Bending Stresses of Steel Web Tapered Tee Section Cantilevers

Although commonly used, no design method is available for steel web tapered tee section cantilevers. This paper investigates the bending stresses of such beams. Relationships between the maximum compressive stress and the degree of taper were investigated. An analytical model is presented to determine the location of the maximum stress when subjected to a uniformly distributed load or a point load at the free end and was validated using finite element analysis and physical tests. It was found that the maximum stress always occurs at the support when subjected to a uniformly distributed load. When subjected to a point load at the free end and the degree of taper is up to seven, it was found that Miller＇s equation could be used to determine the location of the maximum stress. However, it is shown that when the degree of taper is greater than seven, Miller＇s equation does not accurately predict the location and the analytical model should be used. It was also found that the location of the maximum stress was solely dependent on the degree of taper, while a geometric ratio, fl was required to determine the magnitude of the maximum stress. A simple method that predicts the magnitude of the maximum stress is proposed. The average error in the prediction of the magnitude of the maximum stress is found to be less than 1.0%.

Effects of Environments on the Noise of Atomic Force Microscopy Cantilevers

Thermal vibration of the cantilevers is the main source of noise in atomic force microscopy(AFM).When immersed in liquids,the dynamic behavior of the cantilevers will be significantly affected by the environment.In this study,the effects of environments on the noise of AFM were investigated.The results show that the V⁃shaped cantilever exhibited very low noise in high vacuum.The noise in atmospheric environment was also satisfactory.In liquid environments,the noise dramatically increased.The systematic noise was low and dependent on the distance between the tip and substrate.As the velocity increased,the noise of V⁃shaped cantilever was increased in a similar trend.It is also found that the variation trend was more pronounced as the liquid viscosity increased.The noise of rectangular cantilever was lower than that of V⁃shaped cantilever in the same environment.The present study indicates that high vacuum is an ideal environment for single molecule force spectroscopy(SMFS)due to the lower noise and higher resolution.For a better signal⁃to⁃noise ratio,both the cantilever velocity and liquid viscosity should be as low as possible.These results will be helpful when a lower noise is desired in weak force detection.

Hydrodynamic function and spring constant calibration of FluidFM micropipette cantilevers

Fluidic force microscopy(FluidFM)fuses the force sensitivity of atomic force microscopy with the manipulation capabilities of microfluidics by using microfabricated cantilevers with embedded fluidic channels.This innovation initiated new research and development directions in biology,biophysics,and material science.To acquire reliable and reproducible data,the calibration of the force sensor is crucial.Importantly,the hollow FluidFM cantilevers contain a row of parallel pillars inside a rectangular beam.The precise spring constant calibration of the internally structured cantilever is far from trivial,and existing methods generally assume simplifications that are not applicable to these special types of cantilevers.In addition,the Sader method,which is currently implemented by the FluidFM community,relies on the precise measurement of the quality factor,which renders the calibration of the spring constant sensitive to noise.In this study,the hydrodynamic function of these special types of hollow cantilevers was experimentally determined with different instruments.Based on the hydrodynamic function,a novel spring constant calibration method was adapted,which relied only on the two resonance frequencies of the cantilever,measured in air and in a liquid.Based on these results,our proposed method can be successfully used for the reliable,noise-free calibration of hollow FluidFM cantilevers.

A novel method using SiNW to measure stress in cantilevers

A silicon（SiNW） nanowire device,made by the bottom-up method,has been assembled in a MEMS device for measuring stress in cantilevers.The process for assembling a SiNW on a cantilever has been introduced.The current as a function of the voltage applied to a SiNW have been measured,and the different resistances before and after cantilever releasing have been observed.A parameter,η,has been derived based on the resistances.For a fixed sample,a linear relationship between η and the stress in the cantilever has been observed;and,so,it has been demonstrated that the resistance of SiNW can reflect the variation of the cantilever stress.

