Trapezoidal Beam Research Articles

Analysis of Output Performance of a Novel Symmetrical T-Shaped Trapezoidal Micro Piezoelectric Energy Harvester Using a PZT-5H.

In recent years, low-power wireless sensors with high flexibility, portability and computing capability have been extensively applied in areas such as military, medicine and mechanical equipment condition monitoring. In this paper, a novel symmetrical T-shaped trapezoidal micro piezoelectric energy harvester (STTM-PEH) is proposed to supply energy for wireless sensors monitoring the vibrations of mechanical equipment. Firstly, the finite element model (FEM) of the STTM-PEH is established. Secondly, the modal analysis of the T-shaped trapezoidal piezoelectric cantilever beam is carried out by finite element software and its vibration modes are obtained. Additionally, the structural characteristics of the STTM-PEH and the composition of piezoelectric patches are described. Furthermore, the effects of resistance, acceleration coefficient, substrate materials and structural parameters of the output performance of the STTM-PEH are researched. The results indicate that the output power of the STTM-PEH rises first and then falls with a change in resistance, while the output voltage does not increase as resistance increases to a certain extent. Meanwhile, selecting copper as the piezoelectric material of the T-shaped trapezoidal piezoelectric cantilever beam can generate a higher energy output. Finally, how the structural parameters, including piezoelectric patch thickness, substrate thickness and cantilever head length, affect the output performance of the STTM-PEH is studied, which illustrates that the load range of the STTM-PEH can be appropriately broadened by adjusting the length of the cantilever beam head. This research is valuable for designing a novel high performance piezoelectric energy harvester.

Comparative Study on Complex Modulus and Dynamic Modulus of High-Modulus Asphalt Mixture

In the French high-modulus asphalt mixture design system, the complex modulus of the mixture under the conditions of 15 °C and 10 Hz is taken as the design index. However, in China, the dynamic modulus under the conditions of 15 °C, 10 Hz, 20 °C, 10 Hz and 45 °C, 10 Hz was taken as the stiffness modulus index of high-modulus asphalt mixture. The difference in modulus values between the two systems caused the pavement structure layer to be thicker and the construction cost to be higher in China. In order to find out the appropriate modulus value of high-modulus asphalt mixture suitable for China’s modulus parameter conditions to better carry out the reasonable design and evaluation of high-modulus asphalt mixture in China, the modulus of four types of high-modulus asphalt mixtures under the two systems through the two-point bending complex modulus test of the CRT-2PT trapezoidal beam and the SPT uniaxial compression dynamic modulus test were analyzed in this paper. Under the premise of meeting the stiffness modulus index of the French high-modulus asphalt mixture, the relationship conversion models between the dynamic modulus and complex modulus of high-modulus asphalt mixture under different temperatures were established. According to the conversion models, the design evaluation value range of dynamic modulus suitable for China’s condition was recommended. It is recommended that the dynamic modulus of China’s high-modulus asphalt mixture at 15 °C and 10 Hz is not less than 16,000 MPa, the dynamic modulus at 20 °C and 10 Hz is not less than 14,000 MPa, and the dynamic modulus at 45 °C and 10 Hz is not less than 2500 MPa. Five kinds of high-modulus asphalt mixtures used in actual road engineering were tested to verify the reliability of the recommended dynamic modulus values based on the modulus conversion model, and the results are consistent with the recommended value range of the model.

A rotational piezoelectric energy harvester based on trapezoid beam: Simulation and experiment

Rotational piezoelectric energy harvesters which can directly convert mechanical energy into electrical energy are considered as one of the most attractive harvesters for self-powered rotational wireless monitoring systems. In this paper, a trapezoid piezoelectric cantilever beam is proposed to improve the output of rotational piezoelectric energy harvester. Finite element simulation results indicate that the trapezoid beam harvester can bear higher stress than the rectangle beam harvester near the clamping end and show excellent electrical output properties. The experimental results are consistent with the simulation analysis results, and verify that the rotational piezoelectric energy harvesters are endowed with the characters of up-conversion frequency and ring-down pattern. Experimentally, a prototype trapezoid beam harvester has been fabricated to harvest wind energy, which can generate an average output power density of 0.64 mW/cm2 at the matching impedance of 50 kΩ. Our work has demonstrated that the proposed trapezoid beam harvester is a good potential generator for harvesting flow energies and monitoring conditions of rotating machinery.

