Nonlinear behavior analysis of geared rotor bearing system featuring confluence transmission

In this paper, the nonlinear vibration characteristics of geared rotor bearing system and the interactions among gears, shafts, and plain journal bearings were studied. First, with the consideration of backlash, transmission error, time-varying mesh stiffness, and layout parameters, the dynamic model of geared rotor bearing system featuring confluence transmission was proposed. The nonlinear oil-film forces were computed with the Reynolds equation for finite-length journal bearings. Second, the responses of meshing vibration and bearing vibration were discussed. The numerical results revealed that the system exhibited a diverse range of periodic, sub-harmonic, and chaotic behaviors. Under different ranges of rolling frequency, the system got into chaos state through different roads. Moreover, in lower frequency, meshing vibration showed coexist of different periodic motions. Lastly, couplings of nonlinear oil-film force and nonlinear gear mesh force were discussed through a range of rolling frequencies. Gear-bearing dynamic interactions were demonstrated through the analysis of dynamic gear loads and dynamic bearing loads, and the coupling effect behaved different when rolling frequency changed.     

Dynamic characteristics of a beam specimen featuring electrorheological fluids

The experimental investigations are focused on evaluating the elastodynamic response characteristics of beams fabricated in electrorheological (ER) fluids when the beams are subjected to forced vibration. The beams used in this experiment are composed of three kinds of materials: structural material, damping material and sealant material. Beams with different ER fluids and different structural material are made and tested. The results demonstrate clearly the ability to significantly change the vibrational characteristics of beams fabricated in smart composites by changing the electric field intensity imposed on the fluid domains. With the ASTM standard E756-83 equations, the Young's modulus of the beams and the shear modulus of ER fluids are evaluated.     

弱不连续问题高阶有限元离散系统的GAMG法

弱不连续问题(如含夹杂问题)是固体力学计算中的一类重要问题。高阶有限元方法由于其具有更好的逼近效果,是确保数值解在界面保持较高精度的计算方法之一。但与线性元相比,高阶单元需要更多的计算机存储单元,具有更高的计算复杂性。本文利用两水平算法的思想,将高阶有限元离散系统化归于线性元离散系统的求解,为弱不连续问题高阶有限元离散系统设计了一种新的基于几何与分析信息的代数多重网格(GAMG)法,并应用于圆形求解域含单夹杂问题的高阶有限元离散系统的求解。数值试验结果表明,相比于常用GAMG法,新方法的迭代次数基本不依赖于问题规模、单元阶次以及杨氏模量的间断性,CPU计算时间得到明显改善,具有更好的计算效率和鲁棒性,可大大提高弱不连续问题有限元分析的整体效率。     

Nonlinear resonances and wave jumps in media with higher-order dispersion

A new technique for systematically investigating biperiodic (two-wave) steady-state solutions is described with reference to modified Korteweg-de Vries and Schrödinger equations which generalize the conventional model equations for waves on water, in plasmas, and in nonlinear optics [1]. Among these solutions those with ordinary and resonance wave interactions are distinguished. Both singular solutions similar to the solitons of a resonantly interacting wave envelope and solitary waves are found. The soliton-like solutions obtained are used for describing the wave jump structure.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 113–124, July–August, 1996.     

Limit analysis of masonry structures with free discontinuities

We formulate a novel procedure for the limit analysis of two-dimensional masonry structures subject to arbitrary loading conditions. The proposed approach works in the framework of free discontinuity methods, on examining collapse mechanisms that exhibit free crack opening discontinuities. The load bearing capacity and the collapse mechanism of the structure are obtained through a fully variational approach, by minimizing a kinetic functional that admits the collapse crack pattern as a variable. Numerical examples illustrate the practical application of the proposed procedure to the limit analysis of a variety of masonry walls and arches subject to foundation settlements, vertical and horizontal forces.     

Nonlinear dynamics of higher-order rogue waves in a novel complex nonlinear wave equation

Nonlinear Dynamics - A novel complex nonlinear wave equation was recently found by Mukherjee and Kundu (Phys. Lett. A 383:985–990, 2019) and shown that it possesses the first-order rogue...     

Vertical dynamics of a pantograph carbon-strip suspension under stochastic contact-force excitation

In electric trains, a pantograph is mounted on the roof of the train to collect power through contact with an overhead catenary wire. The carbon-strip suspension of a pantograph, along which contact with the catenary occurs, is subjected to harmonic and stochastic contact-force excitations. In this paper, vertical dynamics of the carbon-strip suspension is studied with an aim of improving the reliability and safety of running trains. A single-degree-of-freedom model of the carbon-strip suspension with nonlinear stiffness is developed using parameter values of the DSA X pantograph. Through stochastic averaging, a Fokker–Planck–Kolmogorov equation governing the stationary response of the carbon-strip suspension is set up. Based on the transition probability density of the stationary response, it is found that random jumps and bifurcations in the carbon-strip motion can occur. The possibility of motion bifurcations and the frequency of random jumps warrant consideration in advanced design of carbon-strip suspensions.     

