Розглянуто ряди числових схем для обчислення складних конструкцій фіксаторів кісток. Комплекс числових схем забезпечує дискретно безперервний тип обчислень, який дозволяє в адаптивному режимі обчислювати навантаження не лише в елементах конструкції фіксатора, але і в місцях з'єднання фіксатора з кісткою. Розглянуто числові схеми для дослідження елементів з'єднувачів, які також будуються на базі кінематичних гіпотез. Це дослідження розвиває сучасну методологію прогнозування та контролю, засновану на теорії комплексного континіуму.

Розглянуто методи декомпозиції та синтезу числових схем на базі дискретно-неперервних модальних методів і проаналізовано шляхи дослідження поведінки складних механізмів, зважаючи на їх взаємодію з системою поглиначів динамічної вібрації.

The paper deals with the methods of calculation and optimization of constructions of the impact dynamic vibration absorbers (DVA) for the elongated structures. An efficient numerical approach based on the theoretical-experimental method is proposed to maximize the minimal damping of modes in a prescribed frequency range for the tuned-mass impact systems. Methods of decomposition and numerical synthesis are considered on the basis of an adaptive schemes. The influence of dynamic vibration absorbers and basic design elastic and damping properties is under discussion. A technique is developed to give the optimal DVA's for the elimination of excessive vibration in sinusoidal forced systems.

This study aims to predict the sound transmission properties of composite layered plates structures in the lower frequency range. In present paper a novel procedure to derive the sound isolation parameters for layered plates is under discussion. This paper presents a new stress analysis method for the accurate determination of the detailed stress distributions in laminated plates subjected to cylindrical bending. Some approximate methods for the stress state predictions for laminated plates are presented here. The theoretical model described here incorporates deformations of each sheet of the lamina, which account for the effects of transverse shear deformation, transverse normal strain-stress and nonlinear variation of displacements with respect to the thickness coordinate. The main advantage of the present method is that it does not rely on strong assumptions about the model of the plate. Comparison with the Timoshenko beam theory is systematically made for analytical and approximation variants. The geometrical and mechanical parameters dependent frequency response functions and damping are presented for an arbitrary layered beam. The effective stiffness constants of equivalent to lamina Timoshenko beam (TB) and their damping properties have been determined by using a procedure based on multi-level numerical schemes and eigenfrequencies comparison. Numerical evaluations obtained for the vibration of the equivalent TB have been used to determine the sound transmission properties of laminated composite beams with the system of dynamic vibration absorbers (DVA's). The optimization of beams - DVA's system sound absorption properties is performed in the low frequency range. The results have shown that the presence of a DVA causes a decrease in the sound transmission in the low-frequency range. The extension of the present approach to various layered plates with various DVA's systems will be performed in order to obtain optimal sound insulation.

The main aim of this study is to predict the elastic and damping properties of composite laminated plates. Some approximate methods for the stress state predictions for laminated plates are presented. For simple uniform bending and transverse loading conditions, this problem has an exact elasticity solution. This paper presents a new stress analysis method for the accurate determination of the detailed stress distributions in laminated plates subjected to cylindrical bending. The present method is adaptive and does not rely on strong assumptions about the model of the plate. The theoretical model described here incorporates deformations of each sheet of the lamina, which account for the effects of transverse shear deformation, transverse normal strain-stress and nonlinear variation of displacements with respect to the thickness coordinate. Dynamic and damping predictions of laminated plates for various geometrical, mechanical and fastening properties are defined. The comparison with the Timoshenko beam theory issystematically done for analytical and approximation variants. The values of damping are got at a bend in three- and five-layered plates. For the threelayered plates the equivalent beam of Timoshenko exactly approximates a "sandwich" (with a soft damping kernel) dynamic properties of sandwich in a wide frequency range. For a plate with soft external layers the equivalent beam needs to be found in every frequency range separately. A hard bounded layer multiplies damping in a plate with soft external layers, however only at higher frequency of vibrations. For the high-frequency vibrations of plates the anomalous areas of diminishing of damping (for sandwiches) and increase are got for plates with soft covers. At the moderate amount of approximations the exact divisions of tensions are got in the layers of plates, thus the stresses continuity and surface terms are approximated exactly enough. Unlike the widespread theories of plates with the terms set a priori on surfaces (as a rule levels to the zero tensions) the offered equations allow to satisfy and complicated boundary conditions, instead of only free fastened plates. It allowed to explore the row of important examples for plates fastened in a hard holder and to explore influence of not only plates but also construction of holder on damping.

