Buckling and post-buckling behaviors of higher order carbon nanotubes using energy-equivalent model

This paper aims to investigate the size scale effect on the buckling and post-buckling of single-walled carbon nanotube (SWCNT) rested on nonlinear elastic foundations using energy-equivalent model (EEM). CNTs are modelled as a beam with higher order shear deformation to consider a shear effect and eliminate the shear correction factor, which appeared in Timoshenko and missed in Euler–Bernoulli beam theories. Energy-equivalent model is proposed to bridge the chemical energy between atoms with mechanical strain energy of beam structure. Therefore, Young’s and shear moduli and Poisson’s ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants. Conservation energy principle is exploited to derive governing equations of motion in terms of primary displacement variable. The differential–integral quadrature method (DIQM) is exploited to discretize the problem in spatial domain and transformed the integro-differential equilibrium equations to algebraic equations. The static problem is solved for critical buckling loads and the post-buckling deformation as a function of applied axial load, CNT length, orientations and elastic foundation parameters. Numerical results show that effects of chirality angle, boundary conditions, tube length and elastic foundation constants on buckling and post-buckling behaviors of armchair and zigzag CNTs are significant. This model is helpful especially in mechanical design of NEMS manufactured from CNTs.

     

Effect of thermal and mechanical properties variations on microcantilever mass sensor performance

Ensuring desirable performance for piezoelectric microcantilever sensors constitutes a crucial research subject particularly for the applications such as detection of biochemical entities, virus particles or human biomarkers. However, these sensors’ performance may be affected by the environmental conditions such as temperature variation, and/or the uncertainty in the material properties. The objective of this study is to explore Young modulus uncertainty of microcantilever’s structural layer, thermo-mechanical and geometrical temperature dependency effects, on the natural frequency, bias and sensitivity of microcantilever mass sensors. These effects have been investigated for different sensor lengths and resonant modes. Also, a temperature compensation method which omits the need for bulky non-contact thermometers or fabrication of built-in temperature sensor has been proposed. As theoretical model, Euler–Bernoulli beam theory has been employed and solved by Galerkin expansion procedure. Using this model, it is demonstrated that the sensitivity of microcantilever sensor decreases with increasing the added mass. The microcantilever sensor sensitivity operating at the second resonant mode has been improved almost five times comparing to the first mode sensitivity regardless of microcantilever length. The simulation results show that temperature variation causes thermal frequency shift which in turn introduces a significant mass bias far beyond the sensors’ minimum detectable mass. This mass bias is constant for a given microcantilever in its first and second resonant mode. Additionally, the effect of temperature variation on the sensitivity of the given mass sensors is negligible. However, it has been shown that the variations in sensors sensitivity due to uncertainty of Young modulus remain constant for different lengths and two resonant modes of the microcantilever sensor.     

A new analytical model for switching time of a perforated MEMS switch

In this paper, the design of a low-k meander based MEMS shunt capacitive switch with perforated beam meander has been presented. A closed form analytical model to calculate the switching time of designed structure is proposed. The model is based on modified Mejis and Fokkema’s capacitance model and linearization of non-linear electrostatic force on the switch beam. The model is utilized in evaluating the switching time for uniform as well as non-uniform serpentine meander designs, considering different values of actuation voltage and a wide variation of switching parameters. This work takes into account the beam perforation, fringing field and stiffness effect simultaneously altogether. The results obtained for both the meander designs under every design specifications has been found out to be less than or approximately equal to 100 µs. These model based results are then compared with 3D FEM simulated values. Comparative Analysis indicated that the model results and simulation results are in close agreement with each other.

     

Static bending of perforated nanobeams including surface energy and microstructure effects

This article aims to present comprehensive model and analytical solution to investigate the static bending behavior of regularly squared cutout perforated thin/thick nanobeams incorporating the coupled effect of the microstructure and surface energy for the first time. The perforation influence is considered to be deriving equivalent geometrical and material characteristics. The modified couple stress theory is adopted to incorporate the microstructure effect while the modified Gurtin–Murdoch surface elasticity model is employed to incorporate the surface stress effect in perforated nanobeams. A variational formulation based on minimization of the total potential energy principle is employed to derive the equilibrium equations of perforated nanobeams based on both Euler–Bernoulli and Timoshenko beams theories are developed to investigate the associated effect of the shear deformation due to perforation process. Additionally, Poisson’s effect is also incorporated. Analytical closed-form for the non-classical bending profiles as well as the rotational displacement are developed for both beam theories considering the simultaneous effect of both couple stress and surface stress for both uniformly distributed and concentrated loading patterns. The verification of the developed model is verified and compared with previous works, and an excellent agreement is obtained. The applicability of the developed model is demonstrated and applied to study and analyze the nonclassical bending behavior of regularly squared perforated simply supported beams under different loading conditions. Additionally, effects of the perforation configuration parameters, beam size as well as beam aspect ratio on the bending behavior of perforated beams in the presence of microstructure and surface stress effects are also investigated and analyzed. The obtained results reveal that both couple stress and surface stress significantly affect the bending behavior of regularly squared cutout perforated beam structures. Results obtained are supportive for the design, analysis and manufacturing of perforated NEMS applications.