Theoretical and Experimental Studies on MEMS Variable Cross-Section Cantilever Beam Based Piezoelectric Vibration Energy Harvester.

The piezoelectric vibration energy harvester (PVEH) based on the variable cross-section cantilever beam (VCSCB) structure has the advantages of uniform axial strain distribution and high output power density, so it has become a research hotspot of the PVEH. However, its electromechanical model needs to be further studied. In this paper, the bidirectional coupled distributed parameter electromechanical model of the MEMS VCSCB based PVEH is constructed, analytically solved, and verified, which laid an important theoretical foundation for structural design and optimization, performance improvement, and output prediction of the PVEH. Based on the constructed model, the output performances of five kinds of VCSCB based PVEHs with different cross-sectional shapes were compared and analyzed. The results show that the PVEH with the concave quadratic beam shape has the best output due to the uniform surface stress distribution. Additionally, the influence of the main structural parameters of the MEMS trapezoidal cantilever beam (TCB) based PVEH on the output performance of the device is theoretically analyzed. Finally, a prototype of the Aluminum Nitride (AlN) TCB based PVEH is designed and developed. The peak open-circuit voltage and normalized power density of the device can reach 5.64 V and 742 μW/cm3/g2, which is in good agreement with the theoretical model value. The prototype has wide application prospects in the power supply of the wireless sensor network node such as the structural health monitoring system and the Internet of Things.

Horizontally Assembled Trapezoidal Piezoelectric Cantilevers Driven by Magnetic Coupling for Rotational Energy Harvester Applications

Horizontally assembled trapezoidal piezoelectric cantilevers driven by magnetic coupling were fabricated for rotational energy harvester applications. A dodecagonal rigid frame with an attached array of six trapezoidal cantilevers served as a stator for electrical power generation. A rotor disk with six permanent magnets (PMs) interacted magnetically with the counterpart cantilever’s tip-mass PMs of the stator by rotational motion. Each trapezoidal piezoelectric cantilever beam was designed to operate in a transverse mode that utilizes a planar Ag/Pd electrode printed onto lead zirconate titanate (PZT) piezoelectric thick film. The optimized distance between a pair of PMs of the rotor and the stator was evaluated as approximately 10 mm along the same vertical direction to make the piezoelectric cantilever beam most deflectable without the occurrence of cracks. The theoretically calculated resistance torque was maximized at 46 mN·m for the optimized trapezoidal piezoelectric cantilever. The proposed energy harvester was also demonstrated for wind energy harvester applications. Its harvested output power reached a maximum of approximately 22 mW at a wind speed of 10 m/s under a resistive load of 30 kΩ. The output performance of the proposed energy harvester makes it possible to power numerous low-power applications such as smart sensor systems.

A Rotational Piezoelectric Energy Harvester Based on Trapezoid Beam: Simulation and Experiment

Rotational piezoelectric energy harvesters (RPEHs) which can directly convert mechanical energy into electric energy are considered as one of the most attractive harvesters for self-powered rotational wireless monitoring systems. In this paper, a trapezoid piezoelectric cantilever beam (TB) is proposed to improve the outputs of RPEHs. Finite element simulation (FEM) results indicate that the TB-RPEH can bear higher stress than rectangular beam (RB-RPEH) near the clamping end and show excellent electrical properties. The experimental results are consistent with the simulation analysis results, and verify the RPEHs are endowed with the characters of up-conversion frequency and ring-down pattern. Experimentally, a prototype TB-RPEH has been fabricated to harvest wind energy, which can generate an average output power density of 0.64 mW/cm 2 at the matching impedance of 50 kΩ. The RPEHs studied in this work provide higher power output and are qualified as power sources for charging some electronic devices. Our work has demonstrated that the proposed TB-RPEHs are good potential generators for harvesting flow energies and monitoring conditions of rotating machinery.

