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针对核聚变反应堆中受到复杂磁场作用的限制器叶片,用悬臂导电薄板作为其简化结构,从导电介质所满足的电磁学及力学的基本定律和方程出发,建立了描述其力-电-磁耦合作用下几何非线性动态响应问题的理论模型,给出了数值计算的求解过程,定量模拟了面内磁体力和几何非线性对薄板挠度的影响。仿真结果显示,在横向磁场很小时,面内磁体力和大挠度都不考虑时的线性结果是可靠的,但是随着横向磁场的增加,几何非线性的影响越来越大,面内磁体力的作用也越发明显,且考虑几何非线性得到的挠度峰值要比线性情形的小,这表明了在导电结构设计中必须同时考虑面内磁体力和几何非线性效应。     

平行光管主反射镜组件的非线性有限元分析

为了提高对光学仪器中光机结构分析的精度,引入了非线性分析方法,用非线性有限元法研究了某平行光管主镜组件存在的非线性问题。介绍了产生结构非线性的主要来源,并在接触理论的基础上对主反射镜组件进行了合理的有限元建模。采用接触非线性分析方法对螺钉预紧时反射镜的响应及在自重和温度载荷作用下反射镜的变形进行了分析。将线性和非线性分析结果与实际结果进行了对比,结果表明,采用接触非线性分析方法对反射镜组件进行工程分析减小了分析误差。因此,在工程分析中,对某些接触部位采用非线性分析方法可以提高分析精度,得到的结果更加符合实际。     

Normal Mode Splitting in a Cavity Optomechanical System with a Cubic Anharmonic Oscillator

The strong coupling between a macroscopic mechanical oscillator and a cavity field is essential for many quantum phenomena in a cavity optomechanical system. In this work, we discuss the normal mode splitting in a cavity optomechanical system with a cubic nonlinear movable mirror. We study how the mechanical nonlinearity affects the normal-mode splitting behavior of the movable mirror and the output field. We find that the mechanical nonlinearity can increase the peak separation in the spectra of the movable mirror and the output field. We also find that the heights and linewidths of the two peaks are very sensitive to the mechanical nonlinearity.

     

Estimation of the stresses in a coating growing on a flat plate under nonisothermal conditions

A mathematical model of a coating which grows during magnetron sputtering has been formulated and investigated. To estimate the average mechanical stresses, both the thermal and the chemical diffusion contribution are taken into account. It has been shown that the kinetics of the reaction on the surface is no less important in the evolution of stresses than the relationship between the mechanical properties of the growing coating and of the substrate.     

Predicting the nonlinear tensile behavior of carbon nanotubes using finite element simulation

Carbon nanotubes (CNTs) possess extremely high mechanical properties and could be the ultimate reinforcing materials for the development of nanocomposites. In this work, a Finite Element (FE) model based on the molecular mechanics theory was developed to evaluate tensile properties of single-walled carbon nanotubes (SWCNTs). The deformation and fracture of carbon nanotubes under tensile strain conditions were studied by common FE software, Ansys. In this model, individual carbon nanotube was simulated as a frame-like structure, and the primary bonds between two nearest-neighboring atoms were treated as beam elements. The beam element properties were determined via the concept of energy equivalence between molecular dynamics and structural mechanics. So far, several researches have studied the elastic behavior of CNTs, and its nonlinearity is not well understood. The novelty of the model lies on the use of nonlinear beam elements to evaluate SWNTs tensile failure. The obtained calculated mechanical properties show good agreement with existing numerical and experimental results.     

An electrochemomechanical theory of defects in ionic solids. I. Theory

Charged defects diffuse through an ionic solid under electrochemical driving forces. Such a diffusion process can be affected by mechanical stresses in the solid. A deviation of defect concentration from its stoichiometric value during diffusion can cause volumetric strains in the solid. Such strains will result in mechanical stresses if the ionic solid is under mechanical constraint, or if the defect distribution is non-uniform. We develop a framework to account for the coupling between mechanical stresses and diffusion of charged defects in ionic solids. The framework consists of a system of nonlinear differential/algebraic equations governing the defect concentrations, electrostatic potential and the mechanical stresses. It is believed that this framework is the first fully coupled theory for the interaction between mechanical stresses and electrochemical forces in ionic solids.     

