Mechanics of Solids最新文献

Based on experimental data on the combined loading of an infinite layer weakened by a circular hole in a brittle material, its critical state, determined by the energy criterion, is modeled. The failure criterion is related to the free energy flow through the interaction arc and the linear size. The proposed approach allows us to reflect the dependence of the critical external load on the radius of curvature. A procedure for determining the value of the linear size is proposed and implemented. Using known experimental results, an estimate of the introduced linear parameter for a layer of GVVS-16 gypsum was obtained.

It is noted that, based on observations of fluctuations of the ice cover in natural conditions under the influence of moving loads, i.e., when excitation of flexural gravity waves (FGW), the latter behaves similarly to an elastic isotropic plate. On this basis, a new direction has been proposed in modeling some problems of deformation of the FGW ice cover on elastic films in conventional experimental basins. The possibility of this technology is confirmed by the results of comparing records of deformation by moving loads of an elastic model layer and a natural ice cover. Based on the theory of similarity and dimensions, dependencies were obtained for converting model test data to full scale. It is noted that the costs of conducting such model experiments are disproportionately less than the costs of conducting experiments in ice basins. Ice engineering problems are listed, in solving which the developed FGW modeling technique can be used.

We consider the problem of controlling a spherical robot with a pendulum actuator rolling on a platform that is capable of moving translationally in the horizontal plane of absolute space. The spherical robot is subject to holonomic and nonholonomic constraints. Some point target moves at the level of the geometric center of the spherical robot and does not touch the moving platform itself. The motion program that allows the spherical robot to pursue a target is specified through two servo-constraints. The robot can follow a target from any position and with any initial conditions. Two ways to control this system in absolute space are proposed: by controlling the forced motion of the platform (the pendulum oscillates freely) and by controlling the torque of the pendulum (the platform is stationary or oscillates inconsistently with the spherical robot). The equations of motion of the system are constructed. In the case of free oscillations of the pendulum, the system of equations of motion has first integrals and, if necessary, can be reduced to a fixed level of these integrals. When a spherical robot moves in a straight line, for a system reduced to the level of integrals, phase curves, graphs of the distance from the geometric center of the spherical robot to the target, the trajectory of the selected platform point when controlling the platform, and the square of the control torque when controlling the pendulum actuator are constructed. When the robot moves along a curved path, integration is carried out in the original variables. Graphs of the squares of the angular velocity of the pendulum and the spherical robot itself are constructed, as well as the trajectory of the robot’s motion in absolute space and on a moving platform. Numerical experiments were performed in the Maple software package.

In this work, a novel multi-span metamaterial dual-beam (MMDB) structure is proposed for the effective suppression of ultra-low-frequency vibrations in beam structures. The MMDB is composed of a periodic array of units, with each simply supported unit including beams at the top and bottom, and a spring-mass-spring resonator connecting two beams. For analyzing the dynamic behavior of the MMDB, the spectral element method (SEM) is utilized to establish a dynamic model. A comparative analysis is conducted with a traditional metamaterial dual-beam model, highlighting the advantages of the proposed MMDB. The vibration transmittance of the MMDB under base excitation is analyzed, during which the bandgap frequency beginning from zero is generated. The MMDB is further modeled by the finite element method (FEM), and the simulation results of transmittance agree well with those obtained through SEM, validating the effectiveness of the utilized approach. The band structure of the MMDB structure is further obtained and local resonance and Bragg bandgaps are simultaneously found. Subsequently, parameter study is conducted to investigate the effects of material and geometry parameters on the bandgap characteristics of the MMDB. This work provides valuable guidelines for the design of multi-layer beam structures aimed at efficiently suppressing vibrations within the ultra-low-frequency range.

Utilizing the unsaturated porous elastic media theory, the study investigates the scattering of plane P-waves by a single-layer lined tunnel within an unsaturated half-space. The analysis employs the Fourier–Bessel series expansion for wave functions for this purpose. Through numerical examples, this study analyzes how physical and mechanical parameters like incident wave frequency, angle, saturation, and burial depth affect the surface displacement amplitude in a single-layer lined tunnel within an unsaturated soil half-space under P-wave incidence. Results indicate that saturation significantly influences the surface displacement amplitude. The maximum surface displacement amplitude in the single-layer lined tunnel at low saturation levels exceeds that observed at high soil saturation. The surface displacement amplitude inside the single-layer lined tunnel and on its left side varies sharply and remains high across different incident frequencies. Conversely, the surface displacement amplitude on the right side of the single-layer lined tunnel exhibits a relatively gentle change and is lower. This variation becomes more pronounced with increasing frequency. At a low wave frequency, the displacement amplitude of the single-layer lined tunnel decreases with the increase of the burial depth. When the incident wave frequency is high, the displacement amplitude of the single-layer lined tunnel exhibits a marked change with burial depth increment.

