Coupling dynamic equations of motor-driven elastic linkage mechanism with links fabricated from three-dimensional braided composite materials

A motor-driven linkage system with links fabricated from 3-dimensional braided composite materials was studied. A group of coupling dynamic equations of the system, including composite materials parameters, electromagnetism parameters of the motor and structural parameters of the link mechanism, were established by finite element method. Based on the air-gap field of non-uniform airspace of three-phase alternating current motor caused by the vibration eccentricity of rotor, the relation of electromechanical coupling at the actual running state was analyzed. And the motor element, which defines the transverse vibration and torsional vibration of the motor as its nodal displacement, was established. Then, based on the damping element model and the expression of energy dissipation of the 3-dimentional braided composite materials, the damping matrix of the system was established by calculating each order modal damping of the mechanism.

Three-dimensional stability calculation method for high and large composite slopes formed by mining stope and inner dump in adjacent open pits

The 2D limit equilibrium method is widely used for slope stability analysis.However,with the advancement of dump engineering,composite slopes often exhibit significant 3D mechanical effects.Consequently,it is of significant importance to develop an effective 3D stability calculation method for composite slopes to enhance the design and stability control of open-pit slope engineering.Using the composite slope formed by the mining stope and inner dump in Baiyinhua No.1 and No.2 open-pit coal mine as a case study,this research investigates the failure mode of composite slopes and establishes spatial shape equations for the sliding mass.By integrating the shear resistance and sliding force of each row of microstrip columns onto the bottom surface of the strip corresponding to the main sliding surface,a novel 2D equivalent physical and mechanical parameters analysis method for the strips on the main sliding surface of 3D sliding masses is proposed.Subsequently,a comprehensive 3D stability calculation method for composite slopes is developed,and the quantitative relationship between the coordinated development distance and its 3D stability coefficients is examined.The analysis reveals that the failure mode of the composite slope is characterized by cutting-bedding sliding,with the arc serving as the side interface and the weak layer as the bottom interface,while the destabilization mechanism primarily involves shear failure.The spatial form equation of the sliding mass comprises an ellipsoid and weak plane equation.The analysis revealed that when the coordinated development distance is 1500 m,the error rate between the 3D stability calculation result and the 2D stability calculation result of the composite slope is less than 8%,thereby verifying the proposed analytical method of equivalent physical and mechanical parameters and the 3D stability calculation method for composite slopes.Furthermore,the3D stability coefficient of the composite slope exhibits an exponential correlation with the coordinated development distance,with the coefficient gradually decreasing as the coordinated development distance increases.These findings provide a theoretical guideline for designing similar slope shape parameters and conducting stability analysis.

A Wire-Driven Series Elastic Mechanism Based on Ultrasonic Motor for Walking Assistive System

In order to improve the elderly people's quality of life,supporting their walking behaviors is a promising technology.Therefore,based on one ultrasonic motor,a wire-driven series elastic mechanism for walking assistive system is proposed and investigated in this research.In contrast to tradition,it innovatively utilizes an ultrasonic motor and a wire-driven series elastic mechanism to achieve superior system performances in aspects of simple structure,high torque/weight ratio,quiet operation,quick response,favorable electromagnetic compatibility,strong shock resistance,better safety,and accurately stable force control.The proposed device is mainly composed of an ultrasonic motor,a linear spring,a steel wire,four pulleys and one rotating part.To overcome the ultrasonic motor's insufficient output torque,a steel wire and pulleys are smartly combined to directly magnify the torque instead of using a conventional gear reducer.Among the pulleys,there is one tailored pulley playing an important role to keep the reduction ratio as 4.5 constantly.Meanwhile,the prototype is manufactured and its actual performance is verified by experimental results.In a one-second operating cycle,it only takes 86 ms for this mechanism to output an assistive torque of 1.6 N·m.At this torque,the ultrasonic motor's speed is around 4.1 rad/s.Moreover,experiments with different operation periods have been conducted for different application scenarios.This study provides a useful idea for the application of ultrasonic motor in walking assistance system.

Eigen theory of elastic mechanics for anisotropic solids

Eigen characters of the fundamental equations, equilibrium equation of stress and harmony equation of deformation, of the traditional elastic mechanics under geometrical space were testified by means of the concept of standard space, and the modal equilibrium equation and the modal harmony equation under mechanical space were obtained. Based on them and the modal Hooke’s law, a new system of the fundamental equation of elastic mechanics is given. The advantages of the theory given here are as following: the form of the fundamental equation is in common for both isotropy and anisotropy, both force method and displacement method, both force boundary and displacement boundary; the number of stress functions is equal to that of the anisotropic subspaces, which avoids the man made mistakes; the solution of stress field or strain field is given in form of the modal superimposition, which makes calculation simplified greatly; no matter how complicated the anisotropy of solids may be, the complete solutions can be obtained.

