Mechanics of Solids最新文献

Since the layer of the Earth is non-homogeneous and initially stressed, this paper has framed to discuss propagation of torsional type surface wave in an initially stressed poroelastic medium sandwiched between a non-homogeneous layer with linear type variation in density and rigidity and a half-space of heterogeneous medium with exponential type variation in density and rigidity. Dispersion equation of this kind of wave has been obtained with the help of Whittaker’s expansion and separation of variables method under some specified boundary conditions. The effect of non-homogeneity related with layer and half-space and initial stress of sandwiched medium have been illustrated based on their graphical discussion. It has been found that the presence of non-homogeneity in the material enhances the phase velocity but it also enhances the phase velocity with descending values of initial stress.

The casing system is the skeleton of the aero-engine, and its vibration directly reflects the vibration level of the whole aero-engine. Different from the previous modeling of the casing system as a cylindrical shell, this paper creatively establishes the lumped mass modal coupling vibration model of the bolted connection casing system from the perspective of micro contact mechanics. The bolted connection characteristics and Hertz contact characteristics of micro topography of discontinuous casing are considered, which rarely appear in previous studies on casing system modeling. The paper first completes the interface contact mechanics modeling of bolted connection, and then the establish interface contact mechanics model is effectively verified (by comparing with classical model and finite element model). Based on the established contact mechanics model of the connection interface, a modal coupling model of the casing system is established. The effects of interface stiffness ratio, interface fractal parameters, the number of connection bolts and friction coefficient on the stability of the system are analyzed. This study establishes a bridge between micro contact and macro system vibration analysis, which can be used to establish the dynamic model of similar bolted connection system in engineering.

The article proposes a spatial model of an exoskeleton for the human musculoskeletal system, represented by three movable links of variable length and two-point masses. The stiffness of the links is controlled by changing the voltage supplied to the magnetic rheological fluid, which fills sections of variable length. The model can be used to develop comfortable exoskeletons, the kinematic characteristics of which are close to the kinematic characteristics of the human musculoskeletal system. The model dynamics equations are constructed using local coordinate systems.

The required laws of change of generalized coordinates are specified by the equations of program constraints that determine the dependence of differentiable periodic functions on time. Control moments and longitudinal forces are determined by methods of solving inverse dynamics problems and are realized by changing the magnetic field strengths, which affect the change in the stiffness of the magnetic-rheological fluid. The magnetic field strengths that control the stiffness of the link are implemented by step functions. An animation of the movement of the mechanism has been synthesized, showing the adequacy of the proposed modeling procedure. The constraints of the links are modeled by joints and motors that implement the necessary rotational motion. The dynamics of the model is controlled by changing the lengths of the links and the angles between the links.

The problem of constructing the worst-case disturbance for an oscillator with quadratic damping is considered. The disturbance is carried out by an external force, which is applied to the oscillator body, does not change the direction of its action and has a given impulse (time integral). It is assumed that before the onset of the disturbance the oscillator is in a state of equilibrium. The worst disturbance is considered to be one in which the absolute value of the displacement of the oscillator body from the equilibrium position reaches its maximum value. In the class of disturbances of a rectangular profile with a given impulse, the worst disturbance and the corresponding largest displacement and the time to reach it were found, depending on the parameters of the oscillator.

In many crashworthiness protection conditions, materials with excellent energy absorption have been studied, and safety protection is more and more important. In this paper, several orthogonal trapezoidal aluminum honeycombs with different structures and morphologies were manufactured. Static tests and simulation analysis were carried out with different layers and sorting order and the effects were studied. Deformation mode and the influence of stress were analyzed to obtain a stable structure. The structure is intended to be used as a filling material for the impact limiter of the nuclear spent fuel transport cask.

With the application of tiny components in scientific research and daily life, heat conduction and structural shape change in solids have attracted the idea of researchers. So further refinement of the theoretical model of thermo-viscoelastic hollow cylinders with fractional-order derivatives is the fundamental purpose of this study and development of fractional-order thermoelasticity theory with fractional-order strains to provide theoretical foundations for some thermodynamic practical applications (e.g., pipeline transport of gases or liquids) and selection of elastic and viscoelastic materials. In this paper, the dynamic response of the inner and outer surfaces of an infinitely sizeable hollow cylinder under the action of thermal shock is examined based on the fractional-order two-phase hysteresis theory and viscoelasticity theory. Convective boundary conditions are imposed on the inner and outer surfaces of the hollow cylinder and there is no traction on the inner and outer surfaces. The governing equations of the problem are established and solved by the Laplace transform method. In the numerical calculations, firstly, the effects of viscoelastic parameters on heat transfer as well as the stability of material structure are examined; secondly, the effects of fractional-order strain parameters on the model and their variations are examined; and finally, the effects brought about by the selection of hysteresis factors are examined. The results show that the introduction of the fractional order strain parameter has an important effect on the generalized thermoelastic model, and the viscoelastic parameter has a significant effect on the physical field of the hollow cylinder, especially the displacement and stress.

