An Electromechanical Model for Clamped-Edge Bimorph Disk Type Piezoelectric Transformer Utilizing Kirchhoff Thin Plate Theory.

In this paper, an analytical solution for a clamped-edge bimorph disk-type piezoelectric transformer with Kirchhoff thin plate theory is proposed. The electromechanical equations for transient motions are first derived, and coupled expressions for mechanical response and voltage output are obtained. For the case of excitation around the first resonant frequency, the resulting equations are further simplified. There are analytical solutions for a mechanical response, voltage, current, and power outputs. According to the analytical model, the output voltage is affected by the inner radius of the input and output electrodes, the radius of the piezoelectric transformer (PT), and the thickness ratio between the lead zirconate titanate (PZT) layer and the substrate. When the inner radius of the input electrode approaches zero (electrode becomes circular shape), it achieves maximum output voltage at the first resonance frequency excitation. On the contrary, when the inner radius of the output electrode approaches zero, the output voltage reaches its minimum value. Voltage ratios remain constant as the disk radius changes, and the first resonance frequency is inversely proportional to the square of the disk radius. The voltage ratio is fixed even with the miniaturization of the PT.

Analytical Modeling and Experimental Validation of an Energy Harvesting System for the Smart Plate with an Integrated Piezo-Harvester.

The literature on piezoelectric energy harvesting (PEH) is strongly focused on structures, like cantilever beams with piezoceramic layers, due to the fact that they are easily modelled and implemented. As compared to the number of studies dealing with the aforementioned case, research on 2D structures with an attached piezoceramic patch harvester is very limited. Thus, an analytical modeling and experimental validations of a piezo harvester structurally integrated on a thin plate with SFSF (Simply supported-Free-Simply supported-Free) boundary conditions is presented in this paper. The distributed parameter electroelastic model of a harvester bonded to an aluminum plate with both piezo-patch actuators is developed on the basis of the Kirchhoff plate theory and the modal analysis for physical and modal coordinates. This allows to estimate the steady-state value output voltage for each odd mode in the frequency range of 10⁻300 Hz. Finally, the obtained results for the electroelastic analytical model is experimentally verified on a laboratory stand.

Finite elastic wrinkling deformations of incompressible fiber-reinforced plates.

A two-dimensional plate theory, valid for finite elastic deformations with small strains, is derived for incompressible, fiber-reinforced materials. Single-layer plates and two-layer laminates are considered. Numerical simulations illustrate the substantial effect that fiber reinforcement has on wrinkling patterns in the sheet.

The effects of molecular collisions between the mobile phase and the solute in gas-solid chromatography.

In chromatographic processes, molecular collisions between the mobile phase and the solute result in the transfer of kinetic energy. Based on these interactions, the relationship between the gauge pressure of the carrier gas at the column inlet and the partition frequency of the solute is derived; consequently, the relationship between the column temperature and partition frequency can be obtained. These relationships have been experimentally validated. The change in the peak shape described herein has been successfully explained using this relationship: the partition frequency was calculated from the theoretical plate number of a tailing peak. We propose a new mechanism for peak tailing using plate theory, which states that as the number of plates increases, the symmetry of the peak increases.

Application of a Modified First-Order Plate Theory to Structural Analysis of Sensitive Elements in a Pyroelectric Detector.

Pyroelectric materials, with piezoelectricity and pyroelectricity, have been widely used in infrared thermal detectors. In this paper, a modified first-order plate theory is extended to analyze a pyroelectric sensitive element structure. The displacement, temperature, and electric potential expand along the thickness direction. The governing equation of the pyroelectric plate is built up. The potential distributions with upper and lower electrodes are obtained under different supported boundary conditions. The corresponding numerical results of electric potential are consistent with those obtained by the three-dimensional finite element method. Meanwhile, the theoretical results of electric potential are close to that of experiments. The influence of supported boundary conditions, piezoelectric effect, and plate thickness are analyzed. Numerical results show that the piezoelectric effect reduces the electric potential. The thickness of the pyroelectric plate enhances the electric potential but reduces the response speed of the detector. It is anticipated that the pyroelectric plate theory can provide a theoretical approach for the structural design of pyroelectric sensitive elements.

Mathematical model of ion chronogram from in-tube solid-phase microextraction device coupled with mass spectrometry and optimization framework.

