Nonplanar flow-induced vibrations of a cantilevered PIP structure system concurrently subjected to internal and cross flows

Pipe-in-pipe(PIP)structures are widely used in offshore oil and gas pipelines to settle thermal insulation issues.A PIP structure system usually consists of two concentric pipes and one softer layer for thermal insulation consideration.The total response of the system is related to the dynamics of both pipes and the interactions between these two concentric pipes.In the current work,a theoretical model for flow-induced vibrations of a PIP structure system is proposed and analyzed in the presence of an internal axial flow and an external cross flow.The interactions between the two pipes are modeled by a linear distributed damper,a linear distributed spring and a nonlinear distributed spring along the pipe length.The unsteady hydrodynamic forces due to cross flow are modeled by two distributed van der Pol wake oscillators.The nonlinear partial differential equations for the two pipes and the wake are further discretized by the aid of Galerkin’s technique,resulting in a set of ordinary differential equations.These ordinary differential equations are further numeri cally solved by using a fourth-order Runge-Kutta integration algorithm.Phase portraits,bifurcation diagrams,an Argand diagram and oscillation shape diagrams are plotted,showing the existence of a lock-in phenomenon and figure-of-eight trajectory.The PIP system subjected to cross flow displays some interesting dynamical behaviors different from that of a single-pipe structure.

Effects of supported angle on stability and dynamical bifurcations of cantilevered pipe conveying fluid

The effects of the supported angle on the stability and dynamical bifurcations of an inclined cantilevered pipe conveying fluid are investigated. First, a theoretical model of the pipe is developed through the force balance and stress-strain relationship. Second, the response surfaces, stability, and critical lines of the typical hanging system （H-S） and standing system （S-S） are discussed based on the modal analysis. Last, the bifurcation diagrams of the pipe are presented for different supported angles. It is shown that pipes will undergo a series of bifurcation processes and show rich dynamic phenomena such as buckling, Hopf bifurcation, period-doubling bifurcation, chaotic motion, and divergence motion.

Dynamical Stability of Cantilevered Pipe Conveying Fluid with Inerter-Based Dynamic Vibration Absorber

Cantilevered pipe conveying fluid may become unstable and flutter instability would occur when the velocity of the fluid flow in the pipe exceeds a critical value.In the present study,the theoretical model of a cantilevered fluid-conveying pipe attached by an inerter-based dynamic vibration absorber(IDVA)is proposed and the stability of this dynamical system is explored.Based on linear governing equations of the pipe and the IDVA,the effects of damping coefficient,weight,inerter,location and spring stiffness of the IDVAon the critical flow velocities of the pipe system is examined.It is shown that the stability of the pipe may be significantly affected by the IDVA.In many cases,the stability of the cantilevered pipe can be enhanced by designing the parameter values of the IDVA.By solving nonlinear governing equations of the dynamical system,the nonlinear oscillations of the pipe with IDVA for sufficiently high flow velocity beyond the critical value are determined,showing that the oscillation amplitudes of the pipe can also be suppressed to some extent with a suitable design of the IDVA.

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.

Effects of Span Length and Additional Structure on Flow-Induced Transverse Vibration Characteristic of a Cantilevered Rectangular Prism

We consider the effects of the aspect ratio L/H (where L is the length of a prism, and H is the height of a prism normal to the flow direction) and the size of additional structures (which are a plate and a fin on the surface of a prism) on a vibration characteristic of a cantilevered rectangular prism. The present research is intended to support the analysis of energy harvesting research on the flow-induced vibration in water flow using a magnetostrictive phenomenon. The prisms are constructed from stainless steel and mounted elastically to a plate spring attached to the ceiling wall of the water tunnel. The prisms with aspect ratios of L/H ≥ 5 have reasonably identical vibration characteristics. However, the difference in the vibration characteristic appears distinctly on a rectangular prism with an aspect ratio of L/H = 2.5. The rectangular prism with an aspect ratio of L/H = 10 and a side ratio of D/H = 0.2 has a stable and large response amplitude and oscillates with a lower velocity. The length of the added plate and the size of the added fin influence the velocity of vibration onset. If the length of the added plate and fin size on the rectangular prism with D/H = 0.2 becomes large, the curve of the response amplitude shifts to that of the rectangular prism with D/H= 0.5. The response amplitude of the rectangular prism with/without plate or fin is found to be related to the second moment of area of the prism.

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.

Effect of Moving Endwall on Hub Leakage Flow of Cantilevered Stator in a Linear Compressor Cascade

The cantilevered stator has the advantages of reducing mass and axial length of highly loaded com-pressor.The details of the hub leakage flow resulting from the clearance between the high-speed moving hub and the cantilevered stator hub are unclear.In this paper,the effect of a moving endwall on the hub leakage flow of a cantilevered stator in a linear compressor cascade was studied.After the simulation method was verified with the experimental results,the time-averaged results of unsteady Reynolds averaged Navier-Stokes(URANS)were selected to study a case with a hub clearance of 2 mm.The results show that the effect of the moving endwall of the cantilevered cascade on the general characteristics with below 30%span increases the leakage mass flow rate and reduces the static pressure coefficient at three conditions of 0°,6°,and-7°incidences,and the change is most significant at-7°incidence.The effect of the moving endwall on the total pressure loss coefficient varies with different operating conditions,which decreases by 15.94%at 0°incidence,and increases by 4.77%and 18.51%at 6°incidence and-7°incidence,respectively.The influence of the moving endwall is below 14%span at-7°incidence,below 23%span at 0°incidence,and below 30%span at 6°incidence.These effects correspond to the static pressure coefficient and the difference of static pressure coefficient representing the blade loading.In designing the cantilevered stator and matching between the stages of a multistage compressor,the quantitative research results of this paper have certain guiding significance.

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.

Bending characteristic of a cantilevered magnetostrictive film-substrate system

The bending problem of a film-substrate cantilever with arbitrary film-to-substrate thickness ratio is solved exactly by employing the force equilibrium equation, and then the optimization and application of the bending characteristic of the magne-tostrictive cantilever is discussed. Furthermore, the influence of geometrical and physical parameters of the two cantilever components on the maximum free-end deflection of the cantilever is addressed. The results indicate that as the substrate thickness is kept constant, the greater film-to-substrate stiffness ratio will induce a larger deflection, while for the case of fixed total cantilever thickness, the optimal cantilever deflection is independent of the physical parameters of the materials such as Young’s modulus and Poisson’s ratio.

Design and optimization of cantilevered magnetostrictive film-substrate microactuator

The exact solution for the bending problem of a free-end point loaded film- substrate cantilever with arbitrary film-to-substrate thickness ratio is obtained by using the basic mechanical equilibrium equation. And then the problem of design and optimization for microactuator buildup of film-substrate cantilever is discussed by taking into account the effect of geometrical and physical parameters of the cantilever components. Furthermore, the optimal condition for actuator application is presented and some theoretical problems are clarified. The results show that, in general, the greater the film-to-substrate thickness ratio, the higher the ability of taking load, namely the larger the exerted force of the cantilever when the thickness of substrate is kept constant. When the total thickness of the cantilever is kept constant, however, the free-end exerted force will experience a maximum and this maximum value of the exerted force will decrease with the increasing film-to-sub- strate stiffness ratio. Meanwhile, the optimal thickness ratio corresponding to this maximum exerted force also decreases with the increasing stiffness ratio. Whether for the cases of fixed substrate or fixed total thickness, the influence of Poisson’s ratio of two cantilever components on the exerted force is remarkable, and should not be neglected.

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.