Behavior of High Strength Hybrid Reinforcement Concrete Beams

Six proposed simply supported high strength-steel fiber reinforced concrete (HS-SFRC) beams reinforced with FRP (fiber reinforced polymer) rebars were numerically tested by finite element method using ABAQUS software to investigate their behavior under the flexural failure. The beams were divided into two groups depending on their cross sectional shape. Group A consisted of four trapezoidal beams with dimensions of (height 200 mm, top width 250 mm, and bottom width 125 mm), while group B consisted of two rectangular beams with dimensions of (125 ×200) mm. All specimens have same total length of 1500 mm, and they were also considered to be made of same high strength concrete designed material with 1% volume fraction of steel fiber. Different types and ratios of FRP rebar were used to reinforce these test beams. The study’s principle variables were the amount and type of flexural reinforcement (glass FRP and basalt FRP) and beam cross-sectional shape (rectangular and trapezoidal). The load-deflection behavior and ultimate load capacity of the beams were studied and compared with one another under flexural test with symmetrical two-point loading. The results show that increasing the reinforcement ratio resulted in higher post cracking flexural stiffness, and higher residual strength, as well as caused an increase in the first cracking load and ultimate load capacity ranged from 3 to 16.9%, and 4.6 to 7.3% respectively. When the GFRP rebars replaced by BFRP, the overall beams flexural performance showed outstanding improvements. Moreover the results indicate that increasing the top width of the beam cross section led to a significant enhancement in the first crack load ranged from 16 to 32.4%, also a remarkable increases in the ultimate load capacity in the range of 35.5 to 35.8% were indicated in the trapezoidal beams compared to rectangular beams. However the results show that the deflections were similar and were approximately 1.07–1.54 mm for all test beams. It is worth noting that the general flexural behavior of all the test beams indicated a ductile behavior with a gradual reduction in strength and high residual strength pre to failure due to proposing steel fiber presence.

An investigation on grinding mechanism of alumina ceramic using a grooved grinding wheel with inclined cross section

In this study, a type of the grooved grinding wheel with inclined cross section is designed based on trapezoidal beam. The grinding type of grooved grinding wheel with inclined cross section is used as a new structuring method to process alumina ceramic. The inclined cross-section groove of a grinding wheel can improve the wear-resistant properties of laser macro-structured grinding wheel. First, a pulse laser was used to ablate rectangular cross-section groove and inclined cross-section groove on two bronze-bonded diamond wheels. Second, a grinding test was performed by using the grooved grinding wheel with rectangular cross-section and grooved grinding wheel with inclined cross section. The experimental results showed that the grooved grinding wheel with inclined cross section presented a reduction of grinding forces between 18 and 31.7%, but the better surface was not obtained. In addition, the inclined cross-section groove could reduce stress concentration, thus improving the wear of the grinding wheel surface. This indicates that the grooved grinding wheel with inclined cross section has better grinding performance than the grooved grinding wheel with rectangular cross section owing to the inclined cross-section structures. This provides further evidence for a method of constructing grooved grinding wheel with inclined cross section based on trapezoidal beam design.

Study on Dynamic Modulus Dependence Model for Asphalt Mixture Based on Temperature and Strain Parameters

In order to objectively characterize the nonlinear viscoelastic behavior of asphalt mixture and its dependence on temperature and load, the two-point dynamic flexural tensile modulus test of asphalt mixture at different strain levels, temperatures and loading frequencies is carried out by using French trapezoidal beam tester. By introducing the method of nonlinear operator, the dynamic modulus dependency modeling method for asphalt mixture based on temperature and strain parameters is put forward, the expression of dynamic modulus principal surface of asphalt mixture is established, and the reliability of the dynamic modulus dependent model is evaluated by correlation coefficient test and variance analysis method. The result shows that (1) for the two-point flexural tensile test of trapezoidal beam based on asphalt mixture of full-scale test track, the mean values of dynamic modulus variation coefficient at 0℃ and 45℃ are about 2.5% and 6.2% respectively, the mean values of dynamic modulus variation coefficient at 10 test temperatures is about 4%, the variation level of the test method is low, the error is small, which has a very good parallelism and reliability; (2) for the established dynamic modulus dependent model expression based on temperature and strain parameters, the decision coefficient R2 can reach more than 0.99, the P value of F test is 0, the fitting effect of the model on the test result is good, and there is a significant correlation of dynamic modulus with temperature and strain level; (3) the model can be used to describe the dynamic flexural tensile modulus of asphalt mixture, and the description model of the dynamic modulus can be transformed from principal curve to principal surface. In pavement structure analysis, this model can reflect the nonlinear response phenomenon in actual pavement more objectively, and can avoid the problems such as distortion of the calculation result caused by unreasonable modulus value in structural analysis effectively.