Dynamic crushing characteristics of high strength steel cylinders with elliptical geometric discontinuities

Thin-walled members are commonly used as energy absorbers in engineering structures and often contain cutouts. This study performed numerical simulations of high strength steel cylindrical shells with elliptical cutouts subjected to dynamic axial impact. The LS-DYNA code was the primary analytical tool used to analyze the influence of cutout locations, cutout shapes and symmetry of cutout on the energy absorption capabilities and the crush characteristics of tubes with a cutout. For high strength steel tubes made from a rate sensitive material, the stress-strain curves of different strain rates were used to elucidate the effect of dynamic impact on the strain rate. Our results show that collapse crushing behavior is strongly influenced by the location and symmetry of cutouts and the variation of major axis influences the peak crush load.     

A higher-order analysis of natural convection in a corner

A study of natural convection flow in a right angled corner formed by a semi-infinite vertical plate, which is maintained at the ambient temperature, and a semi-infinite horizontal plate, which is prescribed with a uniform heat flux, is carried out for moderately large values of the Grashof number by the method of matched asymptotic expansions. Higher-order corrections are found for the velocity and temperature fields as well as for the heat transfer and skin friction coefficients. The interaction between the two boundary-layers, which form on the vertical and horizontal plates, takes place through an isothermal outer flow. Eigenvalues and their corresponding eigenfunctions which are associated with the inner expansions have been sought. We are able to continue the solution up to the contribution played by the first eigenvalue and to uniquely find the first eigensolution. Numerical results have been obtained for a wide range of values of the Prandtl number, , but the results are only presented for =0.72 (air) and 6.7 (water). It is found that higher-order corrections to the classical boundary-layer theory are quite significant even for Grashof numbers of order 10⁹.Eine Untersuchung über freie Konvektionsströmung in einer rechtwinkligen Ecke, die aus einer horizontalen und vertikalen, halbunendlichen Platte gebildet wird, wurde für ziemlich hohe Werte der Grashofzahl mit der asymptotisch, erwartungstreuen Schätzung durchgeführt. Bei der vertikalen Platte wird die Umgebungstemperatur konstant gehalten und die Horizontale Platte steht unter gleichmäßigem Wärmefluß. Für die Geschwindigkeits-und Temperaturfelder sind gleich gute Verbesserungen höherer Ordnung gefunden worden, wie für die Wärmeübertragung und den Oberflächenreibungskoeffizient. Die gegenseitige Beeinflussung der beiden Grenzschichten, die sich auf der horizontalen und vertikalen Platte bilden, entstand durch eine isotherme Außenströmung. Eigenwerte und ihre darauf bezogenen Eigenfunktionen, die mit der Expansion verbunden sind, wurden ermittelt. Wir sind in der Lage, die Lösung durch eine Approximation hoher Ordnung zu ersetzen und dadurch eine einzige Eigenlösung zu finden. Die numerischen Ergebnisse sind für weite Bereiche der Prandtlzahl, erhalten worden. Dargestellt wurden jedoch nur die für =0,72 (Luft) und 6,7 (Wasser). Es wurde herausgefunden, daß die Verbesserungen höherer Ordnung für die klassische Grenzschichttheorie sehr bedeutend sind, besonders für die Grashofzahlen der Ordnung 10⁹.     

Nonlinear analysis of a cracked rotor with whirling

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Elastic-plastic analysis of a wheel rolling on a rigid track

A consistent finite element model for a circular wheel is developed based on triangular and quasi-triangular domains and a piecewise linear displacement field. The minimum stress-rate principle of plasticity is used to obtain the solution of this two-dimensional continuum problem with internal unloading. A piecewise approximation of the Tresca yield condition is used. Elastic-plastic solutions of a wheel rolling on a rigid track under its own weight and a hub load are obtained for the first few revolutions until a steady state condition is reached. Shake-down conditions for the wheel are demonstrated.     

Theoretical analysis of dehumidification process in a desiccant wheel

A mathematical model based on the one-dimensional Navier–Stokes equation is described. The current model is capable of predicting the transient and steady-state transport in a desiccant wheel. It reveals the moisture and temperature in both the airflow channels and the sorbent felt, in detail, as a function of time. The predicted results are validated against the data taken from experimental results, with reasonable accuracy. Therefore, the numerical model is a practical tool for understanding and accounting for the complicated coupled operational process inside the wheel. Consequently, it is useful for parameter studies. As a demonstration of its utility, the model is employed to study the effect of felt thickness and passage shape on the performance of a desiccant wheel.     

