General theory of micropolar elastic thin shells

The paper formulates general hypotheses of micropolar elastic thin shells that are given asymptotic validation. Using these hypotheses and three-dimensional Cosserat (micropolar, asymmetric) theory of elasticity, general two-dimensional applied models of micropolar elastic thin shells with independent displacement and rotation fields, constrained rotation and low shear rigidity are constructed to suit dimensionless physical parameters of the shell material. The constructed micropolar shell models take into complete account transverse shear strain and related strain. Models of micropolar elastic thin plates and beams are particular cases of the constructed micropolar shell models. An axially symmetric stress-strain state problem of a hinged cylindrical micropolar shell is considered. Numerical analysis is used to demonstrate effective strength and rigidity characteristics of micropolar elastic shells.     

General dynamic theory of micropolar elastic thin plates with free rotation and special features of their natural oscillations

A general applied two-dimensional theory for the dynamics of micropolar elastic thin plates that takes into account rotationally shear and related deformations is developed on the basis of the method of hypotheses with asymptotic confirmation. A problem of natural oscillations of micropolar elastic thin rectangular plates is solved using it. Special features of the dynamic characteristics of elastic thin plates made of a micropolar elastic material are revealed within the framework of numerical analysis.     

Dynamic model of micropolar elastic thin plates with independent fields of displacements and rotations

A general model of dynamic bending of isotropic micropolar elastic thin plates with independent fields of displacements and rotations is presented. The model has been justified asymptotically based on the solutions for special cases subject to simplifying assumptions. The model incorporates transverse shear deformations. Neglecting transverse shear, a model of the dynamics of micropolar elastic thin plates is also constructed. Then, we study free and forced oscillations and derive the natural frequencies, the amplitudes of the forced oscillations and the resonance conditions for micropolar elastic hinge-supported rectangular and circular plates. Finally, the basic characteristic features of micropolar plates are numerically analysed for different values of various elastic and inertial constants of the micropolar material.     

Mathematical model of the dynamics of micropolar elastic thin beams. Free and forced vibrations

A method of hypotheses has been developed to construct a mathematical model of micropolar elastic thin beams. The method is based on the asymptotic properties of the solution ofan initial boundary value problem in a thin rectangle within the micropolar theory of elasticity with independent displacement and rotation fields. An applied model of the dynamics of micropolar elastic thin beams was constructed in which transverse shear strains and related strains are taken into account. The constructed dynamics model was used to solve problems of free and forced vibrations of a micropolar beam. Free vibration frequencies and modes, forced vibration amplitudes, and resonance conditions were determined. The obtained numerical calculation results show the specific features of free vibrations of thin beams. Micropolar thin beams have a free vibration frequency which is almost independent of the thin beam size, but depends only on the physical and inertial properties of the micropolar material. It is shown for the micropolar material that the free vibration frequency values of beams can be readily adjusted and hence a large vibration frequency separation can be achieved, which is important for studying resonance.     

Driven self-assembly of hard nanoplates on soft elastic shells

The driven self-assembly behaviors of hard nanoplates on soft elastic shells are investigated by using molecular dynamics(MD) simulation method, and the driven self-assembly structures of adsorbed hard nanoplates depend on the shape of hard nanoplates and the bending energy of soft elastic shells. Three main structures for adsorbed hard nanoplates,including the ordered aggregation structures of hard nanoplates for elastic shells with a moderate bending energy, the collapsed structures for elastic shells with a low bending energy, and the disordered aggregation structures for hard shells,are observed. The self-assembly process of adsorbed hard nanoplates is driven by the surface tension of the elastic shell,and the shape of driven self-assembly structures is determined on the basis of the minimization of the second moment of mass distribution. Meanwhile, the deformations of elastic shells can be controlled by the number of adsorbed rods as well as the length of adsorbed rods. This investigation can help us understand the complexity of the driven self-assembly of hard nanoplates on elastic shells.     

Static-geometric analogy in the micropolar theory of elasticity

For a micropolar elastic medium with distributed dislocations and disclinations, an analogy has been established between the equilibrium equations for force and couple stresses and the reduced incompatibility equations for metric and bending strains. The strain boundary conditions have been derived. The physically different but mathematically equivalent boundary-value problems of the three-dimensional micropolar theory of elasticity have been formulated.     

On wave propagation in a random micropolar thermoelastic medium,second moments,and associated Green’s tensor

The couple stress theory developed by Eringen comprises granular materials as also composite fibrous materials. As such, micropolar materials present an inclusive model of composite materials. This article endeavors to study aspects of wave propagation in a random weakly thermal micropolar elastic medium. The smooth perturbation technique has been employed. The classical thermoelasticity has been used. Six different types of waves have been observed to propagate in the random interacting medium. Dispersion equations have been derived. The effects due to random variations of micropolar elastic and thermal parameters have been observed. Change of phase speed occurs on account of randomness. Attenuation coefficients for high-frequency waves have been computed. Second moment properties have been discussed with application to wave propagation in the random micropolar elastic medium. 36 + 1 components of the associated Green’s tensor have been computed. Integrals involving correlation functions have been transformed to radial forms. A special type of correlation function has been used to approximately measure effects of random variations of parameters.     

