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.

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.

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.

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.

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.

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.

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.

Tunnelling performance prediction of cantilever boring machine in sedimentary hard-rock tunnel using deep belief network

Evaluating the adaptability of cantilever boring machine(CBM) through in-depth excavation and analysis of tunnel excavation data and rock mass parameters is the premise of mechanical design and efficient excavation in the field of underground space engineering.This paper presented a case study of tunnelling performance prediction method of CBM in sedimentary hard-rock tunnel of Karst landform type by using tunneling data and surrounding rock parameters.The uniaxial compressive strength(UCS),rock integrity factor(Kv),basic quality index([BQ]),rock quality index RQD,brazilian tensile strength(BTS) and brittleness index(BI) were introduced to construct a performance prediction database based on the hard-rock tunnel of Guiyang Metro Line 1 and Line 3,and then established the performance prediction model of cantilever boring machine.Then the deep belief network(DBN) was introduced into the performance prediction model,and the reliability of performance prediction model was verified by combining with engineering data.The study showed that the influence degree of surrounding rock parameters on the tunneling performance of the cantilever boring machine is UCS > [BQ] > BTS >RQD > Kv > BI.The performance prediction model shows that the instantaneous cutting rate(ICR) has a good correlation with the surrounding rock parameters,and the predicting model accuracy is related to the reliability of construction data.The prediction of limestone and dolomite sections of Line 3 based on the DBN performance prediction model shows that the measured ICR and predicted ICR is consistent and the built performance prediction model is reliable.The research results have theoretical reference significance for the applicability analysis and mechanical selection of cantilever boring machine for hard rock tunnel.

A study of a slim compact piezo inertia actuator

Most previously reported inertia actuators suffer from the problems of low speed and large size.To overcome these shortcomings,this study proposes a slim compact piezo inertia actuator based on the principle of stick–slip drive.Actuated by the transverse motion of a cantilever beam forming part of a monolithic elastomer,this actuator achieves a high velocity.The construction and basic operating principle of the actuator are discussed in detail.Commercial finite element analysis software is employed to determine the appropriate geometry for the monolithic elastomer.To study the actuator’s mechanical characteristics,a prototype is fabricated and a series of experimental tests are performed.According to the results of these tests,the maximum velocity and maximum load force are about 24.03 mm/s and 1.96 N,respectively,and the minimum step size is about 0.47μm.It is shown that the inertia actuator based on a monolithic elastomer with a cantilever beam not only has a slim compact structure,but also exhibits good output characteristics.

Natural vibration of cantilever porous twisted plate with variable thickness in different directions

In this paper,the blade is assumed to be a rotating variable thickness cantilever twisted plate structure,and the natural vibrations of variable thickness cantilever twisted plate made of metal porous material are studied.It is assumed that the thickness of the plate changes along spanwise direction and chordwise direction,respectively,and it changes in both directions.The classical thin shell theory,the first and second fundamental forms of surface and von Karman geometric relationship are employed to derive the total potential energy and kinetic energy of the cantilever twisted plate,in which the centrifugal force potential due to high rotational speed is included.Then,according to the Rayleigh-Ritz procedure and applying the polynomial functions which satisfy the cantilever boundary conditions,the dynamic system expressed by equations of motion is reduced to an eigenvalue problem.By numerical simulation,the frequency curves and the mode shapes of the twisted plate can be obtained to reveal the internal connection between natural vibration and the parameters.A series of comparison studies are performed to verify the accuracy of the present formulation and calculations,in which compared data come from experimental,finite element method and theoretical calculation,respectively.The influence of pre-twist angle,three different forms of thickness taper ratio and rotational speed on natural vibration,mode exchange and frequency veering phenomenon of the system is discussed in detail.In addition,the approach proposed here can efficiently extract analytical expressions of mode functions for rotating variable thickness cantilever twisted plate structures.

