Genadijus Kulvietis

Computer algebra for analyzing the vibrations of nonlinear structures

The aim of this paper is to describe a theoretical background of systematic computer algebra methods for analyzing the free and steady-state periodic vibrations of the nonlinear structures. Many analytical steady-state solution methods are developed but each of them has different capabilities. On the other hand, it is very important to assess the efficiency of analytical methods in terms of the computer algebra system. For this reason, the computer algebra system VIBRAN was used. In this paper, the efficiency of two analytical methods is assessed from the standpoint of the computer algebra system.

Development of Traveling Wave Actuators Using Waveguides of Different Geometrical Forms

The paper covers the research and development of piezoelectric traveling wave actuators using different types of the waveguides. The introduced piezoelectric actuators can be characterized by specific areas of application, different resolution, and torque. All presented actuators are ultrasonic resonant devices and they were developed to increase amplitudes of the traveling wave oscillations of the contact surface. Three different waveguides are introduced, that is, symmetrical, asymmetrical, and cone type waveguide. A piezoelectric ring with the sectioned electrodes is used to excite traveling wave oscillations for all actuators. Operating principle, electrode pattern, and excitation regimes of piezoelectric actuators are described. A numerical modelling of the actuators was performed to validate the operating principle and to calculate trajectories of the contact points motion. Prototype actuators were made and experimental study was performed. The results of numerical and experimental analysis are discussed.

Movement Trajectory Planning Algorithm of Rotating Mobile Piezorobot

his paper presents method for trajectory planning of mobile piezorobots. An algorithm for evaluation of motion trajectory for this kind of robots, describing point-to-point motion by means of the given function is presented. Preliminary experimental results prove the feasibility of proposed mathematical model.

Symbolic calculation of the generalized inertia matrix of robots with a large number of joints

The aim of this paper is to simplify numerical simulation of robots with a large number of joints. Many numerical methods based on different principles of mechanics are developed to obtain the equations that model the dynamic behavior of robots. In this paper, the efficiency of computer algebra application was compared with the most popular methods of forming the generalized inertia matrix of robots. To this end, the computer algebra system was used. Expressions for the generalized inertia matrix of the robots with a large number of joints have been derived, using the computer algebra technique with the following automatic program code generation. As shown in the paper, such an application could drastically reduce the number of floating point product operations, needed for efficient numerical simulation of robots.

Collective Intelligence Utilization Method Based on Implicit Social Network Composition and Evolution in the Scope of Personal Learning Environment

Personal Learning Environment (PLE) is an emerging concept in learning technology field. PLE allows users aggregate content from distributed Web 2.0 services in one place and arrange it in a way that is convenient for a learner. Despite the fact, that PLE operates with social software and is a type of social media, social networking component is used very poorly. A new model of “networked knowledge” utilization in the scope of PLE is presented in this paper. The exclusive feature of this model is learners’ aggregated and generated data analysis and digital identity development based on both sources. Another exclusive feature is constant digital identity update, depending on constantly evolving learners’ implicit network. Such evolution ensures continuous implicit network update along with changing learners’ interests.

POLYNOMIAL ERROR APPROXIMATION OF A PRECISION ANGLE MEASURING SYSTEM

Abstract The paper deals with the calibration of a flat angle measuring system. The article describes a comparative method for using a multi-angular prism (polygon) with autocollimator along with an angle measuring system. The components of angle measuring system is analysed in the paper. The article also presents polynomial error approximation and the obtained results of calibrating the precision angle measuring system as well as discusses preliminary assumptions for further research.

Investigation of the reliability of multiserver computer networks

Performance in terms of reliability of multiserver computer networks motivates this paper. The law of the iterated logarithm on the extreme queue length in open multiserver queueing networks in heavy traffic is derived and applied to a reliability model for multiserver computer networks where we relate the time of failure of a multiserver computer network to the system parameters.

Semi-analytical Approach for Analyzing Vibro-Impact Systems

A semi-analytical approach, combining the features of analytical and numerical computations, is proposed. Separating the linear and nonlinear parts of equations of motion, the harmonic balance method and computer algebra have been synthesized for obtaining analytical solutions of the nonlinear part, whereas the linear part was solved by the numerical methods. On the basis of this technique, the numerical investigation of abrasive treatment process dynamics has been performed and regimes ensuring the most effective treatment process determined.

Computer algebra for the formation of structural matrices of piezoceramic finite elements

This paper deals with the description of a theoretical background of systematic computer algebra methods for the formation of structural matrices of piezoceramic finite elements. The efficiency of computer algebra application was compared here with the numerical integration methods of forming the structural matrices of the finite elements. To this end, the computer algebra system VIBRAN was used. Two popular finite elements for modelling piezoceramic actuators of the sector-type and the triangular one are discussed. All structural matrices of the elements were derived, using the computer algebra technique with the following automatic program code generation.

Piezoelectric Actuator Generating 3D-Rotations of a Sphere

Investigation of a new design piezoelectric actuator based on research of compound ultrasonic systems called shaking beam is presented in the paper. It was developed to rotate the sphere about three different axes and can be used in sophisticated positioning devices. The actuator consists of a vibrating frame, four piezostacks and four overlays. Elliptical motions of the four driving tips, which rotate the sphere, are achieved by using multimode oscillations of the vibrating frame. Control of the spheres motion is performed by managing the amplitude and phase of harmonic input signal on different piezostacks. Numerical modeling based on a finite element method is performed in order to obtain resonance frequencies and modal shapes of the actuator and to calculate the trajectories of contact points movements under different input regimes. A prototype actuator was made and the experimental outcomes of the actuators working surfaces oscillations are given. Results of the numerical and experimental research are analyzed and discussed.