To determine the optimal parameters of the dynamic vibration absorber (DVA), a complete multi-parameter model of the dynamics of machines and structures is required. A model with two degrees of freedom is unacceptable for a sufficiently precise calculation with sufficient accuracy of the oscillations of the design, and thus for an adequate description of its dynamic characteristics. Therefore, in practice, it is necessary to investigate the design using a complex model. In particular, the methods for determining the concentration of mass and stiffness can be used on the basis of a refined theoretical calculation. A number of numerical schemes (NS) are known for complex vibro-loaded structures, in which developed methods of decomposition and synthesis of NS based on new methods of modal synthesis. Also developed is a complex NS of discrete-continuum type, which provides an opportunity in the adaptive mode to calculate stresses not only in the continuum elements, but also in the places of their greatest concentration - in the compounds. In this paper, an efficient numerical approach based on the theoretical-experimental method is proposed to maximize the minimal damping of modes in a prescribed frequency range for general viscous tuned-mass systems. Methods of decomposition and numerical synthesis are considered on the basis of the adaptive schemes. The influence of dynamic vibration absorbers and basic design elastic and damping properties is under discussion. A technique is developed to give the optimal DVA's for the elimination of excessive vibration in sinusoidal and impact forced tall buildings system. One task of this work is to analyze parameters identification of the dynamic vibration absorber and the basic structure. The discrete-continue models of machines dynamics of some elongated element with multi mass DVA's are offered. A technique is developed to give the optimal DVA's for the elimination of excessive vibration in harmonic stochastic and impact loaded systems. The questions of robustness at optimization of DVA are considered. Different types of control management for semi-active DVA's are applied. Examples of DVA's practical implementation are presented.

The study aims to predict elastic and damping properties of composite laminated plates from the measured mechanical characteristics. The elastic constants and damping properties of a laminated element are determined by using experimental data and the results of a multi level theoretical approach. Solution examples for particular problems are given. On the basis of static three-point bending tests, measured eigenfrequencies, and refined calculation schemes, the elastic properties of layered composite beams were identified. For determining Young's and shear moduli, the method of genetic minimization of error function was used. It is shown that, by employing combined criteria, the transverse elastic moduli can be determined uniquely. It is shown that, by employing combined criteria, the transverse elastic moduli can be determined. The elastic modules were also determined from measured vibration eigen-frequencies of the beams. New combined criteria of identification - schemes averaged over the calculation results for a homogeneous beam and for a sandwich with a core identical to the homogeneous beam and rigid outer layers are considered. The error function is chosen as the sum of error functions for the homogeneous beam, and for the sandwich. In the present study, combined identification schemes making it possible to unequivocally determine the transverse modules and Poisson ratio are suggested.

Passive, broadband targeted energy transfer refers to the one-way directed transfer of energy from a primary subsystem to a nonlinear attachment; this phenomenon is realized in damped, coupled, essentially nonlinear impact or particle dynamic vibration absorber (DVA). An impact damper is a passive control device which takes the form of a freely moving mass, constrained by stops attached to the structure under control, i.e. the primary structure. The damping results from the exchange of momentum during impacts between the mass and the stops as the structure vibrates. A particle-based damping system can overcome some limitations of ordinary DVA by using particles as the damping medium and inter- particle interaction as the damping mechanism. Large damping at such family constructions of DVA's does not bring to destruction an elastic DVA element over in critical cases, when working frequency approaches own frequency of DVA, or when the transitional process of acceleration of rotating machines is slow enough and DVA's has time to collect large amplitudes of vibrations. The primary structure is modelled as a spring-mass system. In this paper, an efficient numerical approach based on the theoretical-experimental method is proposed to maximize the minimal damping of modes in a prescribed frequency range for general viscous tuned-mass systems. Methods of decomposition and numerical synthesis are considered on the basis of the adaptive schemes. The influence of dynamic vibration absorbers and basic design elastic and damping properties is under discussion. A technique is developed to give the optimal DVA's for the elimination of excessive vibration in sinusoidal forced rotating system. It is found that the buffered impact damper not only significantly reduces the accelerations, contact force and the associated noise generated by a collision but also enhances the level of vibration control. The interaction of DVA's and basic design elastic and damping properties is under discussion. One task of this work is to analyze parameters identification of the dynamic vibration absorber and the basic structure. The discrete-continue models of machines dynamics of such rotating machines as water pump with the attachment of particle DVA's and elongated element with multi mass impact DVA's are offered. A technique is developed to give the optimal DVA's for the elimination of excessive vibration in harmonic stochastic and impact loaded systems.