Corrigendum to“Noise colour influence on escape times in nonlinear oscillators-experimental and numerical results”[Theor.App.Mech.Lett.13(2023)100420]

The original article includes the incorrectly printed Figs.1,2 and 4.The correct figures are included in this note.Fig.1.(a)Experimental setup:The shaker is used to generate the external,harmonic and random excitation to the base of the metal cantilever.The resulting oscillations are measured with a strain gauge.A nonlinear restoring force follows from the magnets mounted at the cantilever tip and the fixed frame.(b)Measured cantilever response to sinusoidal excitation and experimental procedure:A sweep up is used to realize the high amplitude orbit.When the excitation frequency reaches 39.6 Hz,noise is added to the input and a noise induced escape is observed.(c)Time series of a strain gauge signal:The forcing frequency is 39.6 Hz and the response is initiated in the high energy orbit.After about 37.0 s an escape towards the low amplitude orbit is observed.

Ensemble 1D DenseNet Damage Identification Method Based on Vibration Acceleration

Convolution neural networks in deep learning can solve the problem of damage identification based on vibration acceleration.By combining multiple 1D DenseNet submodels,a new ensemble learning method is proposed to improve identification accuracy.1D DenseNet is built using standard 1D CNN and DenseNet basic blocks,and the acceleration data obtained from multiple sampling points is brought into the 1D DenseNet training to generate submodels after offset sampling.When using submodels for damage identification,the voting method ideas in ensemble learning are used to vote on the results of each submodel,and then vote centrally.Finally,the cantilever damage problem simulated by ABAQUS is selected as a case study to discuss the excellent performance of the proposed method.The results show that the ensemble 1D DenseNet damage identification method outperforms any submodel in terms of accuracy.Furthermore,the submodel is visualized to demonstrate its operation mode.

Design Strategies for Leaning-Type Arch Bridges

This paper presents a study on the design strategy of leaning-type arch bridges.The main characteristics of leaning-type arch bridges are first introduced;Kunshan Yufeng Bridge is taken as an example to discuss different aspects of a design strategy,which includes self-system optimization,selection of beam length and bridge deck position,and other aspects.This paper can be used as a reference to further improve and develop bridge design.

Modeling and power performance improvement of a piezoelectric energy harvester for low-frequency vibration environment

A novel oscillator structure, bimorph piezoelectric cantilever beam with two-stepped variable thicknesses,is proposed to improve the energy harvestingperformance of the vibration energy harvester (VEH) under low-frequency vibration environment. Firstly, the piezoelectric cantilever is segmented to obtain the energy functions based on the Euler-Bernoulli beam assumptions, and the Galerkin approach is utilized to discretize the energy functions. Applying boundary conditions and continuity conditions enforced at separation locations, the electromechanical coupled governing equations for the piezoelectric energy harvesterareintroduced by means of the Lagrange equations. Furthermore, the steady state response expressions are obtained for harmonic base excitations at arbitrary frequencies. Numerical results are computed and the effects ofthe lengths-ratio, thicknesses-ratio,end thicknessand load resistance on the output voltage, harvested power and power density are discussed. Moreover, to verify thecorrectness ofanalytical results, the finite element method (FEM)simulationis also conducted to analyze performance of the proposed VEH, where a good agreement is presented. All the results show thatthe present oscillator structureis moreefficient than the conventional uniform beam structure, specifically, for vibration energy harvesting in low-frequency environment.

Longwall mining “cutting cantilever beam theory” and 110 mining method in China——The third mining science innovation

