SELF EXCITED VIBRATION OF A LINE ELEMENT OF BUILDING LINES STRUCTURE

Structure element of a building connected with the ground in a line is usually modeled as a beam with the Winkler type support. The elastic property of the support is assumed to be linear or with cubic nonlinearity. Unfortunately, the experiments do not prove such an assumption. It is evident that the nonlinearity is with the order which is a real positive number which need not to be an integer. In this paper the generalization of the beam with Winkler support is done by introducing the nonlinearity of any non-integer order. The line structure, i.e., beam has transversal vibrations. The mathematical description of these vibrations is a nonlinear partial differential equation. To solve the equation, we suggest an analytic procedure. The solution is assumed as a product of a time and a displacement function. After averaging, the problem transforms into a second order nonlinear differential equation. The approximate solution has the form of a cosine (ca) Ateb function. Analyzing the obtained results the influence of support properties on the system behavior is considered. The attention is given to the influence of the Winkler-Pasternak foundation, too

PRIVACY AND PERSONAL DATA PROTECTION IN SELF-DRIVING CAR: SUGGESTION FOR LEGAL REGULATION IN SERBIA

This paper deals with legal regulation in the field of the self-driving car (SDC), an autonomous vehicle without a human driver. A survey carried out in Serbia on the acceptability of this vehicle in everyday life indicated the distrust of the population in driving with SDCs due to concerns of violation the privacy, distrust in the protection of personal data and insufficient security and cyber security. For proper functioning and especially for artificial intelligence (AI) decision-making the SDC needs a large set of data, including personal information. In this paper the legal framework for collecting, storing, processing and erasing of personal data for SDCs is developed. Most of regulation are new, due to the technical novelty of the SDC, which uncouples the driver and the vehicle are in the driving process. In the paper, documents and acts which protect privacy according to the EUs General Data Protection Regulation (GDPR) are suggested. Principles for data security and, especially, for cybersecurity of data are legally regulated and proposed to be incorporated into the future law of transportation. The suggested legal regulation would increase the trust of population in the SDC

Dynamics of bodies with time-variable mass

This book deals with the problem of dynamics of bodies with time-variable mass and moment of inertia. Mass addition and mass separation from the body are treated. Both aspects of mass variation, continual and discontinual, are considered. Dynamic properties of the body are obtained applying principles of classical dynamics and also analytical mechanics. Advantages and disadvantages of both approaches are discussed. Dynamics of constant body is adopted, and the characteristics of the mass variation of the body is included. Special attention is given to the influence of the reactive force and the reactive torque. The vibration of the body with variable mass is presented. One and two degrees of freedom oscillators with variable mass are discussed. Rotors and the Van der Pol oscillator with variable mass are displayed. The chaotic motion of bodies with variable mass is discussed too. To support learning, some solved practical problems are included

Ninety years of Duffing’s equation

In the paper the origin of the so named ‘Duffing’s equation’ is shown. The author’s generalization of the equation, her published papers dealing with Duffing’s equation and some of the solution methods are presented. Three characteristic approximate solution procedures based on the exact solution of the strong cubic Duffing’s equation are shown. Using the Jacobi elliptic functions the elliptic-Krylov-Bogolubov (EKB), the homotopy perturbation and the elliptic-Galerkin (EG) methods are described. The methods are compared. The advantages and the disadvantages of the methods are discussed

Strongly nonlinear oscillators: analytical solutions

This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for professionals and engineers who apply these techniques to the field of nonlinear oscillations

AKUSTIČKI METAMATERIJALI: PREGLED VIBRACIONIH KARAKTERISTIKA

In the paper the theoretical consideration of the acoustic metamaterials is given. Metamaterials, which are usually composite, are artificial materials whose properties differ from those observed in nature or in the constituent materials. Metamaterials which are suitable for acoustic wave absorption are presented. Acoustic absorber is a beam made of solid material connected with spring-mass subunits. The purpose of the subunits is to give a band gap where some frequencies of acoustic wave are stopped. Mathematical models for various types of connection of subunits in the metamaterial and absorber are discussed. Based on the analogy between electromagnetic and acoustic waves the concept of negative effective mass is introduced as a basic principle for modeling. Acoustic metamaterial beams based on one, two or multi-frequency vibration absorbers are discussed. Depending on connection of absorbers in the beam, the structure may absorb wave in one-direction (for example the longitudinal one) or waves in two directions (transversal and longitudinal). In the paper an overview of mathematical models and suggestions for further investigation are given.U ovom radu je dat pregled teorije akustičkih metamaterijala. Metamaterijali, koji su obično kompoziti, su veštački stvoreni materijali čije se osobine razlikuju od onih koji odgovaraju prirodnim materijalima. Navedeni su metamaterijali koji su pogodni za absorpciju akustičkih talasa. Akustički absorber je štap napravljen od čvrstog materijala za koji je vezan veći broj celina tzv. elementarnih absorbera sastavljenih od opruge i mase. Ugradnja ovih elementarnih absorbera obezbedjuje zaustavljanje akustičkih talasa  u odrdjenoj oblasti frekvencija. U radu su razmotreni različiti tipovi veza elementarnih absorbera za osnovnu materiju forrmirajući metamaterijal. Na osnovu analogije izmedju elektromagnetnih i akustičkih talasa uveden je koncept negativne efektivne mase kao osnovnog elementa za modeliranje. U radu su prikazani akustički metamaterijali sa absorberima jedne, dve ili više frekvencija. U zavisnosti od veze absorbera u štapu struktura može da absorbuje talase u jednom pravcu (na primer, longitudinbalnom) ili u dva (poprečnom i longitudinalnom).U radu je dat pregled matematičkih modela koji opisuju vibraciona svojstva i daju smernice za dalja istraživanja