Amalia Pielorz

Vibration problems in selected torsional mechanical systems

The paper deals with vibrations of mechanical systems torsionally deformed. These problems can be discussed using two-dimensional or one-dimensional models. After the presentation of basic equations for two-dimensional problems, the study is focused on one-dimensional problems for discrete-continuous systems with a local nonlinearity and on the effect of the local nonlinearity on the behaviour of these systems.

Theoretical investigations of nonlinear loads on gear teeth in single gear transmission

Abstract In the paper the discrete-continuous model of a single gear transmission with nonlinear forces occurring between gear teeth is investigated. It is assumed that gear teeth have nonlinear stiffness having softening characteristics. Three nonlinear functions are proposed for the description of loads occurring on the gear teeth. In the discussion the wave approach is applied, as for the linear case in Nadolski (Archive of Applied Mechanics 1991;61:523–31). The numerical analysis focuses on the investigation of the effect of the assumed nonlinearities of a softening characteristic type on the amplitude–frequency curves for dynamic loads. Also the range of application for the proposed nonlinear functions is determined.

Nonlinear Equations with a Retarded Argument in Discrete-Continuous Systems

The paper deals with dynamic problems of discrete-continuous systems with local nonlinearities, the analysis of which is reduced to solving nonlinear differential equations with a retarded argument. This concerns the discrete-continuous systems subject to torsional, longitudinal, or shear deformations, where the equations of motion for elastic elements are classical wave equations. It is assumed that the characteristics of local nonlinearities are of a soft-type and in the paper they are described by four nonlinear functions. After a short general description of the approach used, the detailed considerations and numerical results are presented for a multimass discrete-continuous system with a local nonlinearity having the characteristics of a soft-type subject to shear deformations.

Finite Oscillation of Viscoelastic Cantilever Strip

SummaryLarge amplitude free vibration of an inextensible initially straight thin viscoelastic cantilever, which is released from rest, from a relaxed deflected form is analysed. The cantilever, which is a thin strip of rectangular cross section is assumed to be composed of standard viscoelastic material. Although large deflections and rotations are considered the strains are small so that linear viscoelastic theory can be incorporated into a non-linear bending theory. It is shown how approximate solutions can be obtained by using Galerkins method and numerical results are presented graphically.

Dynamic investigation of the main journals of two-cylinder engine crankshaft with damping

Abstract The paper considers a model of a crankshaft of a two-cylinder four-stroke engine with using torsional waves and taking into account their reflections. The considered model of the crankshaft consists of elastically deformable main journals and of rigid bodies. The moments of external forces and mass moments are approximated by piece-wisely constant functions. Damping of the considered system is described by an equivalent damping. The analytical solutions for the functions utilized for determining displacements at an arbitrary time instant, have been obtained in the form of recurrence formulae. The stability condition of the solutions is given, under which the displacements of the main journals are relatively small. The plots of displacements have been drawn for selected parameters of the crankshaft for the centrelines of crank pins which can be either coincident or shifted.

Modeling of multimass systems torsionally deformed with variable inertia

Dynamic investigations of multimass discrete-continuous systems having variable moment of inertia are performed. The systems are torsionally deformed and consist of an arbitrary number of elastic elements connected by rigid bodies. The problem is nonlinear and it is linearized after appropriate transformations. It is shown that such problems can be investigated using the wave approach. Some analytical considerations and numerical calculations are done for a two-mass system with a special case of boundary conditions.

ON REGULAR AND IRREGULAR NONLINEAR VIBRATIONS IN TORSIONAL DISCRETE-CONTINUOUS SYSTEMS

The paper deals with regular and irregular nonlinear vibrations of discrete-continuous systems torsionally deformed. The systems consist of an arbitrary number of shafts connected by rigid bodies. In the systems, a local nonlinearity having a soft type characteristic is introduced. This nonlinearity is described by the polynomial of the third degree. General governing equations using the wave approach are derived for a multimass system. Detailed numerical considerations are presented for a two-mass system and a three-mass system. The possibility of occurrence of irregular vibrations is discussed on the basis of the Poincare maps and bifurcation diagrams.

Application of Equations with a Retarded Argument in Physical Systems

The paper deals with physical systems, the analysis of which is reduced to solving ordinary differential equations with a retarded argument. This concerns discrete-continuous systems subject to torsional, longitudinal or shear deformations, where the equations of motion for elastic elements are classical wave equations. After a short general description of the approach used, the detailed considerations and numerical results are presented for a multi-mass discrete-continuous system with a local nonlinearity, undergoing shear deformations.

Criterion of multiple collisions in a simple mechanical system with viscous damping and dry friction

Abstract A criterion has been formulated for single and multiple central collisions of two rigid bodies of a simple mechanical system that can be either conservative or non-conservative. Analytical discussion has been confined to investigations of the possibility of appearance of four successive collisions between the bodies with damping neglected and two collisions when viscous damping and Coulomb dry friction are considered.

Chaotic Vibrations in Multi-Mass Discrete-Continuous Systems Torsionally Deformed with Local Nonlinearities

The paper deals with nonlinear vibrations in discrete-continuous mechanical systems consisting of rigid bodies connected by shafts torsionally deformed with local nonlinearities having hard or soft characteristics. The systems are loaded by an external moment harmonically changing in time. In the study the wave approach is used. Numerical results are presented for three-mass systems. In the study of regular vibrations in the case of a hard characteristic amplitude jumps are observed while in the case of a soft characteristic an escape phenomenon is observed. Irregular vibrations, including chaotic motions, are found for selected parameters of the systems.