An infinite plate loaded with a normal force moving along a complex open trajectory

Introduction. A method for solving the problem on the action of a normal force moving on an infinite plate according to an arbitrary law is considered. This method and the results obtained can be used to study the effect of a moving load on various structures.Materials and Methods. An original method for solving problems of the action of a normal force moving arbitrarily along a freeform open curve on an infinite plate resting on an elastic base, is developed. For this purpose, a fundamental solution to the differential equation of the dynamics of a plate resting on an elastic base is used. It is assumed that the movement of force begins at a sufficiently distant moment in time. Therefore, there are no initial conditions in this formulation of the problem. When determining the fundamental solution, the Fourier transform is performed in time. When the Fourier transform is inverted, the image is expanded in terms of the transformation parameter into a series in Hermite polynomials.Results. The solution to the problem on an infinite plate resting on an elastic base, along which a concentrated force moves at a variable speed, is presented. A smooth open curve, consisting of straight lines and arcs of circles, was considered as a trajectory. The behavior of the components of the displacement vector and the stress tensor at the location of the moving force is studied, as well as the process of wave energy propagation, for which the change in the Umov-Poynting energy flux density vector is considered. The effect of the speed and acceleration of the force movement on the displacements, stresses and propagation of elastic waves is investigated. The influence of the force trajectory shape on the stress-strain state of the plate and on the nature of the propagation of elastic waves is studied. The results indicate that the method is quite stable within a wide range of changes in the speed of force movement.Discussion and Conclusions. The calculations have shown that the most significant factor affecting the stress-strain states of the plate and the propagation of elastic wave energy near the concentrated force is the speed of its movement. These results will be useful under studying dynamic processes generated by a moving load.

Elastic Properties Estimation of Masonry Walls through the Propagation of Elastic Waves. An Experimental Investigation

Structural identification is one of the most important steps when dealing with historic buildings. Knowledge of the parameters, which define the mechanical properties of these kinds of structures, is fundamental in preparing interventions aimed at their restoration and strengthening, especially if they have suffered damage due to strong events. In particular, by using non-destructive techniques it is possible to estimate the mechanical characteristics of load-bearing structures without compromising the artistic value of the monumental buildings. In this paper, after recalling the main theoretical aspects, the use of elastic waves propagation through impact tests for the characterization of the masonry walls of a monumental building is described. The impact test allowed us to estimate the elastic characteristics of the homogeneous solid equivalent to masonry material. This confirms the great potential of the non-destructive diagnostics suitable for analyzing important structural parameters without affecting the preservation of historical masonry structures.

The Emergence of Sequential Buckling in Reconfigurable Hexagonal Networks Embedded into Soft Matrix

The extreme and unconventional properties of mechanical metamaterials originate in their sophisticated internal architectures. Traditionally, the architecture of mechanical metamaterials is decided on in the design stage and cannot be altered after fabrication. However, the phenomenon of elastic instability, usually accompanied by a reconfiguration in periodic lattices, can be harnessed to alter their mechanical properties. Here, we study the behavior of mechanical metamaterials consisting of hexagonal networks embedded into a soft matrix. Using finite element analysis, we reveal that under specific conditions, such metamaterials can undergo sequential buckling at two different strain levels. While the first reconfiguration keeps the periodicity of the metamaterial intact, the secondary buckling is accompanied by the change in the global periodicity and formation of a new periodic unit cell. We reveal that the critical strains for the first and the second buckling depend on the metamaterial geometry and the ratio between elastic moduli. Moreover, we demonstrate that the buckling behavior can be further controlled by the placement of the rigid circular inclusions in the rotation centers of order 6. The observed sequential buckling in bulk metamaterials can provide additional routes to program their mechanical behavior and control the propagation of elastic waves.