     

Laser beam welded structures for a regional aircraft: weight,cost and carbon footprint savings

Laser beam welded structures offer great opportunities for the lightweight design of fuselage structures in order to reduce structural weight for increased fuel efficiency. Our main objective is to validate and demonstrate that laser beam welding (LBW) technology provides the best opportunities in terms of weight reduction, production time and energy consumption for manufacturing aircraft components. To this end, a comparison in terms of energy, process time, cost and carbon footprint is assessed against the ‘conventional’ manufacturing process of riveting, to prove that LBW is actually an environmental friendly process. Manufacturing of a four-stringer stiffened flat subscale component was the case of the present work that was called in the Clean Sky Eco-Design Airframe (EDA) project as the B1 demonstrator (742 mm × 384 mm). The LBW process has been broken down into several sub-processes and activities according to the Activity Based Costing (ABC) methodology and the weight reduction, production time and energy consumption results were compared against the respective of the riveting process. It was proved that for the specific subscale LBW component, it consumes half the energy and can be processed in less than half the time needed (in serial processing of the component) with riveting. Manufacturing of the component with the LBW process (door to door approach) is more environmentally friendly, since it produces 53% less CO_2e emissions than the respective riveted process. This is a clear advantage to this manufacturing process in order to assure a sustainable life cycle of the final product.     

Micromachined SiO<Subscript>2</Subscript> microcantilever for high sensitive moisture sensor

Ultra-sensitive and selective moisture sensors are needed in various industries for processing control or environmental monitoring. As an outstanding sensor platform, surface-stress sensing microcantilevers have potential application in moisture detection. To enlarge the deflection of the microcantilever under surface stress induced by specific reactions, a new SiO₂ microcantilever is developed which features a much lower Young’s modulus than conventional Si or SiN_x microcantilevers. For comparing SiO₂ cantilever with Si cantilevers, a model of the cantilever sensor is given by using both analysis and simulation, resulting in good agreement with the experimental data. The results demonstrate the SiO₂ cantilever can achieve a much higher sensitivity than the Si cantilever. In order to fabricate this device, a new fabrication process using isotropic combined with anisotropic dry etching to release the SiO₂ microcantilever beam by ICP (Inductively Coupled Plasma) was developed and investigated. This new process not only obtains a high etch rate at 9.1 μm/min, but also provides good profile controllability, and a flexibility of device design. Attributed to the high sensitivity, a significant deflection amplitude of the surface modified SiO₂ microcantilever was observed upon exposure to 1% relative humidity. The SiO₂ cantilevers are promising for inexpensive and highly sensitive moisture detection.     

First-order,buckling and post-buckling behaviour of GFRP pultruded beams. Part 1: Experimental study

Although fibre reinforced polymers exhibit several advantages over traditional materials, their widespread acceptance is being delayed by the lack of appropriate design codes. In fact, additional and comprehensive experimental data are needed to assess the accuracy of recently developed analytical and numerical design tools. This work reports an experimental study on the first-order, buckling and post-buckling behaviours of I-section beams made of GFRP pultruded profiles. Tests were first carried out on small-scale (coupon) specimens, in order to determine the most relevant material mechanical properties. Full-scale tests were then conducted on (i) simply supported beams with spans varying from 1.0 m to 4.0 m under 3-point bending and (ii) cantilevers with spans ranging from 2.0 m to 4.0 m subjected to a tip point load applied at the end cross-section centroid or top/bottom flange mid-point. While the first series is aimed at investigating the flexural behaviour under service and failure conditions (including the local buckling of the top flange), the objective of the second series is to study the collapse behaviour stemming from lateral-torsional buckling. The results obtained confirm that, due to the GFRP low Young’s modulus and high strength, the beam structural integrity is often governed by excessive deformation and/or local and global buckling phenomena, rather than by material strength limitations. Moreover, the low shear-to-Young’s modulus ratio implies that the role played by the shear deformation is quite relevant, particularly in stocky beams. The experimental data presented here is used to validate and assess the accuracy of numerical simulations reported in a companion paper (Part 2).     