A mathematical description and experimental outputs exhibited that an ion chronogram from an in-tube solid-phase microextraction (SPME) device linked with mass spectrometry (in-tube-SPME-MS) generally appears as a right-skew unimodal signal with a heavy right tail. Analogous to liquid chromatography coupled with mass spectrometry (LC-MS), in-tube-SPME-MS can utilize the area under its produced ion chronogram for regression analysis and has been shown to be a potential approach for fast quantification of analyte. Different level of unimodity of signal in the ion chronogram could positively or negatively affect the choice of the area used for quantification and finally impact on analysis sensitivity and time efficiency of in-tube-SPME-MS. In the paper, we showed that different in-tube SPME design choices and elution experimental setups produce ion chronograms with controllable varying unimodal peak shape patterns. An improved mathematical model was built based on the plate theory of chromatography and the Van Deemter equation to quantitatively describe the elution process from in-tube-SPME device. A computer simulation was implemented to predict ion chronograms and the results were compared with experimental ion chronograms to show the effectiveness of the model. An optimization framework was further presented based on the model to identify optimal device designs (length and diameter of device) and experimental parameters (flow rate) to track targeted ion chronograms with "desired" peak shape patterns. Empirical elution experiments with the in-tube SPME devices adopting optimized geometric parameters and optimal experimental setups confirmed the consistency between the experimental ion chronograms and the numerical simulations to a certain level.

Flexural failure properties of fiber-reinforced hybrid laminated beam subject to three-point bending.

The present study investigates the flexural failure properties of a hybrid laminate beam subjected to three-point bending. A symmetrically laminated hybrid beam is constructed using high-strain and inexpensive glass fibre on the top layers and low-strain and expensive carbon fiber on the middle layers. Classical lamination plate theory is used to find the stress and strain distribution that occurs due to the bending moment on the compressive side. The theoretical failure limits of the laminated hybrid beam are analyzed considering the targeted span-to-depth ratios, volume fractions of the fibers and hybrid ratios using the Tsai-Wu failure criterion and Matlab codes. Using the graph of failure index versus hybrid ratios, the minimum thickness of carbon fiber needed for the delay of failure and cost efficiency of the laminated hybrid beam is identified by applying the linear interpolation method. The numerical results indicate that the failure index increases with the increasing loading span and decreases when the volume fraction of fiber increases. In particular, the placement of glass fiber on the top layer of the laminated hybrid beam might have contributed to obtaining higher strains and curvatures before the catastrophic failure properties of carbon fiber. The flexural stiffness of the laminates is found to increase when the hybrid ratio increases. Overall, it is noted that the theoretical analysis is one method that is less time-consuming and cost-effective than other alternative approaches, such as finite element methods and experimental tests to estimate the minimum thickness of high-stiffness and the expensive material needed to maintain the strength and stiffness of the hybrid composite structures over long periods.

Thickness-extensible Higher Order Plate Theory with Enforced C1 Continuity for the Analysis of PEEK Medical Implants.

Plate-like structures had been thoroughly studied in literature over years to reduce the computational space from 3D to 2D. Many of these theories suffer either from satisfying the free traction condition or thickness extensibility in addition to the consistency of transverse shear strain energy. This work presents a higher order shear deformation thickness-extensible plate theory (eHSDT) for the analysis of plates. The proposed eHSDT satisfies the condition of free traction as other theories do but it also satisfies the condition of consistency of transverse shear strain energy which is neglected by many theories in the area of plates and shells. The implementation of the proposed theory in displacement-based finite element procedure requires continuity of derivatives across elements. This necessary condition was achieved using the penalty enforcement method for derivative-based nodal degrees of freedom across the standard 9-nodes Lagrange element. The theory was tested for elastic bending deformation of Polyether-ether-ketone (PEEK) which is one of the basic materials for medical implants. The theory showed good accuracy compared to experimental data of the three-points bending test. The present eHSDT was also tested for different conditions with a wide range of aspects ratios (thin to thick plates) and different boundary conditions. The accuracy of the proposed eHSDT was verified against exact solutions for these conditions which showed the advantage over other approaches and commercial finite element packages.

Application of Hashin-Shtrikman bounds homogenization model for frequency analysis of imperfect FG bio-composite plates.

Despite abundant theoretical investigations on the dynamic behavior of functionally graded (FG) structures, the study on frequency analysis of FG bio-composite structures is limited. FG bio-composite materials due to their biocompatibility potentials and good material properties can be applied in biomedical applications, especially dental implants. In this investigation, a natural frequency response of the FG bio-composite plate is analyzed within the framework of the newly developed refined higher-order shear deformation plate theory. Additionally, the imperfection impact on frequency behavior is evaluated while three imperfection distribution patterns are taken into account. The constitutive materials of FG bio-composite plate are Hydroxyapatite and Titanium. The effective material properties of the structure are determined with the help of the upper Hashin-Shtrikman bounds homogenization model. In continuation, to solve the derived governing equations of imperfect FG bio-composite plate, Galerkin's analytical method is employed. Also, the precision of the used theory is validated, the obtained outcomes are compared and an acceptable matching is found. Later, the sensitivity of different considerable variables is comprehensively assessed and discussed.