On the Becker/Döring Theory of Nucleation of Liquid Droplets in Solids

Nucleation of liquid precipitates in semi-insulating GaAs is accompanied by deviatoric stresses resulting from the liquid/solid misfit. A competition of surface tension and stress deviators at the interface determines the nucleation barrier.The evolution of liquid precipitates in semi-insulating GaAs is due to diffusional processes in the vicinity of the droplet. The diffusion flux results from a competition of chemical and mechanical driving forces.The size distribution of the precipitates is determined by a Becker--Dö-ring system. The study of its properties in the presence of deviatoric stresses is the subject of this study. The main tasks of this study are: (i) We propose a new Becker/Döring model that takes thermomechanical coupling into account. (ii) We compare the current model with already existing models from the literature. Irrespective of the incorporation of mechanical stresses, the various models differ due to different environments where the evolution of precipitates takes place. (iii) We determine the structure of equilibrium solutions according to the Becker/Döring model, and we compare these solutions with those that result from equilibrium thermodynamics.     

平行光管主反射镜组件的非线性有限元分析

为了提高对光学仪器中光机结构分析的精度,引入了非线性分析方法,用非线性有限元法研究了某平行光管主镜组件存在的非线性问题。介绍了产生结构非线性的主要来源,并在接触理论的基础上对主反射镜组件进行了合理的有限元建模。采用接触非线性分析方法对螺钉预紧时反射镜的响应及在自重和温度载荷作用下反射镜的变形进行了分析。将线性和非线性分析结果与实际结果进行了对比,结果表明,采用接触非线性分析方法对反射镜组件进行工程分析减小了分析误差。因此,在工程分析中,对某些接触部位采用非线性分析方法可以提高分析精度,得到的结果更加符合实际。     

Finite element simulation for estimating the mechanical properties of multi-walled carbon nanotubes

A finite element simulation technique for estimating the mechanical properties of multi-walled carbon nanotubes is developed. In the present modeling concept, individual carbon nanotube is simulated as a frame-like structure and the primary bonds between two nearest-neighboring atoms are treated as beam elements, the beam element properties are determined via the concept of energy equivalence between molecular dynamics and structural mechanics. As to the simulation of the interlayer van der Waals force which has intrinsic nonlinearity and complicated applying region, a simplifying method is proposed that the interlayer pressure caused by van der Waals force instead of the force itself is to be considered, and we make use of the linear part of the interlayer pressure near the equilibrium condition to avoid the nonlinearity in problem, then linear spring elements whose stiffness is determined by equivalent force concept can be utilized to simulate the interlayer van der Waals force such that significant modeling and computing effort is saved in performing the finite element analysis. Numerical examples for estimating the mechanical properties of nanotubes, such as axial and radial Young’s modulus, shear modulus, natural frequency, buckling load, etc., are presented to illustrate the accuracy of this simulation technique. By comparing to the results found in the literature and the possible analytical solutions, it shows that the obtained mechanical properties of nanotubes by the present method agree well with their comparable results. In addition, the relations between these mechanical properties and the nanotube size are also discussed.     

Domain structure of a tetragonal antiferromagnet

A theory of the 90° and 180° domain structure in an easy-plane tetragonal antiferromagnet with nonuniform internal magnetostrictive and mechanical stresses has been developed. The reconstruction of domain structure in an external magnetic field was investigated. Dependencies of critical fields of stability loss of the 90° and 180° domain structures upon a directional external pressure, and magnetostrictive and nonuniform mechanical stresses have been determined. The dependence of the magnetization curve on mechanical stresses has also been determined.     

Analysis of interfacial thermal stresses for damaged structures: new theoretical model

The use of the composites for the reinforcement of the beams and structures metallic and non-metallic, is one of the recent methods of the rehabilitation by composites, what permits to replace the classic techniques of the assembly based on soldering, bonding, etc. But this technique gives stresses concentrations to the level of the zone of the assembly. The methods of rehabilitation by composites permit to prolong the life span of these structures under a reduced exploitation cost and with less pollution to the environment. In this article, an original survey on the stresses between the structure and the composite (fiber reinforced polymer [FRP]) was finalized, taking account, as well, of the mechanical and thermal loadings, as well as the effects of deformation shear lag. This originality puts in evidence a new theoretical model which takes into account the thermal effect of the stresses concentration that has not been treated seriously by the previous studies.     