The simulation, fabrication technology and characteristic research of micro-pressure sensor with isosceles trapezoidal beam-membrane

A micro-pressure sensor with an isosceles trapezoidal beam-membrane (ITBM) is proposed in this paper, consisting of a square silicon membrane, four isosceles trapezoidal beams (ITBs) and four piezoresistors. To investigate how the elastic silicon membrane affects pressure sensitive characteristics, simulation models based on ANSYS 15.0 software were used to analyze the effect of structural dimension on the characteristics of pressure sensor. According to that, the chips of micro-pressure sensors were fabricated by micro-electro-mechanical system (MEMS) technology on a silicon wafer with [Formula: see text] orientation. The experimental results show that the proposed sensor achieves a better sensitivity of 9.64 mV/kPa and an excellent linearity of 0.09%F.S. in the range of 0–3.0 kPa at room temperature and a supply voltage of 5.0 V, with a super temperature coefficient of sensitivity (TCS) about - 2180 ppm/[Formula: see text] from −40[Formula: see text] to 85[Formula: see text] and low pressure measurement less than 3.0 kPa.

Design and optimization of MEMS piezoelectric energy harvester for low frequency applications

Piezoelectric vibrational energy harvester (PVEH) suits best for harvesting vibrational energy from the environment due to the simplicity in design, operation, and compatibility with the micro electro mechanical system (MEMS) technology. In this work, the effect of geometrical parameters on the performance of an Aluminium Nitride (AlN) based MEMS PVEH is analyzed in detail and optimized for lower resonant frequency and higher output power. Electromechanical modeling and validation are carried out for an energy harvester with various proof mass shapes. The optimized PVEH is having a trapezoidal beam and a triangular-shaped proof mass. The effect of the amount of proof mass coverage on the performance parameters is also analyzed. The least resonant frequency is found for the design in which the proof mass coverage is 57 % of the overall length of the harvester and the power peaks when the proof mass coverage becomes 80 %. The proposed structure generated output power of 0.24 $$\mu$$ W at a resonant frequency of 158.8 Hz when an input acceleration of 0.5 g is applied. Then an array using the proposed structure is simulated and compared to an array of conventional rectangular energy harvesters and it is found that array using the proposed structure provides 1.79 times higher power at a lower resonant frequency than the conventional array.

Flutter characteristics of axially functional graded composite wing system

This paper presents the flutter analysis and optimum design of axially functionally graded box beam cantilever wing section by considering various geometric and material parameters. The coupled dynamic equations of the continuous model of wing system in terms of material and cross-sectional properties are formulated based on extended Hamilton\'s principle. By expressing the lift and pitching moment in terms of plunge and pitch displacements, the resultant two continuous equations are simplified using Galerkin\'s reduced order model. The flutter velocity is predicted from the solution of resultant damped eigenvalue problem. Parametric studies are conducted to know the effects of geometric factors such as taper ratio, thickness, sweep angle as well as material volume fractions and functional grading index on the flutter velocity. A generalized surrogate model is constructed by training the radial basis function network with the parametric data. The optimized material and geometric parameters of the section are predicted by solving the constrained optimal problem using firefly metaheuristics algorithm that employs the developed surrogate model for the function evaluations. The trapezoidal hollow box beam section design with axial functional grading concept is illustrated with combination of aluminium alloy and aluminium with silicon carbide particulates. A good improvement in flutter velocity is noticed by the optimization.

