Mechanics of Solids最新文献

This paper presents a study on the effects of support stiffness on buckling and postbuckling of imperfect plane arch trusses. A imperfect plane truss element model considering large displacements is constructed based on the Updated Lagrangian formulation. This truss element model is used for buckling and postbuckling analysis of a plane arch truss with consideration of support stiffness, in order to investigate the effects of support stiffness on the overall stability of plane arch trusses. Some notable results presented herein include: (1) the relationship between critical load and support stiffness, (2) the load – displacement curves corresponding to different values of support stiffness, (3) the effects of imperfection on postbuckling of trusses. Two examples of plane arch truss are described and the results have been verified against the results of previous studies for a special case (i.e., rigid supports). This study shows that the effects of support stiffness on buckling and postbuckling of imperfect plane arch trusses is very significant and should be taken into account in the analysis of trusses considering large displacements.

The article analyzes the influence of nonlinear (cubic) internal damping (in the Kelvin-Voigt model) and cubic nonlinearity of elastic forces on the dynamics of a rotating flexible shaft with distributed mass. The shaft is modeled by a Bernoulli-Euler rod using the Green function; discretization and reduction of the rotating shaft dynamics problem to an integral equation are performed. It is revealed that in such a system there always exists a branch of limited periodic motions (autovibrations) at a supercritical rotation speed. In addition, with small internal damping, the periodic branch continues into the subcritical region: upon reaching the critical speed, a subcritical Poincare-Andronov-Hopf bifurcation is realized and there is an unstable branch of periodic motions below the branch of stable periodic autovibrations (the occurrence of hysteresis when the rotation speed changes). With an increase in the coefficient of internal friction, the hysteresis phenomenon disappears and at a critical rotation speed, soft excitation of autovibrations of the rotating shaft occurs via the supercritical Poincare-Andronov-Hopf bifurcation.

The problem on free spatial vibrations of an overhead transmission line conductor with an asymmetric mass distribution over the cross-section that is caused by ice deposits, which impart an asymmetric shape to the cross-section, is considered. As a result, an eccentricity between the centers of torsional stiffness and mass in the cross-section is formed; and a dynamic relation of vertical, torsional, and “pendulum” vibrations develops with the conductor leaving the sagging plane. The conductor is modeled as a flexible heavy elastic rod that resists only stretching and torsion. The case of a slightly sagging conductor, when the tension and curvature of its centerline can be considered constant within the span, is investigated. It is also considered that the elasticity of the ice casing is small compared to the elasticity of the conductor. The mathematical model considering the interaction of longitudinal, torsional, and transverse waves polarized in the vertical and horizontal planes is analyzed. The ratios of phase velocities of all types of waves are analyzed and a group of particular subsystems determining partial vibrations is identified. Partial and natural frequencies and vibration modes of the conductor are investigated. Analytical solutions for the problem on determining the spectrum of natural frequencies and spatial vibration modes are obtained. The effect of an ice casing on the spectrum of conductor vibrations is investigated. A dependence of the wave number of torsional vibrations on the frequency is found. Such a dependence is determined not only by the elastic-inertial, but also by the gravitational factor, which is strongly manifested for conductors in long spans, especially subjected to galloping. This circumstance is essential for the analysis of the phenomenon of galloping from the standpoint of linking the occurrence of galloping with the convergence of the frequencies of torsional and transverse modes during conductor icing. It is shown that the ratio of these frequencies causing the self-oscillatory process is considerably complicated.

The rapid development of technology and industry requires the search of new materials which combine high strength, light weight and corrosion resistance. Metal matrix composites reinforced with two-dimensional carbon allotropes exhibit impressive mechanical, physical and tribological properties. Diamane, a two-dimensional diamond, is a very promising material for the production of thin, ultra-high strength coatings and as the reinforcement for metal matrix composites. Simulation methods can considerably improve understanding of the interaction between the diamane and metal phase. Molecular dynamics allow to analyse different properties of new materials on the atomistic level. In the present work, the mechanical properties of new composite – nickel reinforced with diamane – are investigated by molecular dynamics simulation. The structural changes in the Ni/diamane composite during tensile loading are analyzed in detail. The Young’s modulus and ultimate tensile strength of Ni/diamanе composite are 147 and 22.1 GPa, respectively, but they can be increased by increasing the diamane layers in the composite. It was found that dislocation nucleation occurred at the interface between Ni and diamane. The tensile strength of Ni/diamane composite depends on the tensile direction. The results obtained contribute to a better understanding of the processes of formation, deformation behaviour, and mechanical properties of composites based on metal and diamane.