Application of higher-order theories on the propagation of bulk waves in bio-composite plates lying on Kerr substrate.

Because of the critical usage of biomedical applications, their constitutive materials must possess specific properties to satisfy the environmental conditions. Consequently, the selection of the best materials is one of the most important subjects in the manufacturing industry. Bio-composites are outstanding alternatives to customary biomaterials in biomedical applications owing to their supreme material properties. On the other hand, mechanical analyses including static and dynamic analyses of bio-systems should be carried out to optimize the designed biomedical applications like medical implants. Thus, wave dispersion analysis of functionally graded (FG) bio-composite plate could serve for design goals of biomedical structures. In this investigation, the influence of various higher-order shear deformation theories of the plate on the dispersion of bulk waves in FG bio-composite plate lying on Kerr foundation has been explored for the first time. The constituent materials of FG structure are gold alloy as metal phase and hydroxyapatite as ceramic phase. In order to compute the effective properties of the studied structure, the upper Hashin-Shtrikman homogenization scheme has been implemented. Higher-order theories and Hamilton's principle have been applied to derive the governing equations and the obtained equations are analytically solved via a harmonic function. Eventually, the sensitivity of various important parameters has been surveyed and discussed comprehensively. The obtained outcomes have been indicated in detail.

Analytical Study of Stress Distributions around Screws in Flat Mandibular Bone under In-Plane Loading.

A known complication for mechanically loaded bone implants is the instability due to screw loosening, resulting in infection and the non-union of fractures. To investigate and eventually prevent such bone degradation, it is useful to know the stress state in the bone around the screw. Considering only in-plane loadings and simplifying the mandibular bone into an orthotropic laminated plate, the analysis was reduced to a two-dimensional pin-loaded plate problem. An analytic model, based on the complex stress analysis, was introduced to the bone biomechanics field to obtain the stress distributions around the screw hole in the bone. The dimensionless normalized stresses were found to be relatively insensitive to the locations of the screw hole over the mandible. Parametric analyses were carried out regarding the friction coefficient and load direction. It was found that the load direction had a negligible influence. On the contrary, the friction coefficient had a significant effect on the stress distributions. Whether the screw was well bonded or not thus played an important role. The proposed analytic model could potentially be used to study bone failure together with stress-based failure criteria.

An improved analytic model for designing the polymer-composite stepped-plate transducer using the modified Mindlin plate theory.

A stepped-plate transducer (SPT) uses an extensive radiating plate to produce highly-directional ultrasound beams. In this paper, we present an improved analytical model for designing the polymer-composite stepped-plate transducer (PCSPT). The polymer-composite features the lightweight and flexible properties, and there can be little change in the resonant frequency and mode shape when the steps are attached. With the outstanding merit, it is feasible to construct SPTs with polymer-composite steps without taking the steps into consideration. The modified Mindlin plate theory (MMPT) is applied to improve the accuracy in the equivalent circuit model (ECM) that is used to predict the high-frequency vibratory responses. Our analytical model can be used to design well-tuned SPTs to achieve the desired dynamic responses such as resonant frequencies, mode shape and bandwidth for various high-power ultrasonic applications. We use several numerical design examples to illustrate that the design of the transducer can be accomplished without analyzing the sophisticated stepped-plate's behavior. We also perform a series of experiments to verify that the PCSPT is capable of functioning as a high-power ultrasonic transducer.

Modeling the Thermoelastic Bending of Ferric Oxide (Fe2O3) Nanoparticles-Enhanced RC Slabs.

Nanoparticles, by virtue of their amorphous nature and high specific surface area, exhibit ideal pozzolanic activity which leads to the formation of additional C-S-H gel by reacting with calcium hydroxide, resulting in a denser matrix. The proportions of ferric oxide (Fe2O3), silicon dioxide (SiO2), and aluminum oxide (Al2O3) in the clay, which interact chemically with the calcium oxide (CaO) during the clinkering reactions, influence the final properties of the cement and, therefore, of the concrete. Through the phases of this article, a refined trigonometric shear deformation theory (RTSDT), taking into account transverse shear deformation effects, is presented for the thermoelastic bending analysis of concrete slabs reinforced with ferric oxide (Fe2O3) nanoparticles. Thermoelastic properties are generated using Eshelby's model in order to determine the equivalent Young's modulus and thermal expansion of the nano-reinforced concrete slab. For an extended use of this study, the concrete plate is subjected to various mechanical and thermal loads. The governing equations of equilibrium are obtained using the principle of virtual work and solved using Navier's technique for simply supported plates. Numerical results are presented considering the effect of different variations such as volume percent of Fe2O3 nanoparticles, mechanical loads, thermal loads, and geometrical parameters on the thermoelastic bending of the plate. According to the results, the transverse displacement of concrete slabs subjected to mechanical loading and containing 30% nano-Fe2O3 was almost 45% lower than that of a slab without reinforcement, while the transverse displacement under thermal loadings increased by 10%.

