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.

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.

The analytical solutions for orthotropic cantilever beams (Ⅰ):Subjected to surface forces

This paper first gives the general solution of two-dimensional orthotropic media expressed with two harmonic displacement functions by using the governing equations. Then, based on the general solution in the case of distinct eigenvalues, a series of beam problems, including the problem of cantilever beam under uniform loads, cantilever beam with axial load and bending moment at the free end, cantilever beam under the first, second, third and fourth power ofx tangential loads, is solved by the superposition principle and the trial-and-error methods.

The analytical solutions for orthotropic cantilever beams (II):Solutions for density functionally graded beams

In this paper, the specific solutions of orthotropic plane problems with body forces are derived. Then, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally graded orthotropic media, a series of beam problem, including the problems of cantilever beam with body forces depending only on z or on x coordinate and expressed by z or x polynomial is solved by the principle of superposition and the trial-and-error method.

BIPARAMETRIC PERTURBATION SOLUTIONS OF LARGE DEFLECTION PROBLEM OF CANTILEVER BEAMS

The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach. This kind of substitution can transform the basic equation, an integral differential equation into nonlinear algebraic ones, thus simplify computational process. Compared with present results, it indicates that the large deflection problem solved by using pseudolinear analysis can lead to simple and precise results.

ELASTIC EFFECT IN DYNAMIC RESPONSE OF PLASTIC CANTILEVER BEAMS TO IMPACT

A lumped masses-springs model is proposed to analyze the dynamic response of an elastic-plastic cantilever beam resulting from impact. The numerical results are in good agreement with those by finite-element approaches. The simplified model can catch the most essential features of elastic-plastic response of beams; in particular, it demonstrates the effect of elastic deformation on the distribution of bending moment and energy dissipation, and provides valuable quatitative results.

AN ANALYSIS ON CHARACTERISTIC OF MAGNETOELASTICITY OF A MAGNETIC FIELD MICROSENSOR MADE OF CANTILEVERED PLATES WITH FERROMAGNETIC FILMS

The purpose of this paper is to study the magnetomechanicalcharacteristic of a microsensor which is composed of a cantileveredbeam-plate with ferromagnetic films in order to measure the magneticfield from the deformation of plate when the microsensor is locatedin the magnetic field. To this end, a nu- merical approach made up ofthe finite element method for magnetic field and the finitedifference method for deflection of the microsensor is proposed toperform the numerical analysis of deflection under magnetoelasticinteraction. Some quantitative results of a case study for themagnetoelastic characteristic between the mag- netic field anddeflection of the microsensor in the magnetic field are given. Theresults show that this mi- crosensor can be used not only to measurethe magnitude of magnetic intensity, but also to possibly monitor thedirection of the vector of the magnetic field.

Analytic Static Deflection Solutions of Uniform Cantilever Beams Resting on Nonlinear Elastic Rotational Boundary

In the paper,the analytic static deflection solutions of uniform cantilever beams resting on nonlinear elastic rotational boundary are developed by the Modified Adomian Decomposition Method(MADM).If the applied force function is an analytic function,then the deflection function can be derived and expressed in Maclaurin series.A recurrence relation for the coefficients of the Maclaurin series is derived.It is shown that the proposed solution method is accurate and efficient.The solution method can be successfully applied to the uniform cantilever beam and non-linear elastic rotational boundary problem.

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.

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.

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.

Fabrication and Simulation of an Electromagnetic Microrelay

The fabrication and simulation of an electromagnetic microrelay are presented based on micro electromechanical systems (MEMS) technique.The microrelay dimensions of about 4mm×4mm×0 5mm are fabricated with the common technique of micromachining.Compared with the traditional relays,a planar coil is substituted for a solenoid coil to favor the MEMS fabrication.Moreover,a bi supporter cantilever beam with high sensitivity is fabricated to act as the movable electrode of the microrelay.Theoretical calculations and simulations are also carried out with respect to the electromagnetic force yielded by the exciting electromagnetic coil.The structure and parameters concerning the electromagnetic microrelay can be optimized using the results.

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.

Nonlinear Bend Stiffener Analysis Using A Simple Formulation and Finite Element Method

Flexible marine risers are commonly used in deepwater floating systems. Bend stiffeners are designed to protect flexible risel against excessive bending at the connection with the hull. The structure is usually analyzed as a cantilever beam subjected to an inclined point load. As deflections are large and the bend stiffener material exhibits nonlinear stress-strain characteristics, geometric and material nonlinearities are important considerations. A new approach has been developed to solve this nonlinear problem. Its main advantage is its simplicity; in fact the present method can be easily implemented on a spreadsheet. Finite element analysis using ABAQUS is performed to validate the method. Solid elements are used for the bend stiffener and flexible pipe. To simulate the near inextensibility of flexible risers, a simple and original idea of using truss elements is proposed. Through a set of validation studies the present method is found to be in a good agreement with the finite element analysis. Further, parametric studies are performed by using both methods to identify the key parameters and phenomena that are most critical in design. The most important finding is that the common practice of neglecting the internal steel sleeve in the bend stiffener analysis is non-conservative and therefore needs to be reassessed.

Analytical solution for functionally graded anisotropic cantilever beam under thermal and uniformly distributed load

The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.