Roman Starosta

Thermoelastic damping in an auxetic rectangular plate with thermal relaxation—free vibrations

This work describes an extended thermodynamical model to represent coupled thermomechanical interactions in continuum media having negative Poisson?s ratio. In particular, the Zener thermoelastic damping effect is considered for a plate with auxetic characteristics undergoing free vibrations. The extended thermodynamical model is characterized by a thermal relaxation time to avoid the propagation of thermal waves at infinite velocity. The thermal relaxation time used in this work is not Zener?s characteristic time constant. Strong dependence of the thermoelastic damping is observed for auxetic configurations, various plate thicknesses and ambient temperatures.

Anomalous Features of the Thermomagnetoelastic Field in a Vortex Array in a Superconductor: Propagation of Love'S Waves

A magnetic field enters a type-II superconductor along an arrangement of Abrikosov vortices. They interact with each other with the help of the Lorentz force creating a new mechanical field different from that coming from the crystal lattice of a superconducting material. That new field presents some anomalous properties as compared to the classical ones of the material. This article deals with a modeling and description of a number of those anomalous features of a vortex field in a superconductor.

PARAMETRIC AND EXTERNAL RESONANCES IN KINEMATICALLY AND EXTERNALLY EXCITED NONLINEAR SPRING PENDULUM

A weakly nonlinear 2-DOF system, parametrically and externally excited, is studied. An intensive energy transfer between modes of vibrations is discovered. Multiple scales method is used for recognizing resonances occurring in the system. The amplitude response functions for some chosen cases of resonances are obtained and studied. Many of the engineering systems can be investigated in the presented way.

Magnetoelastic surface waves in auxetic structure

In modern technologies searching materials of peculiar features is of a fundamental interest for many researchers and engineers. Negative Poissons ratio materials and structures expand transversely when stretching axially. Nowadays, there is an increasing interest in the development of these novel materials called auxetics. We are interested not only in their mechanical properties, but also in their interaction with external physical fields, e.g. electromagnetic field. It is expected that magnetoelastic surface waves propagation has essential meaning in many other physical and biomechanical applications. The paper aims at investigating propagation of magnetoelastic surface waves along an auxetic elastic halfspace in the presence of an external magnetic field of various orientations related to the limiting plane. Dispersion and existence conditions of those waves have been calculated and analyzed in order to present new features of described interactions. It has occurred that the dispersion properties in the case of the Rayleigh-like magnetoelastic surface waves are significantly different for the auxetic material compared to materials of positive Poissons ratio.

Asymptotic Analysis and Limiting Phase Trajectories in the Dynamics of Spring Pendulum

Spring pendulum is a widely discussed two degree-of-freedom (DOF) mechanical systems in numerous references. In this paper the asymptotic approach and limiting phase trajectories (LPT) have been applied to analyze the two DOF mathematical model of a spring pendulum. The LPT and multiple timescale (MTS) methods are effective tools of the investigation of non-linear systems. Some interesting and important aspects of dynamics of the system are discussed. The main attention is focused on the non-steady-state vibrations when the energy is intensively exchanged. Then with increasing values of the selected parameters, a sudden change in the character of vibrations is observed. These phenomena are very well described by the LPT. The method allows to determine the critical values of the parameters responsible for the mentioned transitions. Our analytical studies are verified by numerical calculations.

Decomposition of the Equations of Motion in the Analysis of Dynamics of a 3-DOF Nonideal System

The dynamic response of a nonlinear system with three degrees of freedom, which is excited by nonideal excitation, is investigated. In the considered system the role of a nonideal source is played by a direct current motor, where the central axis of the rotor is not coincident with the axis of rotation. This translation generates a torque whose magnitude depends on the angular velocity. During the system operation a general coordinate assigned to the nonideal source grows rapidly as a result of rotation. We propose the decomposition of the equations of motion in such a way to extract the solution which is directly related to the rotation of an unbalanced rotor. The remaining part of the solution describes pure oscillation depending on the dynamical behaviour of the whole system. The decomposed equations are solved numerically. The influence of selected system parameters on the rotor vibration is examined. The presented approach can be applied to separate vibration and rotation of motions in many other engineering systems.

Thermoelastic Damping and Thermal Relaxation Time in Auxetics

The paper concerns description of the thermoelastic phenomenon in an auxetic rectangular plate within the extended thermodynamical model. Analyzing vibrations of that plate a dependence of elastic constants on the frequency, particularly of Poissons ratio of auxetic state of the body has been presented. Moreover, considered investigations allow to determine the thermal relaxation time analyzing resonance frequencies of the vibrating plate.

Internal motion of the complex oscillators near main resonance

An analytical study of the two degrees of freedom nonlinear dynamical system is presented. The internal motion of the system is separated and described by one fourth order differential equation. An approximate approach allows reducing the problem to the Duffing equation with adequate initial conditions. A novel idea for an effective study of nonlinear dynamical systems consisting in a concept of the socalled limiting phase trajectories is applied. Both qualitative and quantitative complex analyses have been performed. Important nonlinear dynamical transition type phenomena are detected and discussed. In particular, nonsteady forced system vibrations are investigated analytically.

Plane Motion of a Rigid Body Suspended on Nonlinear Spring-Damper

The paper deals with the analytical investigation of the behaviour of the harmonically excited physical pendulum suspended on the nonlinear spring. The asymptotic method of multiple scales (MS) has been used to derive approximate solutions in the analytical form. The applied approach allows one to perform a qualitative analysis of the behaviour of the system. MS method gives possibility, among others, to recognize resonance conditions which can appear in the system.

Kinematics of a vertical axis wind turbine with a variable pitch angle

A computational model for the kinematics of a vertical axis wind turbine (VAWT) is presented. A H-type rotor turbine with a controlled pitch angle is considered. The aim of this solution is to improve the VAWT productivity. The discussed method is related to a narrow computational branch based on the Blade Element Momentum theory (BEM theory). The paper can be regarded as a theoretical basis and an introduction to further studies with the application of BEM. The obtained torque values show the main advantage of using the variable pitch angle.A computational model for the kinematics of a vertical axis wind turbine (VAWT) is presented. A H-type rotor turbine with a controlled pitch angle is considered. The aim of this solution is to improve the VAWT productivity. The discussed method is related to a narrow computational branch based on the Blade Element Momentum theory (BEM theory). The paper can be regarded as a theoretical basis and an introduction to further studies with the application of BEM. The obtained torque values show the main advantage of using the variable pitch angle.