjected to biaxial compressive loading is also provided. The novelty of this work is that the inhomogeneous ice–rock model is treated as a superposition of two models, namely, a circular pore plate and circular ice, according to the superposition principle. The key is that the stress field distribution law of the ice–rock model is obtained based on the basis of the displacement continuity of the ice–rock interface. The analytical and approximate solutions of the stress intensity factor of a single crack were also obtained by considering the normal phase effect of the crack surface and combining the stress distribution law of the ice–rock model. Comparison with the CAE method was made to verify the correctness of the stress field and stress intensity factor calculation methods. The evolution laws of lateral pressure coefficients, the elastic modulus ratio of ice and rock on the stress field, and the stress intensity factor were analyzed. The effects of lateral pressure coefficients, elastic modulus ratios, and crack distributions on the failure modes were investigated using the extended finite element method (XFEM). This study can provide a theoretical basis for the evaluation of mechanical properties and prediction of the failure modes of frozen rock bodies.

Water entry of an elastic conical shell

The axisymmetric problem of a conical shell impact onto an inviscid and incompressible liquid of infinite depth is studied. The shell is thin, and its deadrise angle is small. The problem is inertia dominated. Gravity, surface tension and viscous effects are not taken into account. The hydrodynamic loads acting on the shell and the shell displacements are determined at the same time. The model by Scolan (J. Sound Vib., vol. 277, issue 1–2, 2004, pp. 163–203) is used to find the flow and hydrodynamic pressure caused by the shell impact. This model is based on the Wagner theory of water impact, which was generalised to axisymmetric problems of hydroelastic slamming. Dry and wet modes of the conical shell, as well as the corresponding frequencies, are calculated. It is shown that a conical shell can be approximated by a circular plate only for a very small deadrise angle. Deflections and strains in the conical shell during the impact stage, when the wetted part of the shell increases at high rate, as well as the hydrodynamic loads, are determined and analysed.

Investigation of the separation of conductive and insulating objects on a laboratory made electrostatic separator

Electrostatic separators are widely used to separate conductive and insulating objects up to some millimetres in size. Modelling of such equipment has been presented in several studies; laboratory and numerical models have been analysed. However, there are such situations, where larger samples of the order of centimetres have to be separated, as milling them into smaller size particles is not allowed or feasible. It was found that electrostatic separation can be used even in such cases but in a different arrangement than in the “traditional” constructions.This paper is a continuation of a previous study, in which the separation of a constructed laboratory separator was examined. The model was built in a circular plate arrangement with high voltage needle electrodes above the edge of cylinder’s mantle, where the discharges are generated. The slope of the circular plate is steadily decreasing, so the samples on the edge of the plate produce an increasing angle of inclination along the circumference. Charged samples stick to the plate, uncharged ones fall off. Some key parameters as rotation speed, electrode distance, voltage level and position of ionizer electrodes were varied.

Jetting bubbles observed by x-ray holography at a free-electron laser: internal structure and the effect of non-axisymmetric boundary conditions

In this work, we study the jetting dynamics of individual cavitation bubbles using x-ray holographic imaging and high-speed optical shadowgraphy. The bubbles are induced by a focused infrared laser pulse in water near the surface of a flat, circular glass plate, and later probed with ultrashort x-ray pulses produced by an x-ray free-electron laser (XFEL). The holographic imaging can reveal essential information of the bubble interior that would otherwise not be accessible in the optical regime due to obscuration or diffraction. The influence of asymmetric boundary conditions on the jet’s characteristics is analysed for cases where the axial symmetry is perturbed and curved liquid filaments can form inside the cavity. The x-ray images demonstrate that when oblique jets impact the rigid boundary, they produce a non-axisymmetric splash which grows from a moving stagnation point. Additionally, the images reveal the formation of complex gas/liquid structures inside the jetting bubbles that are invisible to standard optical microscopy. The experimental results are analysed with the assistance of full three-dimensional numerical simulations of the Navier–Stokes equations in their compressible formulation, which allow a deeper understanding of the distinctive features observed in the x-ray holographic images. In particular, the effects of varying the dimensionless stand-off distances measured from the initial bubble location to the surface of the solid plate and also to its nearest edge are addressed using both experiments and simulations. A relation between the jet tilting angle and the dimensionless bubble position asymmetry is derived. The present study provides new insights into bubble jetting and demonstrates the potential of x-ray holography for future investigations in this field.