The Nonlinear Theory of Quasi-Solid States of Micropolar Elastic Bodies

Doklady Physics - A nonlinear theory of quasi-solid states of micropolar elastic bodies is proposed. Quasi-solid states are a three-dimensional analog of the surface bending and are possible only...     

Quasi-solid states of micropolar elastic bodies

The states of a linearly elastic micropolar body in which there are pure couple stresses are studied, while the force stresses are zero. The plane and spherically symmetric problems are investigated for a micropolar body under conditions of quasi-solid states. The obtained solutions can be useful for experimental determination of the moment constants of micropolar media.     

Dynamic Modeling and Analysis of Wind Turbine Blade of Piezoelectric Plate Shell

This paper presents a theoretical analysis of vibration control technology of wind turbine blades made of piezoelectric intelligent structures. The design of the blade structure, which is made from piezoelectric material, is approximately equivalent to a flat shell structure. The differential equations of piezoelectric shallow shells for vibration control are derived based on piezoelectric laminated shell theory. On this basis, wind turbine blades are simplified as elastic piezoelectric laminated shells. We establish the electromechanical coupling system dynamic model of intelligent structures and the dynamic equation of composite piezoelectric flat shell structures by analyzing simulations of active vibration control. Simulation results show that, under wind load, blade vibration is reduced upon applying the control voltage.     

The new physics of ultrathin elastic conoids

Summary Despite centuries of intense effort amongst mathematicians, and a huge literature in this field, there has previously never been a generally valid mathematical model of ultrathin elastic ?shells? (actually surfaces) of revolution. This survey paper presents the first theoretical framework capable of unifying, into a single coherent body of knowledge, a diversity of shapes associated with elastic bows, car bumper-bars, molluscan shells, even flower-buds and pine-cones. It becomes apparent why conventional analysis enjoys limited success when approximating elastic cones to perturbedcylinders anddiscs. Also the paper provides a theoretical basis for analysing the wrinkling of compressed engineering structures. These successes, the new unification and the simplicity of relevant theory which maynever in principle be capable of working in this context.     

Free vibrations of cylindrical shells with elastic-support boundary conditions

This paper concerns the free vibrations of cylindrical shells with elastic boundary conditions. Based on the Flügge classical thin shell theory, the equations of motion for the cylindrical shells are solved by the method of wave propagations. The wave numbers are obtained by directly solving an eighth order equation. The elastic-support boundary conditions can be arbitrarily specified in terms of 8 independent sets of distributed springs. All the classical homogeneous boundary conditions can be considered as the special cases when the stiffness for each set of springs is equal to either infinity or zero. The present solutions are validated by the results previously given by other researchers and/or obtained using finite element models. The effects on the frequency parameters of elastic restraints are investigated for shells of different geometrical characteristics.     

Vibrations in cylindrical shells with transverse elastic isotropy: Application to III-V nitride nanotubes

The vibrational modes of cylindrical shells with transverse elastic isotropy and arbitrary thickness are calculated in the framework of the elasticity theory and a comparison with the isotropic approach is presented. Cylindrical shells are a good model for nanotubes and here an application for nanotubes of transversely isotropic elastic materials is given. We have obtained the expression for the frequency of the radial breathing mode and it is shown that calculated frequencies coming from that expression compare fairly well with those obtained from different ab initio, force constant model calculations and experimental results. Further, the dispersion relations depend on all the elastic coefficients and therefore they are quite different for nanotubes with hexagonal or wurtzite structure. This demonstrates the need to go beyond the isotropic model to investigate the vibrational spectrum of transversely isotropic elastic material nanotubes and nanowires.     

On the durable critic load in creep buckling of viscoelastic laminated plates and circular cylindrical shells

Based on the first order shear deformation theory and classic buckling theory, the paper investigates the creep buckling behavior of viscoelastic laminated plates and laminated circular cylindrical shells. The analysis and elaboration of both instantaneous elastic critic load and durable critic load are emphasized. The buckling load in phase domain is obtained from governing equations by applying Laplace transform, and the instantaneous elastic critic load and durable critic load are determined according to the extreme value theorem for inverse Laplace transform. It is shown that viscoelastic approach and quasi-elastic approach yield identical solutions for these two types of critic load respectively. A transverse disturbance model is developed to give the same mechanics significance of durable critic load as that of elastic critic load. Two types of critic loads of boron/epoxy composite laminated plates and circular cylindrical shells are discussed in detail individually, and the influencing factors to induce creep buckling are revealed by examining the viscoelasticity incorporated in transverse shear deformation and in-plane flexibility.     