Estimation of FeB layer’s yield strength by comparison of finite element modeling with experimental data

In this study, low alloy steel substrates were borided by pack boriding process, for 2, 4 and 6 h at 900 °C. Microstructural observations were conducted by using SEM. The structural composition of layers consists of boron rich phase (FeB) and iron rich phase (Fe₂B). First, experimental indentation studies were carried out to determine the load–unload curves of FeB layers at different peak loads. Important parameters such as hardness and Young’s modulus of FeB layers, and contact area were obtained from experimental indentation test sample data. After the mechanical characterization of samples, finite element modeling was applied to simulate the mechanical response of FeB layer on low alloy steel substrate by using ABAQUS software package program. The unique contribution of this study different from previous methods is the estimation of the yield strength of FeB layer by combining the experimental indentation works and finite element modeling (FEM).     

Simulations,fabrication, and characterization of d31 mode piezoelectric vibration energy harvester

This paper presents the development work on d₃₁ mode piezoelectric vibration energy harvester. The device structure consists of a fixed-free type cantilever beam with a seismic mass attached at the free end of the beam. On top of the cantilever beam, a ZnO piezoelectric layer is sandwiched between two metal electrodes. The harvester is designed using an FEM tool CoventorWare. The simulations are carried out to estimate the resonance frequency, mises stress, optimal load resistance, and generated power. The optimized design is then implemented using a five mask SOI bulk micromachining process. The fabricated harvester is characterized for frequency response using Polytec MSA-500 Micro System Analyzer. The experimental resonance frequency is found to be 235.38 Hz. The harvester is also evaluated for generated open-circuit voltage when subjected to harmonic acceleration. The open-circuit peak-to-peak voltage for 0.1 g acceleration is found to be 306 mV.

     

Study of residual stress-induced deformation of multilayer cantilever for maskless microplasma etching

In the scanning probe microscopy-based microplasma etching system proposed by our group, the microcantilever probe integrated with microplasma device is a multilayered structure. However, the thin film residual stress generated by microfabrication process may cause undesirable bending deformation of the cantilever. In order to predict and minimize the stress-induced deformation in the cantilever design, we experimentally measure and calculate each thin film stress of the cantilever based on Stoney equation. Then the stress-induced bending deformation of the cantilever is simulated by finite element simulation. By adjusting the thickness of reserved silicon layer of the cantilever, the deflection can be minimized to <5 μm for a 750 μm-length cantilever. Finally the microcantilever probes with different thickness of reserved silicon layer are successfully fabricated by MEMS process. The bending deformation of actual fabricated cantilevers agree well with simulation results, which verifies the feasibility of the cantilever structural design. The results of this paper may lay a foundation for further scanning plasma maskless etching.     

Static pull-in instability and free vibration of functionally graded graphene nanoplatelet reinforced micro-sandwich beams under thermo-electrical actuation

This paper investigates the static pull-in instability and free vibration of a multilayer functionally graded graphene nanoplatelet (GPL) reinforced composite (FG-GPLRC) micro-beam sandwiched between two copper layers subjected to a combined action of an electric voltage and a uniform temperature change based on Euler–Bernoulli beam theory. The GPL nanofillers are uniformly dispersed within each individual layer while its weight fraction changes from layer to layer in the multilayer FG-GPLRC micro-beam. The modified Halpin–Tsai model is used to predict the effective Young’s modulus while the rule of mixture is used to determine the effective Poisson’s ratio, mass density and thermal expansion coefficient. The static pull-in voltage and natural frequency of clamped–clamped micro-beams are obtained by employing Galerkin and iterative method. The effects of GPL distribution pattern, weight fraction, geometry and size as well as the geometry of the beam, the temperature change and the total number of layers on the static and dynamic characteristics of the micro-beams are discussed in detail.

