THE FRACTAL SCALE-INVARIANT STRUCTURE OF A TEMPORAL HIERARCHY IN THE RELAXATION PROCESSES

The phenomena of elastic aftereffects during loading/unloading of viscoelastic and capillary-porous bodies, relaxation of their stresses is accompanied by the energy accumulation and dissipation to be taken into account in the theory of oscillations which also considers the behavior of materials when the force is applied to them, the elastic aftereffect and stress relaxation forms ostensibly opposite energy processes that’s why the main problem to one is to understand and discovery laws for such aftereffects. The goal of the research to show that the distribution of relaxation time in viscoelastic and capillary-porous media may have a scale-invariant structure and that the indirect confirmation of the scale invariance of relaxation time hierarchy can be the principle of temperature-time superposition according to which the experimental relaxation functions obtained for different temperatures can be combined with each other using the appropriate coordinate axes stretching. We used methods of viscoelastic theory, fractal analysis and methods of mathematical physics. So, in this paper, an attempt has been made to harmonize both these theories and numerous experiments on the destruction of materials described in the academic literature. It is shown that the hierarchy of times determining shear and bulk relaxation in viscoelastic/capillary-porous medium has a fractal structure and it was observed that the presence of time fractality eases the modeling of viscoelastic/capillary-porous bodies resulting in the universal relaxation function of a rather simple kind.

THE FRACTAL SCALE-INVARIANT STRUCTURE OF A TEMPORAL HIERARCHY IN THE RELAXATION PROCESSES

The phenomena of elastic aftereffects during loading/unloading of viscoelastic and capillary-porous bodies, relaxation of their stresses is accompanied by the energy accumulation and dissipation to be taken into account in the theory of oscillations which also considers the behavior of materials when the force is applied to them, the elastic aftereffect and stress relaxation forms ostensibly opposite energy processes that’s why the main problem to one is to understand and discovery laws for such aftereffects. The goal of the research to show that the distribution of relaxation time in viscoelastic and capillary-porous media may have a scale-invariant structure and that the indirect confirmation of the scale invariance of relaxation time hierarchy can be the principle of temperature-time superposition according to which the experimental relaxation functions obtained for different temperatures can be combined with each other using the appropriate coordinate axes stretching. We used methods of viscoelastic theory, fractal analysis and methods of mathematical physics. So, in this paper, an attempt has been made to harmonize both these theories and numerous experiments on the destruction of materials described in the academic literature. It is shown that the hierarchy of times determining shear and bulk relaxation in viscoelastic/capillary-porous medium has a fractal structure and it was observed that the presence of time fractality eases the modeling of viscoelastic/capillary-porous bodies resulting in the universal relaxation function of a rather simple kind.

Energy Accumulation and Dissipation of Coal with Preopening under Uniaxial Loading

Energy accumulation and dissipation play an important role during the entire process of rock failure. Some flaws, such as preexisting holes, will influence energy accumulation and dissipation. In order to investigate the energy evolution of coal specimen with preexisting holes under uniaxial compression through numerical approaches, the particle simulation method was used in numerical simulations. In this paper, the energy evolution of coal specimen was theoretically analyzed, and the influence of different hole arrangement, such as diameter, spacing, angle, and number, on the evolution characteristics of energy was also discussed. At the same time, the arrangement of the artificial boreholes for preventing the rockburst was explored. The results show that, compared with the intact coal specimen, the change of diameter, spacing, angle, and the number of holes weakened the coal specimen’s capacity to store energy and release strain energy. When the diameter, the vertical distance, and relative angle of preexisting holes were 15 mm, 10∼15 mm, and 60°, respectively, the energy storage limit reached optimal value. For arrangement of the artificial boreholes, the diameter, spacing, and angle can be designed on the basis of those optimal values. This study has a guiding significance in designing the arrangement of the artificial boreholes for mitigation of rockburst.

Destabilization and energy characteristics of coal pillar in roadway driving along gob based on rockburst risk assessment

Roadway driving along adjacent goafs is an effective method to develop the recovery rate of coal resources. However, rock burst triggered by dynamic destabilization of coal pillars poses a serious threat to safe and efficient mining, thereby significantly restricting the sustainable development of coal mines. In this study, from the perspectives of energy accumulation and dissipation, a mathematical model of coal pillars is established and the energy equilibrium relationship of the mechanical system is analysed. The rock burst mechanism of coal pillars in gob-side entry is obtained based on a fold catastrophe mathematical model. Results indicate that the rock burst triggered by the instability is a destabilization phenomenon. If the stiffness factor of the mechanical system is less than 1 and the external force is enough to lead coal pillars to the peak stress point, then rock burst disaster occurs. The engineering analysis and numerical simulation are conducted to study the rock burst in the gob-side entry that occurred in Xin'an coal mine. Stress release caused by mining can reduce the risk of rock burst to a certain extent. The amount of elastic energy released is 6.4512 × 10 7 J, which is close to the observation data and verifies the correctness and rationality of the research method. The research result provides a theoretical basis and technical guidance for rock burst prevention and control in roadway driving along adjacent goafs.

Mathematical Model of a Shape Memory Alloy Spring Intended for Vibration Reduction Systems

The article discusses a prototype of a Shape Memory Alloy (SMA) spring intended for controlled vibration reduction systems. The spring has been subject to experiments and the article presents selected static and dynamic characteristics. The experiments were conducted at the Dynamics and Control of Structures Laboratory of the AGH University of Science and Technology. They permitted the formulation of a mathematical model for the SMA spring. The model takes into account the phenomena of energy accumulation and dissipation. The parameters of the spring model have been determined, based on the experimental data. The model takes into account the relationship of stiffness and damping to alloy temperature and the frequency of excitation. It has been demonstrated that the properties of the spring may be altered under controlled conditions. The spring model was then used in simulations. They served as the basis for the determination of the frequency response characteristics, which were then compared to the characteristics of a real spring. The mathematical model developed may be applied in the design of passive, semi-active, and active vibration reduction systems, as well as in the synthesis of adaptive smart vibration reduction systems.