Eigen elastic mechanics and its variation principle

The fundamental equations and the corresponding boundary condition of elastic mechanics under mechanical representation are given by using the conception of eigen space and elastic variation principle. It is proved theoretically that the solution of anisotropic elastic mechanics consists of modal ones, which are obtained respectively from the modal equation of the different subspaces. A simple application is also given.

Modeling and analysis of nonlinear mechanics of a super-thin elastic rod

Nonlinear mechanics for a super-thin elastic rod with the biological background of DNA super-coiling macromolecules is an interdisciplinary research area of classical mechanics and molecular biology. It is also a subject of dynamics and elasticity because elastic bodies are analyzed via the theory of dynamics. It is in frontiers of general mechanics （dynamics and control）. This dissertation is devoted to model a constrained super-thin elastic rod and analyze its stability in equilibrium. The existing research results are summarized. Analytical mechanics is systematically applied to model the elastic rod. The Schroedinger equation for complex curvatures or complex bending moments is, respectively, extended from the case of circular crosssections to that of non-circular ones. The equilibrium of a rod constrained on a surface is investigated.

Three-dimensional admittance analysis of lithospheric elastic thickness over the Louisville Ridge

Using bathymetry and altimetric gravity anomalies, a 1°×9 1° lithospheric effective elastic thickness（Te） model over the Louisville Ridge and its adjacent regions is calculated using the moving window admittance technique. For comparison, three bathymetry models are used： general bathymetric charts of the oceans, SIO V15.1,and BAT_VGG. The results show that BAT_VGG is more suitable for calculating T e than the other two models. T e along the Louisville Ridge was re-evaluated. The southeast of the ridge has a medium Te of 10–20 km, while Te increases dramatically seaward of the Tonga-Kermadec trench as a result of the collision of the Pacific and IndoAustralian plates.

MESHLESS ANALYSIS FOR THREE-DIMENSIONAL ELASTICITY WITH SINGULAR HYBRID BOUNDARY NODE METHOD

The singular hybrid boundary node method （SHBNM） is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares （MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The ＇boundary layer effect＇, which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method （RHBNM） can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.

Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space I: Newtonian Mechanics

We present the usefulness of the diagrammatic approach for analyzing two dimensional elastic collision in momentum space. In the mechanics course, we have two major purposes of studying the collision problems. One is that we have to obtain velocities of the two particles after the collision from initial velocities by using conservation laws of momentum and energy. The other is that we have to study two ways of looking collisions, i.e. laboratory system and center-of-mass system. For those two major purposes, we propose the diagrammatic technique. We draw two circles. One is for the center-of-mass system and the other is for the laboratory system. Drawing these two circles accomplish two major purposes. This diagrammatic technique can help us understand the collision problems quantitatively and qualitatively.

Stress Field Analysis of Homogeneous Roof by Truss Support Based on Elasticity Mechanics Solution

This paper takes the solution of Boussinesq model, Cerrutl model and Mindlin model as basic solution of elasticity mechanics. on the basis of research conclusion of the accuracy property or rock bolt stress field studied in reference [7], satisfictory elaticity mechanics solution of homogeneous roof rock stress field is given and the rule of stress field change with various parameters is studied.

Operationalized principle of elastic mechanics

The fundamental mechanical equations were studied under the mechanical space. The differential stress operator and strain operator were obtained. There were strain energy operator and Hamilton operator for elastic body in same way, and the following results were testified. 1) The equilibrium equation of force is equivalent to the harmony equation of deformation under the mechanical space. They are all the basic mode of eigen equation of stress or strain operator. 2) The eigen value of stress or strain operator is corresponding to the order of kinetic energy of elastic body, and the elastic wave represents the non basic mode. 3) The eigen functions of stress operator or strain operator corresponding to some kinetic energy order are fields of modal stress or modal strain in same order. 4) The eigen equations of strain energy operator are the fundamental equations of elastic mechanics which are expressed with the potential functions. [

An elastic mechanics model and computation method for geotechnical material

Internal friction characteristic is one of the basic properties of geotechnical materials and it exists in mechanical elements all the time. However,until now internal friction is only considered in limit analysis and plastic mechanics but not included in elastic theory for rocks and soils. We consider that internal friction exists in both elastic state and plastic state of geotechnical materials,so the mechanical unit of friction material is constituted. Based on study results of soil tests,the paper also proposes that cohesion takes effect first and internal friction works gradually with the increment of deformation. By assuming that the friction coefficient is proportional to the strain,the internal friction is computed. At last,by imitating the linear elastic mechanics,the nonlinear elastic mechanics model of friction material is established,where the shear modulus G is not a constant. The new model and the traditional elastic model are used simultaneously to analyze an elastic foundation. The results indicate that the displacements computed by the new model are less than those from the traditional method,which agrees with the fact and shows that the mechanical units of friction material are suitable for geotechnical material.