考虑铺层角的复合材料圆柱壳自由振动三维弹性准确解

为了获得任意角度铺层的多层复合材料圆柱壳的自由振动准确解,在三维弹性理论的基础上,结合分层理论和状态空间法,建立横向位移和应力的传递矩阵,轴向和环向位移采用双螺旋模式的位移函数,对任意角度铺层复合材料圆柱壳简支边界条件下的自由振动进行了理论推导,得到了自由振动方程的精确形式。与文献理论解和有限元计算结果对比,结果表明,关注频率在2倍的环频率以下时,薄壳的固有频率计算精度能控制在1%以内,厚壳的固有频率计算精度能控制在2%以内。对于厚壳的计算可将壳体沿厚度方向划分为多层来处理,这样能有效提高计算精度。计算分析了铺层角对壳体固有频率的影响,环向模态数较低时,固有频率随着铺层角的增加呈抛物线变化趋势;环向模态数较高时,固有频率随着铺层角的增大单调递增。该理论方法同样适用于均质各向同性壳和正交各向异性圆柱壳。      

Resonance scattering of sound by spheroidal elastic bodies and shells

The resonances of spheroidal elastic bodies (prolate and oblate) in the form of solid bodies and shells are determined using dynamic elasticity theory and Debye potentials. In addition to analytic solutions, results of computer calculations are presented for the angular characteristics and scattering cross sections of spheroidal elastic bodies.     

The nonlocal elastomagnetoelectrostatics of disordered micropolar media

The interactions of electric, magnetic, and elastic subsystems in nonlinear disordered micropolar media that possess a bending–torsion tensor and an nonsymmetric strain tensor have been studied in the framework of phenomenological elastomagnetoelectrostatics. A system of nonlinear equations for determining the ground state of these media has been obtained by the variational method. It is shown that nonuniform external and internal rotations not only create elastic stresses, but also generate additional electric and magnetic fields, while nonuniform elastic stresses and external fields induce internal rotations. The nonlocal character of the micropolar media significantly influences elementary excitations and nonlinear dynamic processes.     

Natural vibrations and stability of shells of revolution interacting with an internal fluid flow

A finite-element algorithm is proposed to investigate the dynamic behavior of elastic shells of revolution containing a quiescent or a flowing inviscid fluid in the framework of linear theory. The fluid behavior is described using the perturbed velocity potential. The shell behavior is treated in the framework of the classical shell theory and variational principle of virtual displacements incorporating a linearized Bernoulli equation for calculation of hydrodynamic pressure acting on the shell. The problem reduces to evaluation and analysis of the eigenvalues in the connected system of equations obtained by coupling the equations for velocity perturbations with the equations for shell displacements. For cylindrical shells, the results of numerical simulations are compared with recently published experimental, analytical and numerical data. The paper also reports the results of studying the dynamic behavior of shells under various boundary conditions for the perturbed velocity potential. The investigation made for conical shells has shown that under certain conditions an increase in the cone angle can change a divergent type of instability to a flutter type.     

ELASTIC WAVE SCATTERING AND DYNAMIC STRESS CONCENTRATIONS IN CYLINDRICAL SHELLS WITH A CIRCULAR CUTOUT

In this paper, based on the theory of elastic wave motion for open cylindrical shell, wave scattering and dynamic stress concentrations in open cylindrical shells with a hole are studied by making use of small parameter perturbation methods and boundary-integral equation techniques. The boundary-integral equations and iterative imminent series of scattered waves around the cavity of the cylindrical shell are derived. By employing this method, the approximately analytical solutions of scattered waves on the edge of cutout are gained. The computational formula for getting the dynamic stress concentration factors on the contour of cavity is developed. As an example, the numerical results of these dynamic stress concentration factors are graphically presented and discussed. The analytical methods put forward in the present work have practical significances for solving the problem of elastic wave scattering and dynamic stress concentrations in cylindrical shells with a circular cutout.     

A modified Fourier series solution for vibration analysis of truncated conical shells with general boundary conditions

Free vibration analysis of truncated conical shells with general elastic boundary conditions is presented in this paper. An accurate modified Fourier series solution is developed, in which, regardless of the boundary conditions, each displacement of the conical shell is invariantly expressed as a new form of improved series expansions composed of a standard Fourier series and closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series expansion. All the expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh–Ritz method. By using the present method, conical shells with arbitrary boundary conditions including all classical and elastic end restraints can be solved in a unified form. The accuracy and convergence of the current approach are validated by numerical examples and comparison with FEM results and those from the literature, and excellent accuracy is demonstrated. Comprehensive studies on the effects of elastic restraint parameters, semi-vertex angle and the ratio of length to radius are also reported. Some new results are presented for cases with elastic boundary restraints which may serve as benchmark solution for future researches.