Mechanical memory operations in piezotransistive GaN microcantilevers using Au nanoparticleenhanced photoacoustic excitation

Nonlinear oscillations in micro-and nanoelectromechanical systems have emerged as an exciting research area in recent years due to their promise in realizing low-power,scalable,and reconfigurable mechanical memory and logic devices.Here,we report ultralow-power mechanical memory operations utilizing the nonlinear oscillation regime of GaN microcantilevers with embedded piezotransistive AlGaN/GaN heterostructure field effect transistors as highly sensitive deflection transducers.Switching between the high and low oscillatory states of the nonlinear oscillation regime was demonstrated using a novel phase-controlled opto-mechanical excitation setup,utilizing a piezo actuator and a pulsed laser as the primary and secondary excitation sources,respectively.Laser-based photoacoustic excitation was amplified through plasmonic absorption in Au nanoparticles deposited on a transistor.Thus,the minimum switching energy required for reliable memory operations was reduced to less than a picojoule(pJ),which translates to one of the lowest ever reported,when normalized for mass.

Artificial-intelligence-assisted mass fabrication of nanocantilevers from randomly positioned single carbon nanotubes

Nanoscale cantilevers(nanocantilevers)made from carbon nanotubes(CNTs)provide tremendous benefits in sensing and electromagnetic applications.This nanoscale structure is generally fabricated using chemical vapor deposition and/or dielectrophoresis,which contain manual,time-consuming processes such as the placing of additional electrodes and careful observation of single-grown CNTs.Here,we demonstrate a simple and Artificial Intelligence(Al)-assisted method for the effcient fabrication of a massive CNT-based nanocantilever.We used randomly positioned single CNTs on the substrate.The trained deep neural network recognizes the CNTs,measures their positions,and determines the edge of the CNT on which an electrode should be clamped to form a nanocantilever.Our experiments demonstrate that the recognition and measurement processes are automatically completed in 2 s,whereas comparable manual processing requires 12 h.Notwithstanding the small measurement error by the trained network(within 200 nm for 90%of the recognized CNTs),more than 34 nanocantilevers were successfully fabricated in one process.Such high accuracy contributes to the development of a massive field emitter using the CNT-based nanocantilever,in which the output current is obtained with a low applied voltage.We further showed the benefit of fabricating massive CNT-nanocantilever-based field emitters for neuromorphic computing.The activation function,which is a key function in a neural network,was physically realized using an individual CNT-based field emitter.The introduced neural network with the CNT-based field emitters recognized handwritten images successfully.We believe that our method can accelerate the research and development of CNT-based nanocantilevers for realizing promising future applications.

Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell:an experimental and numerical study

The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.

Nanomotion of bacteria to determine metabolic profile

In addition to their visible motion such as swimming(e.g.,with the help offlagella),bacteria can also exhibit nanomotion that is detectable only with highly sensitive instruments,and this study shows that it is possible to detect bacterial nanomotion using an AFM detection system.The results show that the nanomotion characteristics depend on the bacterial strain,and that nanomotion can be used to sense the metabolic activity of bacteria because the oscillations are sensitive to the food preferences of the bacteria and the type of surrounding medium.

Deformation mechanism and roof pre-splitting control technology of gob-side entry in thick hard main roof full-mechanized longwall caving panel

This paper explores the deformation mechanism and control technology of roof pre-splitting for gob-side entries in hard roof full-mechanized longwall caving panel(LTCC).The investigation utilizes a comprehensive approach that integrates field monitoring,theoretical analysis,and numerical simulation.Theoretical analysis has illuminated the influence of the length of the lateral cantilever beam of the main roof(LCBM)above the roadway on the stability of the gob-side entry behind the panel.Numerical simulations have further revealed that the longer LCBM results in heightened vertical stress within the coal pillar,developed cracks around the roadway,and more pronounced damage to the roadway.Moreover,numerical simulations also demonstrate the potential of roof pre-splitting technology in optimizing the fracture position of the hard roof.This technology significantly reduces the length of the LCBM,thereby alleviating stress concentration in the coal pillars and integrated coal rib while minimizing the destruction of the gob-side entry.Therefore,this manuscript first proposes the use of roof pre-splitting technology to control roadway deformation,and automatically retain the entry within a hard roof LTCC panel.Field implementation has demonstrated that the proposed automatically retained entry by roof pre-splitting technology effectively reduces gob-side entry deformation and achieves automatically retained entry.

