Nonlinear Mathematical Models of Metamaterials Defined as “Mass-in-Mass” and “Damper-in-Mass” Chains

To describe dynamic processes in an acoustic (mechanical) metamaterial, there are proposed models that are a one-dimensional chain containing the same masses connected by linearly elastic (or nonlinearly elastic) elements (springs) with the same stiffness. In this case, it is assumed that each mass contains inside itself a series connection of another mass and an elastic element or viscous element (damper).

Investigation of dynamics of elastic element of vibration device

ва подхода к решению аэрогидродинамической части задачи, основанные на методах теории функций комплексного переменного и методе Фурье. В результате применения каждого подхода решение исходной задачи сведено к исследованию дифференциального уравнения с частными производными для деформации элемента, позволяющего изучать его динамику. На основе метода Галеркина произведены численные эксперименты для конкретных примеров механической системы, подтверждающие идентичность решений, найденных для каждого дифференциального уравнения с частными производными. The dynamics of an elastic element of a vibration device, simulated by a channel, inside which a stream of a liquid flows, is investigated. Two approaches to solving the aerohydrodynamic part of the problem, based on the methods of the theory of functions of a complex variable and the Fourier method, are given. As a result of applying each approach, the solution to the original problem is reduced to the study of a partial differential equation for the deformation of an element, which makes it possible to study its dynamics. Based on the Galerkin method, the numerical experiments were carried out for specific examples of mechanical system, confirming the identity of the solutions found for each partial differential equation.

About the weight and size parameters of electromagnetic stiffness correctors

A significant reduction in the levels of general ship vibrations can be achieved by using vibration isolators with a “floating” section of zero stiffness in vibration protection suspensions. In such devices, in parallel to the main elastic element, the so-called stiffness corrector (compensator) is switched on - a device with a negative coefficient of static stiffness, equipped with a restructuring system that ensures the retention of the corrector elements when the relative position of the vibrating and protected objects, caused by a change in static forces acting on these objects. One of the variants of the corrector is an electromagnetic stiffness corrector, in which the power characteristic with a negative stiffness coefficient is provided by two electromagnets with a common armature turned on in opposite directions. The disadvantage of such correctors is the dependence of their overall dimensions on the value of the permissible relative displacement of the vibrating and protected objects. The article deduced mathematical expressions that approximately determine the dependence of the overall dimensions of the stiffness corrector electromagnets on the value of the calculated relative displacement of the vibrating and protected objects, the possible field of application of vibration isolators Xwith electromagnetic stiffness correctors is determined.

Study of a Stripper Header for Grain Harvesting as a Vibrating System

Introduction. Grain losses caused by stripping defects are the main problem to be solved in designing a stripper header. To reduce these losses, a design of a stripper header with a vibration drive is proposed. This device combines the processes of stripping grain crops and the vibration effect of the stripping fingers upon the ears of plants. The most important stage of the mathematical description of these processes is composing the differential equation of the stripping fingers motion. Materials and Methods. A computational-graphic diagram of an oscillatory system with one degree of freedom is proposed. To compose the differential equation of the stripping fingers motion, a method based on the application of the Lagrange equation was used. The oscillations of the system under studying arise from the motion of a point in the system according to a given law. The problem of kinematic excitation is reduced to the problem of force perturbation. This stage of the study was carried out without taking into account the resistance forces. Results. An equation for motion of stripping fingers making vibrational reciprocating movements is obtained. It is proposed to select the elastic element in the design scheme and consider a more general case of the stripping fingers movement. In this case, the movement of the stripping fingers is considered to be difficult. A characteristic feature of the mathematical description is the presence of a generalized force of potential forces. The differential equation of motion of a comb in the presence of an elastic element and the solution of this equation are composed. Discussion and Conclusion. Forced oscillations of a system without resistance, excited by a harmonic disturbing force, are harmonic oscillations with constant amplitude. On close values of the angular frequency of vibration of the drive output link and the root of the ratio of the stiffness coefficient of the elastic element to the stripping fingers mass, the case of resonance takes place. The system parameters must be selected so as to avoid this negative phenomenon.