Fracture toughness is an important parameter in industry for measuring material properties. In order to obtain the fracture toughness of standard thickness materials it is necessary to go through a large number of fracture toughness experiments, but the cost is high. And in practice there are not that many eligible experimental materials to be able to conduct the experiment. If fracture toughness data are obtained for small specimens. Fracture toughness data for large and thick specimens can be predicted by the toughness scaling model (TSM). The relationship between fracture toughness based on Weibull’s principle of stress equivalence. Can effectively make up for the defect of the specimen’s own constraint degree is insufficient. The parameters of the Toughness scaling model are decisive for the accuracy of the predicted fracture toughness data. The traditional TSM calibration procedure is complex. Using a simplified Toughness scaling model can reduce many arithmetic steps in engineering. And this method was applied to calibrate the parameters for three materials. It was found that the predicted probability of failure-fracture toughness curves at a crack tip of 0.02 mm–0.03 mm for the low constraint specimens were informative although there was some error. Also, the linear relationship between the magnitude of the Weibull stress and the fracture toughness is independent of the material type. It is only related to the magnitude of parameter m.

The problem on optimal rotation of a solid (spacecraft) from an arbitrary initial to a prescribed final angular position in the presence of restrictions on the control variables is studied. The turnaround time is set. To optimize the rotation control program, a combined quality criterion that reflects energy costs is used. The minimized functional combines in a given proportion the integral of the rotational energy and the contribution of control forces to the maneuver. Based on the Pontryagin’s maximum principle and quaternion models of controlled motion of a solid, an analytical solution of the problem has been obtained. The properties of optimal movement are revealed in analytical form. To construct an optimal rotation program, formalized equations and calculation formulas are written. Analytical equations and relations for finding optimal control are given. The key relations that determine the optimal values of the parameters of the rotation control algorithm are given. In addition, a constructive scheme for solving the boundary value problem of the maximum principle for arbitrary turning conditions (initial and final positions and moments of inertia of a solid) is described. For a dynamically symmetric solid, a closed-form solution for the reorientation problem is obtained. A numerical example and mathematical modeling results that confirm the practical feasibility of the developed method for controlling the orientation of a spacecraft are presented.

The soil layer of the roadbed is an uneven unsaturated soil layer in practical engineering. The goal of this article is to consider the uneven gradient distribution of soil particle compression modulus and soil skeleton compression modulus along the depth of unsaturated roadbed soil. Introducing an uneven gradient factor is to propose a power function continuous variation model for the soil particle compression modulus and soil skeleton compression modulus of the roadbed soil along the depth of the soil layer. Then, the model is coupled with Biot’s theory of unsaturated porous media to establish a dynamic response model for non-uniform unsaturated soil layer roadbed under uniform moving loads, and provided a method for using Fourier series to solve the model. Analysis the influence of soil particle compression modulus and soil skeleton compression modulus on the dynamic response of unsaturated soil layers under uniform moving loads. The results indicate that the deformation displacement is positively correlated with the non-uniform gradient factor of modulus. The deeper the depth, the weaker the influence of the non-uniform gradient factor on the peak pore water pressure. At the same location from the vibration source, the influence of the non-uniform gradient factor of soil particle compression modulus on the peak pore water pressure is not significantly different from the influence of soil skeleton compression modulus on the peak pore water pressure. However, the gradient factor of soil particle compression modulus has a greater impact on the peak deformation displacement than the factor of skeleton compression modulus. Thus, clarified the influence of the non-uniform gradient factor of soil particle compression modulus and soil skeleton compression modulus along depth on the dynamic response of the non-uniform unsaturated soil layer roadbed under uniform moving load.

The model of horizontal layered structure in elastic solids has a wide range of applications in our real-world scientific research. To explore the propagation characteristics of cylindrical Rayleigh waves in a horizontally layered structure, we decompose the displacement using the Helmholtz decomposition method in the cylindrical coordinate system in order to use potential functions to describe the displacement and stress of the medium. Following this, the paper employs the transfer matrix method to derive the dynamic equations of axisymmetric Rayleigh waves in a horizontally layered elastic solid. After that, the equations are solved to obtain the Rayleigh wave dispersion curves and displacement expressions with Bessel function under these conditions. Lastly, through the calculations of four representative numerical examples, this paper verifies the consistency of the algorithm in calculating cylindrical Rayleigh wave dispersion curves and its agreement with experimental measurements, while demonstrating the characteristics of cylindrical Rayleigh wave displacement.