     

Transient flow of microcapsules through convergent–divergent microchannels

The study deals with a microfluidic method to investigate the transient behavior of microcapsules in flow. The technique consists of investigating ovalbumin microcapsules passing through a convergent–divergent microchannel made of PolyDiMethylSiloxane. We work with three types of square microchannel with, respectively, cross section values of h × h = 30 × 30, 50 × 50 and 70 × 70 μm. The microchannels length is L = 3h. We analyze the kinetics of deformation of the microcapsules in the microchannels for velocity ranging from 2 to 5 cm/s and for microcapsule size ratio d/h ranging from 0.9 to 2.5. The relaxation process at the pore outlet is modeled using an exponential relaxation law. We show that that the relaxation time at the divergent outlet depends on the microcapsule size ratio d/h. Thanks to the analytical expression of the relaxation, we extract a shear modulus of the membrane equal to 0.04 N/m. This value is consistent with the value of 0.07 N/m that we found using the steady state analysis performed in cylindrical glass capillaries. Thus, it is interesting to notice that the microcapsule behavior based on a simple analytical model can be successfully described despite the complex flow situation consisting of deformable microcapsule in confined square microchannels.     

Fabrication and flow-sensor application of flexible thermal MEMS device based on Cu on polyimide substrate

A Cu on polyimide (COP) substrate was proposed as a MEMS material, and the fabrication process for a flexible thermal MEMS sensor was developed. The COP substrate application to MEMS devices has the advantage that typical MEMS structures fabricated in a SOI wafer in the past—such as a diaphragm, a beam, a heater formed on a diaphragm—can also be easily produced in the COP substrate in the flexible fashion. These structures can be used as the sensing element in various physical sensors, such as flow, acceleration, and shear stress sensors. A flexible thermal MEMS sensor was produced by using a lift-off process and sacrificial etching of a copper layer on the COP substrate. A metal film working as a flow sensing element was formed on a thin polyimide membrane produced by the sacrificial etching. The fabricated flexible thermal MEMS sensor was used as a flow sensor, and its characteristics were evaluated. The obtained sensor output versus the flow rate curve closely matched the approximate curve derived using King’s law. The rising and falling response times obtained were 0.50 and 0.67 s, respectively.

     

Elastic–plastic modeling of heat-treated bimorph micro-cantilevers

This paper models the residual stress distributions within micro-fabricated bimorph cantilevers of varying thickness. A contact model is introduced to calculate the influence of contact on the residual stress following a heat treatment process. An analytical modeling approach is adopted to characterize bimorph cantilevers composed of thin Au films deposited on thick poly-silicon or silicon-dioxide beams. A thermal elastic–plastic finite element model (FEM) is utilized to calculate the residual stress distribution across the cantilever cross-section and to determine the beam tip deflection following heat treatment. The influences of the beam material and thickness on the residual stress distribution and tip deflections are thoroughly investigated. The numerical results indicate that a larger beam thickness leads to a greater residual stress difference at the interface between the beam and the film. The residual stress established in the poly-silicon cantilever is greater than that induced in the silicon-dioxide cantilever. The results confirm the ability of the developed thermal elastic–plastic finite element contact model to predict the residual stress distributions within micro-fabricated cantilever structures with high accuracy. As such, the proposed model makes a valuable contribution to the development of micro-cantilevers for sensor and actuator applications.

     

Coupled twist–bending static and dynamic behavior of a curved single-walled carbon nanotube based on nonlocal theory

The static and dynamic behavior of a curved single-walled carbon nanotube which is under twist–bending couple based on nonlocal theory is analyzed. The nonlocal theory is used to model the mechanical behavior of structure in small scale. The obtained differential equations are solved using a simply supported boundary condition and Navier analytical method. Moreover the twisted vibration and bending of curved nanotube is analyzed and also the armchair model is assumed in this study. The following parameters were studied in this paper: the effect of nonlocal parameter, the curved nanotube’s opening angel, the Young’s modulus and the mode number is studied. The results were verified with the previous literature which showed an excellent agreement. The results of this paper can be used as a benchmark for future investigations.

     

用于扫描刻蚀加工的微悬臂梁优化设计

扫描刻蚀加工是一种基于并行探针驱动、集成微小等离子体刻蚀原理的新型微纳米加工手段。特种悬臂梁是扫描刻蚀加工系统中的核心器件,其性能直接影响到系统的可靠性。该特种悬臂梁为集成压电陶瓷驱动薄膜的多层复合梁,在加工工艺过程中所引起的材料内部的残余应力,将导致复合梁加工释放后的弯曲变形,影响扫描刻蚀加工系统的性能。基于弹性薄板理论建立含残余应力项的多层复合梁的理论模型。利用有限元法对多层复合梁进行数值仿真,结合田口优化方法,对多层薄膜的厚度进行优化设计。     

