Wave theory of the laminated plates with approximate consideration of the transverse shear

Composite materials are widely used in the production of aircraft for various purposes. Having several unique properties, composites, due to their heterogeneous structure, are poorly resistant to shock loads. Impulse action spreads inside the material in the form of stress waves, which are reflected on internal inhomogeneities, can overlap, and create very significant bursts of stress. This often leads to the well-known types of failure – spalling and delamination. Practice shows that these fractures occur almost immediately after the loading impulse. To verify the spalling strength, it is necessary to consider the initial unsteady phase of the response to the external impulse. There are sufficiently reliable theories to verify this strength; usually, they do not take transverse shear into account, otherwise the solution becomes unnecessarily cumbersome and poorly observable. Nevertheless, attempts are often made to refine the calculations by approximate consideration of transverse shear. This article presents the wave theory of laminated plates with approximate consideration of transverse shear. The possibility of specifying the calculation of impulse-loaded plates is considered. The inconsistency of the resulting model is proved.

Internal friction influence on the calculation results and rod system optimization under impulse action

An algorithm for calculating elastic rod systems under the action of impulse loads, using a complex model of internal friction in the material, has been developed and implemented in software. Very short (instantaneous) and extended in time impulses are considered as variants of impulse action. The importance of taking into account the vibration energy dissipation due to internal friction in the material of the structure is shown, considering impulse effects. The implemented software module is used to calculate the dynamic responses of the system in the search for the optimal solution of the control program for the selected variable parameters, target and restrictive functions. The problem of optimizing a flat frame system loaded with static and impulse loads has been posed and solved. An algorithm for finding an optimal solution is considered. Variants of dividing variable parameters into generalized groups are discussed. The minimum volume of material, spent on the structure, is taken as an optimality criterion. Analysis of the influence of the pulse duration of a given value on the calculation results without and with internal friction, as well as a comparative analysis of the optimal designs obtained without and with internal friction in the material and various tolerances for horizontal displacements. The results obtained indicate a significant effect of internal friction on the characteristics of the optimal design, especially with active movement restrictions.

Modified Cauchy Problem with Impulse Action for Parabolic Shilov Equations

For parabolic Shilov equations with continuous coefficients, the problem of finding classical solutions that satisfy a modified initial condition with generalized data such as the Gelfand and Shilov distributions is considered. This condition arises in the approximate solution of parabolic problems inverse in time. It linearly combines the meaning of the solution at the initial and some intermediate points in time. The conditions for the correct solvability of this problem are clarified and the formula for its solution is found. Using the results obtained, the corresponding problems with impulse action were solved.

Investigation of solutions of weakly perturbed boundary value problems for systems with impulse action

The paper is devoted to the investigation of the existence and construction of solutions of weakly perturbed linear boundary value problems for systems with impulse action in the case when the generating boundary value problem with impulse action has no solutions for arbitrary right-hand sides. The relevance of this topic is due primarily to the importance of practical application of the theory of boundary value problems in various fields of science and technology - the theory of nonlinear oscillations, the theory of motion stability, control theory, a variety of geophysical problems. On the other hand, the question of the existence and construction of solutions of boundary value problems occupies one of the central and fundamentally important places in the qualitative theory of ordinary differential equations.

TOTAL ENERGY OF HARMONIC OSCILLATOR WITH IMPULSE ACTION

The problem of finding the total energy of a harmonic oscillator with pulsed action at fixed moments of time is considered. Both for the case of the homogeneous equation of harmonic oscillations and for the case of the equation of harmonic oscillations in the presence of external perturbation, formulas for the total energy of the oscillatory system are obtained. The case of periodic impulse effects is analyzed. The conditions under which in this oscillatory system there are periodic modes are specified. It is shown that under the fulfillment of these conditions on the values of impulse action and external perturbation, the total energy of the vibrational system is also a periodic function of the time variable.

Determination of the skip force effect on guides in mine shaft

An analytical solution is presented to the problem of determining the force effect of lifting vessel (skip) on guides during its movement in the mine shaft. Forces values are obtained using acceleration data from sensors of motion smoothness through monitoring system. The technique developed allows to determine skip force effect on guides along all axes of horizontal coordinate system. A transition from a force to impulse action is provided. The interrelation of force action surges with guides profile deviations is analyzed. The results of this study can be widely used to identify the areas in the mine shaft where emergency could potentially occur.