Numerical Investigation of Flow around Two Tandem Identical Trapezoidal Cylinders

The trapezoidal beam structure is ubiquitous in giant engineering equipment, while their aerodynamic characteristics have not been clearly understood. Numerical simulation method was adopted to investigate the flow around two tandem identical trapezoidal cylinders. The study was conducted using a Reynolds number of 2.2 × 104, and with a spacing ratio varying from 0.5 to 10. The incompressible two-dimensional finite volume method was used for solving Reynolds-Averaged Navier–Stokes (RANS) equations with realizablek−εmodel. The effects of cylinder geometry and spacing between the cylinders on aerodynamic characteristics, unsteady flow patterns, time-averaged flow characteristics, and flow instability was studied. The results show that the flow around the two tandem trapezoidal cylinders is highly dependent on the spacing ratio. The flow modes can be classified into: extended-body regime (Mode I,S∗ ≤ 1), reattachment regime (Mode II, 2 ≤ S∗ ≤ 3), and binary regime (Mode III,S∗ ≥ 4). We explored their respective flow characteristics and distinctions through the force/pressure coefficients, time-average streamwise velocity, and the flow field evolution.

ДО РОЗРАХУНКУ ГЕОМЕТРИЧНИХ ПАРАМЕТРІВ ПОДАТЛИВИХ ГРАНЕЙ КЛИНІВ

Development of recommendations for calculating the geometry of cams with flexibility facet, which have console beams with variable moment of section resistance along their length for provide strength conditions and specified deflections. Method of search, description, analogous and information analysis is used to audit the many possible decisions regarding the subject of research, the experience in the field of knitting machines of automatic half-hose machine and methods of cross and longitudinal sections from the classical position of resistance of materials. Mathematical support for the complex approach of working out of cams of various designs with flexibility working facets according to the criteria of strength, flexibility and minimization of geometric dimensions using the beam shape coefficient of deflections is presented. The advantages of beams with equal resistance along its length in comparison with homogeneous beams having constant section sizes are shown. The dependences are given, which advisable to determine the dimensions of the root and final sections of a trapezoidal beam with a free end load of concentrated force, and also formulas for calculating the shape coefficient by deflection with sufficient accuracy and convenience in engineering calculations. Further development of the theory and methodology of designing elements of knitting systems of automatic half-hose machine based on load modes, dimensions restrictions and technological process requirements. Questions are presented that contribute to a comprehensive approach to the improvement of cams designs with flexibility facet based on calculated recommendations, taking into account their specificity. The information helps to improve the quality and efficiency of cam design solutions to meet the requirements for strength and flexibility using the economic index of section.

Design, Modeling, and Simulation of Two‐Piece Trapezoidal Piezoelectric Devices for Sensing and Energy Harvesting

The objective of the research is to design a high power energy harvester device through a two‐piece trapezoidal geometry approach. The performance of the composite two‐piece trapezoidal piezoelectric PZT‐PZN polycrystalline ceramic material is simulated using COMSOL Multiphysics. Results are analysed using the series configuration of a two‐piece trapezoidal composite bimorph cantilever which vibrates at the first fundamental frequency. The two‐piece trapezoidal composite beam designs resulted in a full‐width half‐maximum electric power bandwidth of 2.5 Hz while providing an electric power density of 16.81 mW/cm3 with a resistive load of 0.08 MΩ. The authors believe that these results could help design a piezoelectric energy harvester to provide local energy source which provides high electric power output.

Distributed-parameter Dynamic Modeling and Bifurcation Analysis of a Trapezoidal Piezomagnetoelastic Energy Harvester

In this paper, the effect of the bimorph profile on the nonlinear dynamic behavior and performance of a vibratory piezomagnetoelastic energy harvester is investigated. The proposed model is composed of upper and lower piezoelectric layers on a trapezoidal cantilever beam with one attached tip magnet as well as two external magnets. The magnetic field of two external magnets generates magnetic forces and moment on the tip magnet. The bimorph structure is considered as a distributed-parameter system, and the external forces are obtained by analyzing the magnetic field of the external magnets. Equations of motion are obtained using electromagnetic Lagrange equations based on the generalized Hamilton principle and the Euler-Bernoulli beam theory. The proposed model for the bimorph and magnetic forces is validated by previously published experimental results. In order to compare the nonlinear behavior of the rectangular and trapezoidal beam profiles, the bifurcation diagrams are depicted for various control parameters such as the separation distances of the magnets, beam root width, and beam tip width. Verification of the bifurcation diagrams is performed by the phase plane portraits and Poincare maps. Also, the harvested power level is compared for different profiles of the bimorph. Moreover, the simultaneous effects of exciting frequency and bifurcation parameters on the system performance are investigated by the waterfall diagrams. The obtained results show that the trapezoidal beam profile with a lower tip width has higher performance than the rectangular beam. In trapezoidal beam profiles, the subharmonic and chaotic motions have relatively higher output powers than periodic motions.