Three-Dimensional Static Analysis of Nanoplates and Graphene Sheets by Using Eringen’s Nonlocal Elasticity Theory and the Perturbation Method

A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity theory is used to capture the small length scale effect on the static behaviors of these.The perturbation method is used to expand the 3D nonlocal elasticity problems as a series of two-dimensional(2D)nonlocal plate problems,the governing equations of which for various order problems retain the same differential operators as those of the nonlocal classical plate theory(CST),although with different nonhomogeneous terms.Expanding the primary field variables of each order as the double Fourier series functions in the in-plane directions,we can obtain the Navier solutions of the leading-order problem,and the higher-order modifications can then be determined in a hierarchic and consistent manner.Some benchmark solutions for the static analysis of isotropic and orthotropic nanoplates and GSs subjected to sinusoidally and uniformly distributed loads are given to demonstrate the performance of the 3D nonlocal asymptotic theory.

Prediction of three-dimensional elastic behavior of filament-wound composites based on the bridging model

This work provides a method to predict the three-dimensional equivalent elastic properties of the filament-wound composites based on the multi-scale homogenization principle.In the meso-scale,a representative volume element(RVE)is defined and the bridging model is adopted to establish a theoretical predictive model for its three-dimensional equivalent elastic constants.The results obtained through this method for the previous experimental model are compared with the ones gained respectively by experiments and classical laminate theory to verify the reliability of this model.In addition,the effects of some winding parameters,such as winding angle,on the equivalent elastic behavior of the filament-wound composites are analyzed.The rules gained can provide a theoretical reference for the optimum design of filament-wound composites.

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.

MATERIAL MULTIPOLE MECHANICS OF ELASTIC DIELECTRIC COMPOSITES

The overall mechanical and electrical behaviors of elastic dielectric composites are investigated with the aid of the concept of material multipoles. In particular, by introducing a statistical continuum material multipole theory, the effects of the electric-elastic interaction and the microstructure (size, shape, orientation,...) of inhomogeneous particles on the overall behaviors of the composites can be obtained. A basic solution for an ellipsoidal elastic inhomogeneity with electric polarization in an infinite elastic dielectric medium is first given, which shows that classical Eshelby 's elastic solution is modified by the presence of electric-elastic interaction. The overall macroscopic constitutive relations and their overall macroscopic material parameters accounting for electroelastic interaction effect are then derived for the elastic dielectric composites. Some quantitative calculations on the problems with statistical anisotropy, the shape effect and the electric-elastic interaction are finally given for dilute composites.

Hamiltonian Mechanics Systems on Three-Dimensional Almost Kenmotsu Manifolds

In this study,we concluded the Hamiltonian equations on(M3,φ,ξ,η,g𝑔),being a model.Finally introduce,some geometrical and physical results on the related mechanic systems have been discussed.

Non-pneumatic mechanical elastic wheel natural dynamic characteristics and influencing factors

Non-pneumatic tire appears to have advantages over traditional pneumatic tire in terms of flat proof and maintenance free.A mechanical elastic wheel(MEW) with a non-pneumatic elastic outer ring which functions as air of pneumatic tire was presented.The structure of MEW was non-inflatable integrated configuration and the effect of hinges was accounted for only in tension. To establish finite element model of MEW, various nonlinear factors, such as geometrical nonlinearity, material nonlinearity and contact nonlinearity, were considered. Load characteristic test was conducted by tyre dynamic test-bed to obtain force-deflection curve. And the finite element model was validated through load characteristic test. Natural dynamic characteristics of the MEW and its influencing factors were investigated based on the finite element model. Simulation results show that the finite element model closely matched experimental wheel. The results also show that natural frequency is related to ground constraints, material properties, loads and torques. Influencing factors as above obviously affect the amplitude of mode of vibration, but have little effect on mode of vibration shape. The results can provide guidance for experiment research, structural optimization of MEW.

Dynamic Modeling and Analysis of 5‑PSS/UPU Parallel Mechanism with Elastically Active Branched Chains

To study the characteristics of the 5-prismatic–spherical–spherical(PSS)/universal–prismatic–universal(UPU)parallel mechanism with elastically active branched chains,the dynamics modeling and solutions of the parallel mechanism were investigated.First,the active branched chains and screw sliders were considered as spatial beam elements and plane beam element models,respectively,and the dynamic equations of each element model were derived using the Lagrange method.Second,the equations of the 5-PSS/UPU parallel mechanism were obtained according to the kinematic coupling relationship between the active branched chains and moving platform.Finally,based on the parallel mechanism dynamic equations,the natural frequency distribution of the 5-PSS/UPU parallel mechanism in the working space and elastic displacement of the moving platform were obtained.The results show that the natural frequency of the 5-PSS/UPU parallel mechanism under a given motion situation is greater than its operating frequency.The maximum position error is -0.096 mm in direction Y,and the maximum orientation error is -0.29°around the X-axis.The study provides important information for analyzing the dynamic performance,dynamic optimization design,and dynamic control of the 5-PSS/UPU parallel mechanism with elastically active branched chains.

CALCULATION OF ELASTIC ERROR OF PLANAR MECHANISM—AN EQUIVALENT METHOD

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