With the third innovation in science and technology worldwide, China has also experienced thismarvelous progress. Concerning the longwall mining in China, the ＂masonry beam theory＂ （MBT） wasfirst proposed in the 1960s, illustrating that the transmission and equilibrium method of overburdenpressure using reserved coal pillar in mined-out areas can be realized. This forms the so-called ＂121mining method＂, which lays a solid foundation for development of mining science and technology inChina. The ＂transfer rock beam theory＂ （TRBT） proposed in the 1980s gives a further understanding forthe transmission path of stope overburden pressure and pressure distribution in high-stress areas. In thisregard, the advanced 121 mining method was proposed with smaller coal pillar for excavation design,making significant contributions to improvement of the coal recovery rate in that era. In the 21st century,the traditional mining technologies faced great challenges and, under the theoretical developmentspioneered by Profs. Minggao Qian and Zhenqi Song, the ＂cutting cantilever beam theory＂ （CCBT） wasproposed in 2008. After that the 110 mining method is formulated subsequently, namely one stope face,after the first mining cycle, needs one advanced gateway excavation, while the other one is automaticallyformed during the last mining cycle without coal pillars left in the mining area. This method can beimplemented using the CCBT by incorporating the key technologies, including the directional presplittingroof cutting, constant resistance and large deformation （CRLD） bolt/anchor supporting systemwith negative Poisson＇s ratio （NPR） effect material, and remote real-time monitoring technology. TheCCBT and 110 mining method will provide the theoretical and technical basis for the development ofmining industry in China.

Innovation and future of mining rock mechanics

The 121 mining method of longwall mining first proposed in England has been widely used around the world.This method requires excavation of two mining roadways and reservation of one coal pillar to mine one working face.Due to considerable excavation of roadway,the mining roadway is generally destroyed during coal mining.The stress concentration in the coal pillar can cause large deformation of surrounding rocks,rockbursts and other disasters,and subsequently a large volume of coal pillar resources will be wasted.To improve the coal recovery rate and reduce excavation of the mining roadway,the 111 mining method of longwall mining was proposed in the former Soviet Union based on the 121 mining method.The 111 mining method requires excavation of one mining roadway and setting one filling body to replace the coal pillar while maintaining another mining roadway to mine one working face.However,because the stress transfer structure of roadway and working face roof has not changed,the problem of stress concentration in the surrounding rocks of roadway has not been well solved.To solve the above problems,the conventional concept utilizing high-strength support to resist the mining pressure for the 121 and 111 mining methods should be updated.The idea is to utilize mining pressure and expansion characteristics of the collapsed rock mass in the goaf to automatically form roadways,avoiding roadway excavation and waste of coal pillar.Based on the basic principles of mining rock mechanics,the“equilibrium mining”theory and the“short cantilever beam”mechanical model are proposed.Key technologies,such as roof directional presplitting technology,negative Poisson’s ratio(NPR)high-prestress constant-resistance support technology,and gangue blocking support technology,are developed following the“equilibrium mining”theory.Accordingly,the 110 and N00 mining methods of an automatically formed roadway(AFR)by roof cutting and pressure releasing without pillars are proposed.The mining methods have been applied to a large number of coal mines with different overburdens,coal seam thicknesses,roof types and gases in China,realizing the integrated mode of coal mining and roadway retaining.On this basis,in view of the complex geological conditions and intelligent mining demand of coal mines,an intelligent and unmanned development direction of the“equilibrium mining”method is prospected.

Suppression of multiple modal resonances of a cantilever beam by an impact damper

Impact dampers are usually used to suppress single mode resonance. The goal of this paper is to clarify the difference when the impact damper suppresses the resonances of different modes. A cantilever beam equipped with the impact damper is modeled. The elastic contact of the ball and the cantilever beam is described by using the Hertz contact model. The viscous damper between the ball and the cantilever beam is modeled to consume the vibrational energy of the cantilever beam. A piecewise ordinary differential-partial differential equation of the cantilever beam is established, including equations with and without the impact damper. The vibration responses of the cantilever beam with and without the impact damper are numerically calculated. The effects of the impact absorber parameters on the vibration reduction are examined. The results show that multiple resonance peaks of the cantilever beam can be effectively suppressed by the impact damper. Specifically, all resonance amplitudes can be reduced by a larger weight ball. Moreover, the impacting gap is very effective in suppressing the vibration of the cantilever beam. More importantly, there is an optimal impacting gap for each resonance mode of the cantilever beam, but the optimal gap for each mode is different.