Bending strength degradation of a cantilever plate with surface energy due to partial debonding at the clamped boundary

This paper investigates the bending fracture problem of a micro/nanoscale cantilever thin plate with surface energy,where the clamped boundary is partially debonded along the thickness direction.Some fundamental mechanical equations for the bending problem of micro/nanoscale plates are given by the Kirchhoff theory of thin plates,incorporating the Gurtin-Murdoch surface elasticity theory.For two typical cases of constant bending moment and uniform shear force in the debonded segment,the associated problems are reduced to two mixed boundary value problems.By solving the resulting mixed boundary value problems using the Fourier integral transform,a new type of singular integral equation with two Cauchy kernels is obtained for each case,and the exact solutions in terms of the fundamental functions are determined using the PoincareBertrand formula.Asymptotic elastic fields near the debonded tips including the bending moment,effective shear force,and bulk stress components exhibit the oscillatory singularity.The dependence relations among the singular fields,the material constants,and the plate's thickness are analyzed for partially debonded cantilever micro-plates.If surface energy is neglected,these results reduce the bending fracture of a macroscale partially debonded cantilever plate,which has not been previously reported.

Inter-well internal resonance analysis of rectangular asymmetric cross-ply bistable composite laminated cantilever shell under transverse foundation excitation

The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell,in cases of 1:2 inter-well internal resonance and primary resonance.The transverse foundation excitation is applied to the fixed end of the structure,and the other end is in a free state.The first-order approximate multiple scales method is employed to perform the perturbation analysis on the dimensionless two-degree-of-freedom ordinary differential motion control equation.The four-dimensional averaged equations are derived in both polar and rectangular coordinate forms.Deriving from the obtained frequency-amplitude and force-amplitude response curves,a detailed analysis is conducted to examine the impacts of excitation amplitude,damping coefficient,and tuning parameter on the nonlinear internal resonance characteristics of the system.The nonlinear softening characteristic is exhibited in the upper stable-state,while the lower stable-state demonstrates the softening and linearity characteristics.Numerical simulation is carried out using the fourth-order Runge-Kutta method,and a series of nonlinear response curves are plotted.Increasing the excitation amplitude further elucidates the global bifurcation and chaotic dynamic snap-through characteristics of the bistable cantilever shell.

Recent Construction Technology Innovations and Practices for Large-Span Arch Bridges in China

Arch bridges provide significant technical and economic benefits under suitable conditions.In particular,concrete-filled steel tubular(CFST)arch bridges and steel-reinforced concrete(SRC)arch bridges are two types of arch bridges that have gained great economic competitiveness and span growth potential due to advancements in construction technology,engineering materials,and construction equipment over the past 30 years.Under the leadership of the author,two record-breaking arch bridges—that is,the Pingnan Third Bridge(a CFST arch bridge),with a span of 560 m,and the Tian’e Longtan Bridge(an SRC arch bridge),with a span of 600 m—have been built in the past five years,embodying great technological breakthroughs in the construction of these two types of arch bridges.This paper takes these two arch bridges as examples to systematically summarize the latest technological innovations and practices in the construction of CFST arch bridges and SRC arch bridges in China.The technological innovations of CFST arch bridges include cable-stayed fastening-hanging cantilevered assembly methods,new in-tube concrete materials,in-tube concrete pouring techniques,a novel thrust abutment foundation for nonrocky terrain,and measures to reduce the quantity of temporary facilities.The technological innovations of SRC arch bridges involve arch skeleton stiffness selection,the development of encasing concrete materials,encasing concrete pouring,arch rib stress mitigation,and longitudinal reinforcement optimization.To conclude,future research focuses and development directions for these two types of arch bridges are proposed.