Analysis of a novel RF MEMS switch using different meander techniques

In this paper, two types of RF MEMS switches namely step structure and Normal beam structure are designed and analyzed using different meander techniques. Three techniques namely plus, zigzag and three-square meander were used to lower the pull-in voltage. The actuating beam is designed with the rectangular perforations affects the performance of a switch by lowering the pull-in voltage, switching speed and results in better isolation. In this paper a comparative analysis is done for all three meander techniques with and without perforations on the beam. Total six structures have been designed with the combination three meanders and two different beam structures. The proposed stepdown structure exhibits high performance characteristics with a very low pull-in voltage of 1.2 V having an airgap of 0.8 µm between the actuation electrodes. The gold is used as beam material and HfO₂ as the dielectric material such that the upstate and downstate capacitance is seen as 1.02 fF and 49 fF. The FEM analysis is done to calculate the spring constant and thereby the pull-in voltage and behavior of the switch is studied with various parameters. The switch with a step structure and three-square meander configuration has shown best performance of all by requiring a pull-in voltage of 1.2 V and lower switching time of 0.2 µs. The proposed switch also exhibits good RF performance characteristics with an insertion loss below − 0.07 dB and return loss below − 60 dB over the frequency range of 1–40 GHz. At 28 GHz a high isolation of − 68 dB is exhibited.

     

Design of SAW sensor for longitudinal strain measurement with improved sensitivity

This paper presents the design of a highly sensitive surface acoustic wave (SAW)-based sensor with novel structure for the longitudinal strain measurement. The sensor utilizes thin lithium niobate (LiNbO₃) diaphragm as the sensing element rather than the bulk substrate. The application of the diaphragm effectively decreases the cross-sectional area of the strain sensitive element, and meanwhile reduces the resistance between the sensor and the specimen. The newly designed strain sensor is to operate around a frequency of 50 MHz. The insertion loss of − 12 dB and quality factor of 63 are obtained analytically from impulse-response model. The sensor performance with tensile testing of the steel beam is predicted by the finite element method. The prestressed eigenfrequency analysis is conducted with the COMSOL commercial software. The simulation shows the resonance frequency of the sensor shifts linearly with the strain induced in the testing beam. For the SAW sensor with traditional configuration applying 1 mm thick substrate, the strain sensitivity is obtained as 0.41 ppm/με. For the sensor with the novel design employing thin diaphragm with the thickness of 200 μm, the strain sensitivity is increased to 0.83 ppm/με. With the availability of the bulk micromachining of LiNbO₃, the application of the piezoelectric diaphragm as sensing element in SAW strain sensor can be an alternative way to enhance the sensor sensitivity.

     

Size effect on mechanical properties of TiO2 capped nanotubes investigated using in situ transmission electron microscopy

In situ transmission electron microscopy nanoindentation tests are used to measure the compressive fracture and mechanical properties of individual titanium oxide (TiO₂) capped nanotubes. The average critical loads ranged from 3.6 to 9.6 μN. Individual TiO₂ capped nanotubes with lengths of 8–10 μm were found to have Young’s modulus values of ~2.2–9.4 GPa and work energy values of ~3.1–6.6 × 10^?13 J. The results indicate that the Young’s modulus and tensile strength depend on capped nanotube length.     

Implementation of non-probabilistic methods for stability analysis of nonlocal beam with structural uncertainties

In this study, a non-probabilistic approach-based Navier’s method (NM) and Galerkin weighted residual method (GWRM) in terms of double parametric form have been proposed to investigate the buckling behavior of Euler–Bernoulli nonlocal beam under the framework of Eringen’s nonlocal elasticity theory, considering the structural parameters as imprecise or uncertain. The uncertainties in Young’s modulus and diameter of the beam are modeled in terms of triangular fuzzy numbers. The critical buckling loads are calculated for hinged–hinged, clamped–hinged, and clamped–clamped boundary conditions, and these results are compared with the deterministic model in special cases, demonstrating robust agreement. Further, a random sampling technique-based method, namely Monte Carlo simulation technique (MCST), has been implemented to compute the critical buckling loads of uncertain systems. Also, the critical buckling loads obtained from the uncertain model in terms of lower bound and upper bound by the non-probabilistic methods, viz. NM and GWRM, are again verified with the MCST with their time periods, demonstrating the efficacy, accuracy, and effectiveness of the proposed uncertain model. A comparative study is also carried out among the non-probabilistic methods and MCST to demonstrate the effectiveness of methods with respect to time. Additionally, a parametric study has been performed to display the propagation of uncertainties into the nonlocal system in the form of critical buckling loads.