Nonlinear analysis of piezoelectric wind energy harvesters with different geometrical shapes

Piezoelectric wind energy harvesters consisting a bluff body and a piezoelectric cantilever beam have great potential for powering small-sized wireless devices. To achieve a higher energy output, the beam is designed for large deformation. This results in the nonlinear nature of the energy harvesters. In this paper, a nonlinear model of a piezoelectric wind harvester with different geometrical parameters is developed. A comparison of the energy harvesting performance of these energy harvesters with different geometrical parameters is provided. Results show that the onset speeds of galloping for trapezoidal and exponential piezoelectric energy harvesters are significantly lower than those of rectangular beam. The average power output density of the beam with exponential shape is larger than trapezoidal and rectangular beams. Therefore, designing a beam with exponentially varying shape can obtain the largest power density and therefore can reduce the cost of piezoelectric wind energy harvester.

Design and Analysis of a Combined Strain-Vibration-Temperature Sensor with Two Fiber Bragg Gratings and a Trapezoidal Beam.

A combined sensor to simultaneously measure strain, vibration, and temperature has been developed. The sensor is composed of two Fiber Bragg gratings (FBGs) and a vibration gainer. One FBG is used to measure strain, while the other measures vibration and temperature. The gainer has a mass block which is used to increase its sensitivity to vibration. The main beam of the vibration gainer was designed as a trapezoid in order to reduce the strain gradient while sensing vibration. In addition, an interrogation method was used to eliminate interactions between measured parameters. Experiments were carried out to analyze the performance of the proposed sensor. For individual strain measurement in the range of 0–152 με, the sensitivity and nonlinearity error were 1.878 pm/με and 2.43% Full Scale (F.S.), respectively. For individual temperature measurement in the range of 50–210 °C, the sensitivity and nonlinearity error were 29.324 pm/°C and 1.88% F.S., respectively. The proposed sensor also demonstrated a sensitivity of 0.769 pm/m·s−2 and nonlinearity error of 1.83% F.S. for vibration measurement in the range of 10–55 m/s2. Finally, simultaneously measuring strain, temperature, and vibration resulted in nonlinearity errors of 4.23% F.S., 1.89% F.S., and 2.23% F.S., respectively.

A Finite Element Study of The Elastic Properties of a Cracked Cellular Structure with Trapezoidal Beams

The elastic properties of a cracked cellular structure of close-to-zero Poisson’s ratio with trapezoidal beams are studied by the finite element method in this paper. The effects of the crack length and crack angle on the non-dimensional equivalent modulus, including elastic moduli in the x-direction, y-direction, and the shear moduli are analyzed.

Vibration energy harvesters with optimized geometry, design, and nonlinearity for robust direct current power delivery

With an ever-growing Internet-of-things, vibration energy harvesting has attracted broad attention to replace consumable batteries to power the many microelectronic devices. To this end, an energy harvester must deliver the required power to an electrical load over a long time horizon. Yet, design practices for energy harvesters often report strategies based on maximizing output voltage and wide frequency range of operation, which is not directly related to performance-robust functioning. Motivated to provide valuable insight to practical development of vibration energy harvesters, this research develops an analytical modeling framework and optimization technique to guide attention to piezoelectric laminated energy harvesting cantilevers with balanced and robust performance characteristics. The model is numerically and experimentally validated to confirm the efficacy of the optimization outcomes. The results indicate that laminated trapezoidal beam shapes with monostable configuration are the best solution to broaden the frequency range of enhanced dynamic behavior, minimize strain at the clamped beam end, and maximize the output voltage in a rectifier circuit. The results also find that the selection of tip mass may not be highly influential for the overall performance so long as the beam shape, beam length, and placement of nonlinearity-induced magnets are appropriately chosen.