Numerical and theoretical study of large-scale failure of strata overlying sublevel caving mines with steeply dipping discontinuities

The deformation and fracture evolution mechanisms of the strata overlying mines mined using sublevel caving were studied via numerical simulations.Moreover,an expression for the normal force acting on the side face of a steeply dipping superimposed cantilever beam in the surrounding rock was deduced based on limit equilibrium theory.The results show the following:(1)surface displacement above metal mines with steeply dipping discontinuities shows significant step characteristics,and(2)the behavior of the strata as they fail exhibits superimposition characteristics.Generally,failure first occurs in certain superimposed strata slightly far from the goaf.Subsequently,with the constant downward excavation of the orebody,the superimposed strata become damaged both upwards away from and downwards toward the goaf.This process continues until the deep part of the steeply dipping superimposed strata forms a large-scale deep fracture plane that connects with the goaf.The deep fracture plane generally makes an angle of 12°-20°with the normal to the steeply dipping discontinuities.The effect of the constant outward transfer of strata movement due to the constant outward failure of the superimposed strata in the metal mines with steeply dipping discontinuities causes the scope of the strata movement in these mines to be larger than expected.The strata in the metal mines with steeply dipping discontinuities mainly show flexural toppling failure.However,the steeply dipping structural strata near the goaf mainly exhibit shear slipping failure,in which case the mechanical model used to describe them can be simplified by treating them as steeply dipping superimposed cantilever beams.By taking the steeply dipping superimposed cantilever beam that first experiences failure as the key stratum,the failure scope of the strata(and criteria for the stability of metal mines with steeply dipping discontinuities mined using sublevel caving)can be obtained via iterative computations from the key stratum,moving downward toward and upwards away from the goaf.

Analytical and Numerical Study of the Hydro-Mechanical Behavior of a Cantilever Retaining Wall in Upward Seepage Conditions

Poor design of ground water evacuation mechanisms is often blocked and leads to the rise of ground water behind the wall. As a result, free water behind the wall that is not quickly evacuated, increases the lateral pressure and thus favors overturning failure. The resolution of the overturning problem in cantilever retaining walls caused by hydro-mechanical interaction was studied. An analytical and numerical method was used to study this type of wall-floor interaction. Then Coulomb’s design criterion against overturning to develop a mathematical model that compute analytical factor of safety against overturning in different water conditions and heel lengths was used. The modeling and simulation of this system in the Cast3m software which took into account a wide variety of floor and wall properties were performed. The numerical factor of safety against rollover was obtained, and the graphs for the factor of safety versus heel length and immersion depth for both methods were plotted. From (0 ≤ Hw ≤ H/3), water effect is not dangerous to wall stability against overturning and from (H/3 Hw ≤ H), water effect is very dangerous to wall stability against overturning. For analytical and numerical methods, the heel can be predimensioned against overturning as: Lc: [0.27H 0.38H], [0.29H 0.43H] for 0 ≤Hw ≤ H/3;[0.33H 0.45H], [0.39H 0.53H] for H/3 Hw ≤ 2H/3;[0.5H 0.6H], [0.50H 0.67H] for 2H/3 Hw≤ H. The numerical method guaranteeing more safety than the analytical method, Cantilever retaining walls can thus be pre-dimensioned considering Clayey-Sand soil in hydro-mechanical conditions.

The Effects of the Longitudinal Axis of Loading upon Bending, Shear and Torsion of a Thin-Walled Cantilever Channel Beam

Three aluminium channel sections of US standard extruded dimension are mounted as cantilevers with x-axis symmetry. The flexural bending and shear that arise with applied axial torsion are each considered theoretically and numerically in terms of two longitudinal axes of loading not coincident with the shear centre. In particular, the warping displacements, stiffness and stress distributions are calculated for torsion applied to longitudinal axes passing through the section’s centroid and its web centre. The stress conversions derived from each action are superimposed to reveal a net sectional stress distribution. Therein, the influence of the axis position upon the net axial and shear stress distributions is established compared to previous results for each beam when loading is referred to a flexural axis through the shear centre. Within the net stress analysis is, it is shown how the constraint to free warping presented by the end fixing modifies the axial stress. The latter can be identified with the action of a ‘bimoment’ upon each thin-walled section.

Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under transverse shear and axial torsional loading are each considered theoretically. These analyses involve the location of the shear centre at which transverse shear forces when applied do not produce torsion. This centre, when taken to be coincident with the centre of twist implies an equivalent reciprocal behaviour. That is, an axial torsion applied concentric with the shear centre will twist but not bend the beam. The respective bending and shear stress conversions are derived for each action applied to three aluminium alloy extruded channel sections mounted as cantilevers with a horizontal principal axis of symmetry. Bending and shear are considered more generally for other thin-walled sections when the transverse loading axes at the shear centre are not parallel to the section = s centroidal axes of principal second moments of area. The fixing at one end of the cantilever modifies the St Venant free angular twist and the free warping displacement. It is shown from the Wagner-Kappus torsion theory how the end constrained warping generates an axial stress distribution that varies with the length and across the cross-section for an axial torsion applied to the shear centre. It should be mentioned here for wider applications and validation of the Vlasov theory that attendant papers are to consider in detail bending and torsional loadings applied to other axes through each of the centroid and the web centre. Therein, both bending and twisting arise from transverse shear and axial torsion applied to each position being displaced from the shear centre. Here, the influence of the axis position upon the net axial and shear stress distributions is to be established. That is, the net axial stress from axial torsional loading is identified with the sum of axial stress due to bending and axial stress arising from constrained warping displacements at the fixing. The net shear stress distribution overlays the distributions from axial torsion and that from flexural shear under transverse loading. Both arise when transverse forces are displaced from the shear centre.

Poly-Silicon Micromachined Switch

By using LPCVD SiO 2 and poly silicon as sacrificial layer and cantilever respectively,a poly silicon micromachined RF MEMS(radio frequency microelectronic mechanical system) switch is fabricated.During the fabrication process,the stress of poly silicon is released to prevent poly silicon membrane from bending,and the issue of compatibility between RF switch and IC process technology is also resolved.The low residual tensile stress poly silicon cantilever is obtained by the optimization.The switch is tested,and the preliminary test results show:the pull down voltage is 89V,and the switch speed is about 5μs.The switch provides the potential to build a new fully monolithic integrated RF MEMS for radar and communications applications.

Fabrication and Numerical Simulation of a MicromachinedContact Cantilever RF-MEMS Switch

This paper reports a contact cantilever MEMS switch. The designed switch has a metal cantilever that acts as an electrostatically activated switch with processing options to achieve dielectric isolation of the controlvoltage path from the signal path. To obtain good material properties,an ANSYS FEA tool is used to optimize the structure. The RF MEMS switch is fabricated via a surface micromachining process. The switch has an actuation voltage of 12V,which is close to the simulated value of 11V. The measured and the HFSS simulated isolations are both higher than - 20dB from 0.05 to 10GHz. The measured insertion loss is less than - 0.9dB, relatively larger than the simulated loss of less than - 0.2dB from 0.05 to 10GHz. This is because a contact resistance introduced due to poor physical contact between the bottom lines and the metal cantilever.

Analysis and Design for a Micro Mechanical Optical Switch

The mechanical and electric characteristics of a cantilever beam micro opto mechanical switch are studied theoretically,with which the dependence of the flexion on the applied voltage is derived,as well as the formula of the threshold voltage.The applied voltage,having no connection with the width of the beam,is in inverse proportion to the square of the beam's length.The deflection at the beam's tip cannot exceed 1/3 of the distance between two adjacent electrodes.These results are the basis of the switch design and development.

A GaAs-Based MOEMS Tunable RCE Photodetector with Single Cantilever Beam

A GaAs-based micro-opto-electro-mechanical-systems(MOEMS) tunable resonant cavity enhanced(RCE) photodetector with a continuous tuning range of 31nm under a 6V tuning voltage is demonstrated.The single cantilever beam structure is adopted for this MOEMS tunable RCE photodetector.The maximum and minimum peak quantum efficiency during the tuning are 36.9% and 30.8%,respectively.The maximum and minimum full-width-at-half-maximum (FWHM) are 20nm and 14nm,respectively.The dark current density is 7.46A/m2 without bias.