Моделирование динамического воздействия авиационного двигателя на крыло самолета при отрыве лопатки вентилятора

One of the requirements for a projected aircraft is the ability to continue flying and land in the event of a breakdown of one of the engines. One of the calculated cases of engine breakdown is a fan blade breakaway. This phenomenon causes large vibrations of both the engine itself and the aircraft structure.Design model and method for studying engine vibrations with damage in the form of blade breakaway have been developed; numerical studies of unsteady vibrations of an engine suspended on a pylon have been carried out. Herewith, the following load options are considered: engine operation with fan imbalance before shutdown, which is performed by the pilot; sharp braking and jamming of the fan rotor as a result of breakage of the front elastic support of the rotor, which can occur when the blade breaks off; braking the rotor after turning off the engine.The front bearing of the rotor is ball the bearing installed in elastic elements "squirrel wheel". The ball bearing is modeled as a rigid joint. Outside the elastic element, there are two thin-walled shells, which are intermediate load-bearing elements. With an increase in the imbalance of the fan rotor, the gap in the oil damper closes, the damper housing sits on the shells, switching on their rigidity to work. Thus, the stiffness characteristic of the support is bilinear. The stiffness coefficients of the elastic element "squirrel wheel" and the front support shells are determined by the method of numerical simulation. The fan rotor is modeled as a solid body on bearing supports. The stator of the engine is modeled by a rigid body on an elastic suspension. The pylon and the elastic engine mount elements are modeled by beams of variable cross-section operating simultaneously in tension, torsion and bending.A numerical analysis of the transient vibration processes of the D-436-148FM engine on the pylon of the An-178 airplane is carried out. The most dangerous case of damage as the breakdown of the bearing support after the fan blade breakaway is investigated. The results of the calculations are the graphs of the forces in the bearing arrangements and in the hinges of the engine mounting depended on time.

Contractile behavior of the gastrocnemius medialis muscle during running in simulated hypogravity

Vigorous exercise countermeasures in microgravity can largely attenuate muscular degeneration, albeit the extent of applied loading is key for the extent of muscle wasting. Running on the International Space Station is usually performed with maximum loads of 70% body weight (0.7 g). However, it has not been investigated how the reduced musculoskeletal loading affects muscle and series elastic element dynamics, and thereby force and power generation. Therefore, this study examined the effects of running on the vertical treadmill facility, a ground-based analog, at simulated 0.7 g on gastrocnemius medialis contractile behavior. The results reveal that fascicle−series elastic element behavior differs between simulated hypogravity and 1 g running. Whilst shorter peak series elastic element lengths at simulated 0.7 g appear to be the result of lower muscular and gravitational forces acting on it, increased fascicle lengths and decreased velocities could not be anticipated, but may inform the development of optimized running training in hypogravity. However, whether the alterations in contractile behavior precipitate musculoskeletal degeneration warrants further study.

Comparative study of theoretical and real deflection of a simple and reinforced concret joist

This research aims to determine the actual deflection of a concrete joist and to correlate the result with the theoretical deflection. This is based on the theories of elasticity as the double integration method, considering the homogeneous, isotropic and linearly elastic material from an ideal theoretical model. The construction of a concrete joist does not make a 100% homogeneous, isotropic and linearly elastic element, since its manufacture depends on many conditions such as the choice of aggregates, water, the manufacture of cement, tests carried out for the elaboration of the mix design, the operator who is going to perform the mix and the construction of the joist. The variation of the real deflection with respect to the theoretical one has been investigated. For this, 30 simple concrete joists and 30 reinforced concrete joists were manufactured. The dimensions of these joists were 15cm x15cmx53.5cm (b x h x L). The reinforcement of the last 30 joists was 4 Փ 1/4 "as longitudinal reinforcement and Փ 1/4" @ 0.10 m of transverse reinforcement. The joists were tested for flexion by measuring the maximum deflection and compared with the theoretical one, calculated by the double integration method, having much greater experimental results than those calculated with the theory of the double integration method, not being within the ranges expected in literature