Buckling Analysis on Resin Base Laminated Plate Reinforced with Uniform and Functional Gradient Distribution of Carbon Fiber in Thermal Environment.

The present paper aims to investigate the buckling load of functionally graded carbon-fiber-reinforced polymer (FG-CFRP) composite laminated plates under in-plane loads in a thermal environment. The effective material properties of the CFRP composite are calculated by the Mori-Tanaka homogenization method. The theoretical formulations are based on classical laminate plate theory (CLPT) and the von Kármán equations for large deflections. The governing equations are derived based on the principle of virtual work and then solved through the Navier solution. Results are obtained for the critical buckling load and temperature effect of a simply supported plate subjected to in-plane loading. A detailed numerical study is conducted to provide important insights into the effects of the functionally graded carbon fiber (CF) distribution pattern and volume fraction, total number of layers, temperature, geometrical dimension and lamination angle on the buckling load of functionally carbon-fiber-reinforced composite plates. Finally, the validation is compared with the Reddy and finite element analyses, which show consistency with each other.

Investigation on the improvement of mechanical properties and surface quality of the polylactic acid (PLA) fused filament fabrication parts manufactured without and with vibrations dependent utilization.

Fused Filament Fabrication (FFF), is one of the most widely used additive manufacturing technologies today, which has been used for a variety of applications. Due to the layer-by-layer manufacturing process, FFF parts are inferior to those fabricated by traditional methods in terms of tensile properties, which is one of the most significant defects that hinder the development of this technique. In this study, a vibration was utilized during the FFF process by piezoelectric ceramics electric plates to improve the mechanical properties of the built parts and surface quality of PLA FFF parts. Subsequently, an investigation of the tensile and the surface quality of PLA FFF specimens built-in X and Z-direction fabricated individually without and with vibrations utilized has been done. Furthermore, a theoretical model has been established to predict the tensile strength and plasticity of FFF parts fabricated without and with vibrations utilized based on classical laminated plate theory, with the anisotropic and laminated characteristics taken into consideration. Young's modulus model has been established based on the laminated plate theory and flexural vibration theoretical approaches of a plate for the PLA FFF parts manufactured without and with vibrations utilized respectively. Compared with the previous models this model provides the tensile strength and plasticity of FFF parts both manufactured without and with vibrations utilized. The results indicate that the predicted tensile strength and plasticity of the PLA FFF parts manufactured with vibrations utilized have a good consistency with the experimental ones, meanwhile, vibration utilization can significantly improve the surface quality of the PLA FFF samples manufactured in the Z-direction, and the scanning electron microscopy (SEM) analysis confirmed that vibration utilization can improve the forming quality of FFF manufactured parts.

Wave Dispersion Behaviors of Multi-Scale CNT/Glass Fiber/Polymer Nanocomposite Laminated Plates.

In this paper, wave propagation in multi-scale hybrid glass fiber (GF)/carbon nanotube (CNT)/polymer nanocomposite plates is studied for the first time by means of refined higher-order plate theory. The hybrid nanocomposite consists of CNTs and glass fibers (GF) as reinforcing components distributed within a polymeric matrix. A hierarchical micromechanical approach is used to predict the effective mechanical properties of the hybrid nanocomposite, including the three-dimensional (3D) Mori-Tanaka method and the rule of mixture. Moreover, a refined-type higher-order shear deformation theory (HSDT) is implemented to take into account the influence of the shear deformation on the motion equations of the system. Then, the governing equations are achieved on the basis of the energy-based Hamilton's principle. Finally, the derived equations will be solved analytically for the purpose of extracting the natural frequency of the continuous system. A set of numerical examples are provided to cover the effects of various parameters on the wave dispersion characteristics of the plate. It can be declared that the hybrid nanocomposite system can achieve higher wave frequencies compared with other types of composite structures. Additionally, it is found that the selection of the lay-ups and length-to-diameter ratio plays a significant role in the determination of the sandwich plate's acoustic response.