The Jacobi stability analysis of the nonlinear dynamical system on base of Kosambi–Cartan–Chern theory is considered. Geometric description of time evolution of the system is introduced, that makes it possible to determine five geometric invariants. Eigenvalues of the second invariant (the deviation curvature tensor) give an estimate of Jacobi stability of the system. This approach is relevant in applications where it is required to identify the areas of Lyapunov and Jacobi stability simultaneously. For the nonlinear system – the double pendulum – the dependence of the Jacobi stability on initial conditions is investigated. The components of the deviation curvature tensor corresponding to the initial conditions and the eigenvalues of the tensor are defined explicitly. The boundary of the deterministic system transition from regular motion to chaotic one determined by the initial conditions has been found. The formulation of the inverse eigenvalue problem for the deviation curvature tensor associated with the restoration of significant parameters of the system is proposed. The solution of the formulated inverse problem has been obtained with the use of optimization approach. Numerical examples of restoring the system parameters for cases of its regular and chaotic behavior are given.

The scattering problem of the steady-state 0-order SH guided wave with a semicircular dip at the boundary of a zoning piezoelectric field and a linear crack in the inner plate is investigated using the complex variable function method, multiple coordinate method, and Green’s function. The guided wave expansion method is utilized in the construction of the SH guided wave, and the multiple mirror method is utilized to fulfill the requirements of stress freedom and electrical insulation. Under the time harmonic load with a semicircular depression in the zonal piezoelectric field, Green’s function represents the fundamental solution. By using the crack cutting method, it is possible to calculate the dynamic stress concentration factor and dynamic stress intensity factor values of the crack tip when both the crack and semicircle sag engage in joint action. The DSCF of a semicircular concave edge and the DSIF of a linear crack are studied in terms of the influence of various piezoelectric parameters, including wave number, crack length, and band domain thickness. The results indicate that it is important to study low frequency, make reasonable selections for piezoelectric parameters, and consider the length of a linear crack when dealing with the interaction between zonal piezoelectric materials with a semicircular sag and a linear crack.

The paper presents a numerical and analytical method for determining the modulus of elasticity of the soil, based on experimental results on the natural frequencies of vibration of a pile embedded in a soil mass and their theoretical dependence on the modulus of elasticity of the soil. Experimental results on the dynamic behavior of a pile embedded in a soil mass and numerical results based on the finite element method, which provide the construction of the dependence of the natural frequencies of vibration of the pile on the modulus of elasticity of the soil, are given. As a demonstration of the reliability and efficiency of the method under consideration, a comparison of numerical results on the natural frequencies of vibrations of the pile with different weights at its free end at the found dependence of the modulus of elasticity of the soil and the corresponding experimental results is given.

A two-dimensional problem of elasticity theory on an isotropic strip with a central semi-infinite crack is considered. The load in the form of a concentrated force is assumed to be applied at an arbitrary point of the strip. Using invariant mutual integrals and solutions for a strip loaded with bending moments and longitudinal forces applied at infinity, expressions for stress intensity factors (SIF) for the problem under consideration are obtained. The cases of forces applied at the crack faces, at the strip boundaries and at the internal points of the strip are considered. Asymptotic expressions are obtained for the cases of application of forces far from the crack tip and forces applied at the crack faces near its tip. The obtained solutions are shown to coincide with known solutions for special cases: loads in the form of a pair of normal forces applied to the crack faces and forces applied far from the crack tip.

Within the framework of the spatial variant of the “deformable Earth-Moon” problem in the solar gravitational field for the viscoelastic Earth model, tidal deformations caused by long-period lunar disturbances are determined. The dynamics of the Earth’s pole motion with Chandler and annual frequencies is analyzed taking into account the obtained expressions for the centrifugal moments of inertia of the Earth. Using numerical integration of the equations of pole motion, it is shown that the found structure of variations in the centrifugal moments of inertia leads to oscillations in the amplitudes of the Chandler and annual harmonics with an 18-year period of precession of the Moon’s orbit.

In this paper, the mechanics of micropolar elastic solids is extended to a more general thermoelastic media in order to take account of the effect of temperature on their states and mechanical behavior. Since a thermoelastic micropolar medium conducts heat, it is required to include one or another mechanism of thermal propagation in the basic equations of micropolar thermoelasticity. A model of thermoelastic micropolar medium CGNII is developed on ground of the wave principle of heat transfer (i.e., thermal conductivity of the second type known from previous discussions by Green and Naghdi), characterized by zero internal entropy production. All the basic equations of the theory presented in this study are derived from the conventional balance equations of continuum mechanics and the fundamental thermodynamic inequality. Constitutive equations for a linear anisotropic thermoelastic micropolar medium (CGNII) are obtained by using a quadratic energy form for the Helmholtz free energy. Special attention is paid to hemitropic micropolar medium, when the components of one of the fourth rank constitutive pseudotensors demonstrate sensitivity to mirror reflections of three-dimensional space. A closed system of coupled differential equations is given in terms of translational displacement vector, spinor displacement vector and thermal displacement. It is important since can be used in formulations of applied problems of thermomechanics related to the wave heat transfer mechanism in micropolar elastic media.