The study of dynamical processes in problems of mesofracture layers exploration seismology by methods of mathematical and physical simulation

The article is devoted to the study of the propagation of elastic waves in a fractured seismic medium by methods of mathematical modeling. The results obtained during it are compared with the results of physical modeling on similar models. For mathematical modeling, the grid-characteristic method with hybrid schemes of 1-3 orders with approximation on structural rectangular grids is used. The ability to specify inhomogeneities (fractures) of various complex shapes and spatial orientations has been implemented. The description of the developed mathematical models of fractures, which can be used for the numerical solution of exploration seismology problems, is given. The developed models are based on the concept of an infinitely thin fracture, the size of the opening of which does not affect the wave processes in the fracture area. In this model, fractures are represented by boundaries and contact boundaries with different conditions on their surfaces. This approach significantly reduces the need for computational resources by eliminating the need to define a mesh inside the fracture. On the other hand, it allows you to specify in detail the shape of fractures in the integration domain, therefore, using the considered approach, one can observe qualitatively new effects, such as the formation of diffracted waves and a multiphase wavefront due to multiple reflections between the surfaces, which are inaccessible for observation when using effective fracture models actively used in computational seismic. The obtained results of mathematical modeling were verified by physical modeling methods, and a good agreement was obtained.

О разрушении упругих полимерных материалов под воздействием электронного пучка

An explanation for a feature found in several experiments in the general picture of the destruction of non-brittle polymers under the influence of a shock wave initiated by a powerful electron beam is proposed. The distance of the cracking region from the surface of the material affected by the beam to a finite length in depth is associated with the three-dimensional nature of the propagation of elastic waves. The universality of the effect is demonstrated by the simplest isotropic model, which shows that large tensile stresses are effectively generated inside the target at its sufficiently large transverse and longitudinal size, even without taking into account nonlinear and shear processes.

On the question of mathematical modeling of the plasma deposition process in the restoration of agricultural machinery parts

This article deals with the mathematical description of technological processes of plasma spraying, which has recently been actively used in the repair and restoration of friction parts of agriculture. The influence of elastic wave velocities on the physical-mechanical and thermophysical characteristics of plasma sputtering is studied. In the course of the study, equations were developed that determine the velocity of propagation of elastic waves in a two-component medium under plasma sputtering.

High-frequency homogenization in periodic media with imperfect interfaces

In this work, the concept of high-frequency homogenization is extended to the case of one-dimensional periodic media with imperfect interfaces of the spring-mass type. In other words, when considering the propagation of elastic waves in such media, displacement and stress discontinuities are allowed across the borders of the periodic cell. As is customary in high-frequency homogenization, the homogenization is carried out about the periodic and antiperiodic solutions corresponding to the edges of the Brillouin zone. Asymptotic approximations are provided for both the higher branches of the dispersion diagram (second-order) and the resulting wave field (leading-order). The special case of two branches of the dispersion diagram intersecting with a non-zero slope at an edge of the Brillouin zone (occurrence of a so-called Dirac point) is also considered in detail, resulting in an approximation of the dispersion diagram (first-order) and the wave field (zeroth-order) near these points. Finally, a uniform approximation valid for both Dirac and non-Dirac points is provided. Numerical comparisons are made with the exact solutions obtained by the Bloch–Floquet approach for the particular examples of monolayered and bilayered materials. In these two cases, convergence measurements are carried out to validate the approach, and we show that the uniform approximation remains a very good approximation even far from the edges of the Brillouin zone.

Characterization, stability, and application of domain walls in flexible mechanical metamaterials

Domain walls, commonly occurring at the interface of different phases in solid-state materials, have recently been harnessed at the structural scale to enable additional modes of functionality. Here, we combine experimental, numerical, and theoretical tools to investigate the domain walls emerging upon uniaxial compression in a mechanical metamaterial based on the rotating-squares mechanism. We first show that these interfaces can be generated and controlled by carefully arranging a few phase-inducing defects. We establish an analytical model to capture the evolution of the domain walls as a function of the applied deformation. We then employ this model as a guideline to realize interfaces of complex shape. Finally, we show that the engineered domain walls modify the global response of the metamaterial and can be effectively exploited to tune its stiffness as well as to guide the propagation of elastic waves.