Analysis of Size-Dependent Linear Static Bending, Buckling, and Free Vibration Based on a Modified Couple Stress Theory.

The purposes of this paper are to study bending, buckling, and vibration by considering micro-scale effects using the Kirchhoff thin-plate theory and to consider small deflections, neglecting higher-order nonlinear terms. The governing equations for the bending, buckling, and vibration of the system are obtained using the equilibrium method coupled with the Kirchhoff thin-plate theory and a modified couple stress theory (MCST). The concept of the equivalent bending stiffness (EBS) of micro-thin plates is proposed to describe the scale effect. The Navier method is used to obtain analytical solutions for the bending, buckling, and free vibration of thin plates under simply supported boundary conditions with scale effects. The numerical results are presented to investigate the influence of scale effects on deflection, critical buckling load, buckling topography, and thin-plate natural frequency. The results show that the scale effect increases the equivalent stiffness of the thin plate, which leads to a decrease in deflection, a larger critical buckling load, and an increase in natural frequency, but does not affect the buckling topography. The MSCT is invalid when the thickness is greater than 10 times the scale effect parameter, thus defining the scope of application of the scale effect. This research study may contribute to the design of micro-scale devices such as MEMSs/NEMSs.

Static Analysis of Skew Functionally Graded Plate Using Novel Shear Deformation Theory.

In this article, the static response of a functionally graded material (FGM) plate is studied via hybrid higher-order shear deformation theory which uses hyperbolic and polynomial shape functions and includes the effect of thickness stretching. The composition of the plate comprises metallic and ceramic phases. The ceramic volume fraction varies gradually along with the thickness following the power law. The mechanical properties of the FGM plate are determined by the rule of mixtures and the Mori-Tanaka homogenization scheme. The displacement fields are defined to satisfy the requirement of traction-free boundary conditions at the bottom and top surfaces of the plate surface removing the need for determination of shear correction factor. A C0 continuity FE model is developed for the present mathematical model. Nine-node isoparametric elements with eight nodal unknowns at each node are developed. The present model comparison with existing literature is completed and found to be coherent. Inhouse MATLAB code is developed for the present work. Sinusoidal and uniformly distributed loading is analyzed in the present work. The parametric study is undertaken to explore the effect of the side-to-thickness ratio, aspect ratio, thickness, and volume fraction index on stresses and transverse displacements.

Isogeometric Analysis of Graphene-Reinforced Functionally Gradient Piezoelectric Plates Resting on Winkler Elastic Foundations.

In this paper, the refined plate theory (RPT), Hamilton's principle, and isogeometric analysis (IGA) are applied to investigate the static bending, free vibration and buckling behaviors of functionally graded graphene-platelet-reinforced piezoelectric (FG-GRP) plates resting on a Winkler elastic foundation. The graphene platelets (GPLs) are distributed in polyvinylidene fluoride (PVDF) as a power function along the plate thickness direction to generate functionally gradient materials (FGMs). The modified Halpin-Tsai parallel model predicts the effective Young's modulus of each graphene-reinforced piezoelectric composite plate layer, and the rule of the mixture can be used to calculate the effective Poisson's ratio, mass density, and piezoelectric properties. Under different graphene distribution patterns and boundary conditions, the effects of a plate's geometric dimensions, GPLs' physical properties, GPLs' geometric properties and the elastic coefficient of the Winkler elastic foundation on deflections, frequencies and bucking loads of the FG-GRP plates are investigated in depth. The convergence and computational efficiency of the present IGA are confirmed versus other studies. Furthermore, the results illustrate that a small amount of GPL reinforcements can improve the FG-GRP plates' mechanical properties, i.e., GPLs can improve the system's vibration and stability characteristics. The more GPL reinforcements spread into the surface layers, the more effective it is at enhancing the system's stiffness.

Application of flexural and membrane stress analysis to distinguish tensile and compressive moduli of biologic materials.

Three-point bending is often used during the mechanical determination of tissue material properties. When taken to failure, the test samples often experience high deformations. The objective of this study was to present beam and plate theories as analytical tools for determining tensile and compressive elastic moduli during the transition from flexure to membrane stress states. Samples of cartilage, a highly flexible connective tissue having differing tensile and compressive moduli, were tested. Three-point bending tests were conducted on auricular (ear) and costal (rib) cartilage harvested from pigs. The influence of span length variation and Poisson's ratio assumptions were statistically assessed. Tensile elastic moduli of the ear (3.886 MPa) and rib (6.131 MPa) were derived from high-deformation bending tests. The functional assessment described here can be applied as a design input approach for tissue reconstruction and tissue engineering, considering both hard and soft tissue applications.