Statistical mechanics of the 2-dimensional focusing nonlinear Schrödinger equation

We study a natural construction of an invariant measure for the 2-dimensional periodic focusing nonlinear Schrödinger equation, with the critical cubic nonlinearity. We find that a phase transition occurs as the coupling constant defining the strength of the nonlinearity is increased, but that the natural construction, successful for the 1-dimensional case and for the 2-dimensional defocusing case, cannot produce an invariant measure. Our methods rely on an analysis of a statistical mechanical model closely related to the spherical model of Berlin and Kac.     

Envelope solitons in acoustically dispersive vitreous silica

Acoustic radiation-induced static strains, displacements, and stresses are manifested as rectified or 'dc' waveforms linked to the energy density of an acoustic wave or vibrational mode via the mode nonlinearity parameter of the material. An analytical model is developed for acoustically dispersive media that predicts the evolution of the energy density of an initial waveform into a series of energy solitons that generates a corresponding series of radiation-induced static strains (envelope solitons). The evolutionary characteristics of the envelope solitons are confirmed experimentally in Suprasil W1 vitreous silica. The value (- 11.9 ± 1.43) for the nonlinearity parameter, determined from displacement measurements of the envelope solitons via a capacitive transducer, is in good agreement with the value (- 11.6 ± 1.16) obtained independently from acoustic harmonic generation measurements. The agreement provides strong, quantitative evidence for the validity of the model.     

Static model of a violin bow: influence of camber and hair tension on mechanical behavior

Experienced bow makers empirically know the influence of wood, tapering, and camber on the playing and tonal qualities of a bow. However, the way each parameter affects the bow mechanical behavior is not clearly established. An in-plane finite element model is developed to highlight the link between the adjustable design parameters and the mechanical behavior of a bow. This model takes into account geometric nonlinearity as well as compliance of the hair. Its validity is discussed from measurements on a bow. Results from simulations are compared to experimental results from previous studies. The consequences of adjusting hair tension and camber are then investigated.     

粗糙接触界面超声非线性效应的概率模型

提出描述粗糙接触界面超声非线性效应的概率模型,利用分段均匀概率函数描述粗糙接触界面劲度系数变化,结合表面粗糙峰的几何分布特征,得到界面粗糙度和两侧表面相对运动对声波的非线性调制作用。实验观测了铝合金材料的粗糙接触界面的高次谐波现象和阈值现象,进一步分析了归一化非线性参数与界面加载压力、粗糙度之间的关系。实验测量结果与概率模型的理论预测一致,证明了该模型的正确性,为利用超声非线性效应评价粗糙接触界面提供了理论依据。      

Theory of multinonlinear media and its application to the soliton processes in ferrite–ferroelectric structures

A theory is developed to describe the wave processes that occur in waveguide media having several types of nonlinearity, specifically, multinonlinear media. It is shown that the nonlinear Schrödinger equation can be used to describe the general wave process that occurs in such media. The competition between the electric wave nonlinearity and the magnetic wave nonlinearity in a layered multinonlinear ferrite–ferroelectric structure is found to change a total repulsive nonlinearity into a total attractive nonlinearity.     

Defect formation processes and their influence on mechanical stresses in green glow gallium phosphide structures

Defect formation and their influence on internal mechanical stresses in epitaxial gallium phosphide layers grown from a gallium melt with the addition of finely-dispersed gallium nitride particles in an atmosphere of hydrogen with ammonia are investigated in this paper. It is established that an increase from 0.04 to 0.1 vol. % in the ammonia content in the gas mixture will result in growth in the quantity of defects, in particular, inclusions of the second phase, as well as internal mechanical stresses, while for an NH₃ content greater than 0.1 vol. % – in the formation of shallow cracks and stress relaxation. The dependence between the internal mechanical stresses, the volume fraction, and the dispersion of the GaN inclusions in gallium phosphide is shown. The results obtained are discussed within the framework of the proposed model.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 23–27, January, 1991.     

Effect of alternating mechanical stresses on change of polarization of barium titanate

Experimental results for the change of polarization of barium titanate single crystals in weak pulsed fields under the action of alternating mechanical stresses are given. It is shown that the effect of alternating stresses on the domain structure reduces to the following processes; periodic reorientation of the domains and a change in dielectric viscosity.