The present paper is aimed at studying the reflection of thermoelastic waves under the generalized thermoelasticity theory is employed to study the reflection of plane harmonic waves from a semi-infinite elastic solid under the effect of the magnetic field in a vacuum. The formulation is applied under the thermoelasticity theory with three-phase-lag. The expressions for the reflection coefficients, which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves, are obtained. Similarly, the reflection coefficient ratio variations with the angle of incident under different conditions are shown graphically. Comparisons are made with the results predicted by different theories Lord-Shulman theory (L-S), the Green-Naghdi theory of type III (G-N III) and the three-phase-lag model (3PHL) in the absence and presence of a magnetic field. The new results obtained clear that the external parameters and theories applied have strong impact on the phenomenon and applicable on the related topics as geophysics, acoustics, aerospace. astronomy, …, etc

In this study we apply multi-temperatures theory to the two-dimensional deformation of a homogeneous, isotropic, thermoelastic half-space with voids under the influence of initial stress. The problem was developed within the context of Lord-Shulman theory. The methodology used here is normal mode analysis to solve the problem and get exact expressions for displacements, stresses, strain, conductive temperature, thermodynamic temperature, and change in volume fraction field. These quantities constructed in the physical domain are displayed graphically. The numerical results of these quantities for magnesium crystal-like material are shown to represent the influence of multi- temperatures and initial stress.

Boundary conditions play a crucial role from theoretical and experimental perspectives in comprehending the dynamics of wave propagation in elastic solids. Stress free boundary conditions, are achieved by setting the surface tractions to zero, while for rigid surface boundary conditions displacements, are equated to zero. Despite utility of these two types of boundary conditions, it is crucial to acknowledge that these conditions are the extreme idealizations, and real-world scenarios often fall somewhere between the extremes of stress free and rigid surface boundary conditions. In the current investigation, the elastically restrained boundary conditions (ERBC) are proposed to examine the propagation of plane waves at the surface of semi-infinite elastic media. The elastically restrained boundary conditions act as an intermediate link between traction-free and rigid surface conditions. In the study, a microstructural couple stress half-space is considered to comprehend the propagation of surface waves. The impacts of boundary conditions are depicted through three parameters called as normal stiffness (left( {{{k}_{n}}} right)), shear stiffness (left( {{{k}_{t}}} right)), and rotational stiffness (left( {{{k}_{r}}} right)). The characteristic length scale parameter (l) within the couple stress model represents the influence of microstructural effects. Dispersion relations have been derived analytically and the classical cases of stress-free (Rayleigh type wave), rigid surface boundary conditions are obtained as the special cases. Mathematical results have been illustrated graphically.

Plane stress solutions in plasticity have qualitative features not inherent to other deformation modes. Examples are a particular condition of the non-existence of solutions and the necessity to verify that the conditions under which the assumption of plane stress is acceptable are satisfied. Therefore, analytical and semi-analytical solutions are advantageous over numerical solutions, even though the former require simplified constitutive equations. A typical approach for deriving analytical and semi-analytical solutions to axisymmetric problems is to assume Tresca’s yield criterion or another yield criterion represented by linear equations in terms of the principal stresses. Such yield criteria are piecewise linear, and the solution to a boundary value problem usually involves several plastic regimes, making it cumbersome. Moreover, using piecewise linear yield criteria may significantly affect predicted strain distributions compared to smooth yield criteria, which are more accurate for most metals. The present paper provides a general axisymmetric elastic perfectly plastic solution for an arbitrary isotropic yield criterion under plane stress conditions. The flow theory of plasticity based on the associated plastic flow rule is used. Obtaining quantitative results requires evaluating ordinary integrals by a numerical method. The solution is especially simple if one of the boundary conditions requires that the stress components are constant on a surface surrounded by a plastic region. A numerical example of using the solution is presented.