Finite Element Method-Based Elastic Analysis of Multibody Systems. A Review

This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the finite element method. To write the equations of motion, the most used methods are presented, namely the Lagrange equations method, the Gibbs–Appell equations, Maggi’s formalism and Hamilton’s equations. While the method of Lagrange’s equations is well documented, other methods have only begun to show their potential in recent times, when complex technical applications have revealed some of their advantages. This paper aims to present, in parallel, all these methods, which are more often used together with some of their engineering applications. The main advantages and disadvantages are comparatively presented. For a mechanical system that has certain peculiarities, it is possible that the alternative methods offered by analytical mechanics such as Lagrange’s equations have some advantages. These advantages can lead to computer time savings for concrete engineering applications. All these methods are alternative ways to obtain the equations of motion and response time of the studied systems. The difference between them consists only in the way of describing the systems and the application of the fundamental theorems of mechanics. However, this difference can be used to save time in modeling and analyzing systems, which is important in designing current engineering complex systems. The specifics of the analyzed mechanical system can guide us to use one of the methods presented in order to benefit from the advantages offered.

Equivalent Electronic Circuit of a System of Oscillators Connected With Periodically Variable Stiffness

In this paper, we have shown the electronic circuit equivalence of a mechanical system consists of two oscillators coupled with each other. The mechanical design has the effects of the magnetic, resistance forces and the spring constant of the system is periodically varying. We have shown that the system’s state variables, such as the displacements and the velocities, under the effects of different forces, lead to some nonlinear behaviors, like a transition from the fixed point attractor to the chaotic attractor through the periodic and quasi-periodic attractors. We have constructed the equivalent electronic circuit of this mechanical system and have verified the numerically obtained behaviors using the electronic circuit.

Functioning Fuzzy Logic in Optimizing the Solar Systems Work

Fuzzy logic has been used in many fields, either to control a specific movement, improve the productivity of a machine, or monitor the work of an electrical or mechanical system or the like. In this chapter, we will discuss what are the basic factors that must be taken to use the fuzzy logic in the aforementioned matters in general, and then focus on its employment in the field of renewable energy. Three main axes for renewable energy are solar panels, a wind turbine and finally, solar collectors. The key to working and the basis of the static system is the mechanism for selecting the inputs that directly affect the output in addition to the methods and activation functions of the fuzzy logic.

Investigation of the influence of an additional viscoelastic support mass-inertial characteristics on the rectangular plate non-stationary deformation

Modeling additional supports that affect the non-stationary deformation of lamellar structural elements is associated with a number of idealizations and assumptions. Many sources describe the deformation of supported structural elements using absolutely rigid additional supports or stiffeners. In reality, additional supports have viscoelastic properties (viscous and elastic components). When studying non-stationary vibrations, one should also take into account the mass-inertial properties of additional supports. Goal. The goal of the work is: 1) refinement of the existing mathematical model of an additional viscoelastic support by taking into account the influence of its mass-inertial characteristics; 2) study of the influence of these characteristics on the non-stationary deformation of a rectangular plate. Methodology. The non-stationary deformation of beams or plates is described by systems of partial differential equations. For these objects, good results are given by models based on the hypotheses of S.P. Timoshenko, taking into account the inertia of rotation and shear. Such systems of equations can be solved by expanding the sought functions (displacements and angles of rotation) in the corresponding series and using the direct and inverse integral Laplace transform. The determination of the unknown reaction of the additional viscoelastic support, taking into account its mass-inertial characteristics, is carried out on the basis of solving the Volterra integral equations. Results. In this work, an analytical and numerical solution in a general form is obtained, which makes it possible to determine the dependence of the change in time of reaction between the plate and the additional support for various parameters of the mechanical system. Originality. The solution to this problem is based on the further development by the authors of an approach to modeling additional supports in the form of additional unknown non-stationary loads, which are determined from the analysis of Volterra integral equations. Practical value. Examples of calculations for the considered mechanical system at three different values of mass are given. It is shown that the mass-inertial characteristics of the additional support cause a noticeable effect on the oscillatory process, and the changes concern both amplitude and phase characteristics.

THE CHANCES FOR REDUCTION OF VIBRATIONS IN MECHANICAL SYSTEM WITH LOW-EMISSION SHIPS COMBUSTION ENGINES

Development of diesel engines is focused on reduction of exhaust gas emissions, increase of efficiency of the fuel mixture combustion and decrease of fuel consumption. Such engines are referred to as low-emission engines. Low- engines trends bring higher engine power outputs, torques and also increase of vibrations and noisiness level. In order to reduce these vibrations of diesel engines, it is necessary to apply different dynamical elements, which are able to increase an adverse impact of exciting amplitudes. One of the results is application of a pneumatic dual-mass flywheel. The pneumatic dual-mass flywheel is a dynamical element that consists of two masses (the primary and the secondary mass), which are jointed together by means of a flexible interconnection. This kind of the flywheel solution enables to change resonance areas of the mechanical system which consequently leads to reduction of vibrations.

CONTINUOUS TUNING OF SHIP PROPULSION SYSTEM BY MEANS OF PNEUMATIC TUNER OF TORSIONAL OSCILLATION

Mechanical system drives consist of driving machines and gearing mechanisms interconnected by shafts and couplings. In terms of dynamics it is possible to say that every driving mechanism is able to oscillate. Especially piston devices can create excessive torsional oscillation, vibrations, as well as noise. Important task of a designer is to reduce torsional oscillation in mechanical systems. Presently this problem is mainly solved by the flexible shaft couplings that are selected with regard to the dynamic properties of the given system. It means that every torsional oscillating mechanical system needs to be suitably tuned. The aim of this paper is to present the possibilities of controlling of dangerous torsional oscillations of the mechanical systems by the means of new method, i.e. its optimal tuning by means of the pneumatic coupling with self-regulation, which were developed by us.