Theoretical analysis of a wheel driven root crop harvester

A prototype of a wheel driven trailer was developed to simulate a wheel driven trailed root crop harvester. The mobility of the prototype tractor-trailer system was improved by driving the trailer wheels by a mounted engine. A mathematical model to predict the mobility and the stability of the system was developed. The model was validated by field experiments conducted in plowed, rotary tilled and untilled fields. The model was found to predict performance with a high accuracy. Parameter studies were conducted to investigate the effects of several design parameters, such as the peripheral velocity ratio (R_s), the weight of the trailer (m₁), the trailer's C.G. location (L_L) and the height of a hitch point (h), on the mobility and the stability of the system.     

Contact of a rotating wheel with a flat

The contact problem of a wheel having a small flat, pressed onto an elastically similar half-plane, is considered. The contact law and pressure distribution is found, for all angular positions of the wheel, i.e. for all orientations of the flat under quasi-static conditions, and the evolving distributions tracked out, as the wheel rotates.     

Analysis of characteristics of rogue waves for higher-order equations

Nonlinear Dynamics - For various nonlinear physical equations, we describe the features of their rogue waves using simplified forms of their intensities and also by finding ‘volumes’....     

Nonlinear characteristics of the interaction of a turbulent boundary layer with a wavy surface

A nonlinear interaction of a turbulent boundary layer with a wavy surface of a solid body or a liquid whose level has a deviation in the form of a traveling monochromatic wave is studied. For the waviness of small curvature, a calculation procedure is proposed for the amplitude dependence of the drag coefficient and complex elasticity which characterizes the back action of the flow on the surface inflection. The analysis is based on the use of an isotropic algebraic model of turbulent viscosity and an orthogonal system of curvilinear coordinates that follow the surface inflections. The interaction between the flow and the surface wave is described within the framework of a quasi-linear model, and a two-scale, mean-flow model is used to determine the transverse structure of the flow in a smoothly expanding boundary layer. Institute of Applied Physics, Russian Academy of Sciences, Nizhnii Novgorod 603600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 72–84, November–December, 1998.     

Nonlinear aeroservoelastic analysis of a controlled multiple-actuated-wing model with free-play

In this paper, the effects of structural nonlinearity due to free-play in both leading-edge and trailing-edge outboard control surfaces on the linear flutter control system are analyzed for an aeroelastic model of three-dimensional multiple-actuated-wing. The free-play nonlinearities in the control surfaces are modeled theoretically by using the fictitious mass approach. The nonlinear aeroelastic equations of the presented model can be divided into nine sub-linear modal-based aeroelastic equations according to the different combinations of deflections of the leading-edge and trailing-edge outboard control surfaces. The nonlinear aeroelastic responses can be computed based on these sub-linear aeroelastic systems. To demonstrate the effects of nonlinearity on the linear flutter control system, a single-input and single-output controller and a multi-input and multi-output controller are designed based on the unconstrained optimization techniques. The numerical results indicate that the free-play nonlinearity can lead to either limit cycle oscillations or divergent motions when the linear control system is implemented.     

Nonlinear deformation analysis of a U-shaped bellows with varying thickness

Summary The nonlinear integral equations for a U-shaped bellows with compressed angle and varying wall-thickness are derived according to the simplified Reissner theory of large deflection for revolution shells and integral-equation method. The iteration procedure for nonlinear analysis is developed by means of the integral equation iteration in conjunction with the gradient method. Numerical solutions for a U-shaped bellows under the action of axial compression force and internal pressure are obtained, which are compared with previous theories and experiments. The present results are shown to have a good accuracy, and may be applied directly to the design of bellows. Received 13 November 1997; accepted for publication 6 July 1999     

Experimental analysis of soil reaction on a lug of a movable lug wheel

A movable lug wheel was tested in a soil bin test apparatus to determine its traction performance and to measure the soil reaction forces on its lugs. Similar tests were also conducted using a fixed lug wheel. The effects of the lug motion pattern, lug spacing and horizontal load on pull and lift forces were studied. From the experiments it is confirmed that the movable action of the lug plate could generate superior pull and lift forces in comparison with the fixed lug wheel. Among the test wheels, lug motion pattern-2 generated the highest pull and lift forces. Within the range of the test conditions, there was no significant difference in pull and lift forces of the lug plate between the test lug wheels with 12 lugs and 15 lugs at the same level of horizontal and vertical loads. The increase of horizontal load up to 200 N generally increased the pull force and generated smaller rolling resistance before the lug left the soil, but did not increase the lift force significantly. The patterns of pull force, lift force and drawbar pull generated under a constant slip were slightly different from those under a constant horizontal load. Finally, the results were also elucidated by their actual lug trajectories in soil.