Transverse and longitudinal vibrations in axially moving strings

Varying-length cable systems are widely applied in a vast class of engineering problems which arise in industrial, civil, aerospatial, mechanical, and automotive applications. Due to external excitations, large oscillations can occur when cables are lifted up or down. This phenomenon is caused by resonance. In general, resonance is harmful, and...

Transversal waves and vibrations in axially moving continua

On Aspects of Asymptotics for Axially Moving Continua

In this thesis two models for axially moving continua have been studied: a string-like model and a beam-like model. Mathematically, a string-like model is described by a wave equation and a beam-like model is usually described by the Euler-Bernoulli beam equation. A string-like model has been used to describe the transversal vibrations of a...

Towards parameter limits of displacement boundary value problems for Mohr-Coulomb models

To solve problems in geotechnical engineering often numerical methods such as the Finite Element Method (FEM) are used. This method can be applied for example for the calculation of the strength of dikes, the determination of the stability of (rail)road embankments, the prediction of deformations due to landfills, or the analysis of subsurface...

On asymptotics for difference equations

In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the oscillator equations can be derived from these...

On a single degree of freedom oscillator with a time-varying mass

In this thesis the free and forced vibrations of a single degree of freedom oscillator with a periodically time-varying mass have been studied. Linear and weakly non-linear oscillator equations have been considered. The forced vibrations of the oscillator are partly due to small masses which are T-periodically hitting and leaving the oscillator...

On aspects of vibration of axially moving continua

In axially moving structures like conveyor belt systems, magnetic tapes, and so on, vibrations occur due to the presence of different kinds of imperfections in the systems. For these structures internal resonances can lead to severe vibrations. Resonance free conveyor belt systems can be constructed if the frequencies of the system are known. In...

On aspects of boundary damping for cables and vertical beams

Elastic structures are susceptible to wind- and earthquake-induced vibrations. These vibrations can damage a structure or cause human discomfort. To suppress structural vibrations, various types of damping mechanisms, active or passive, can be applied. In this thesis the model of a weakly damped, standing Euler-Bernoulli beam in a (turbulent)...

On aspects of asymptotics for beam and plate equations

On the dynamics of an inclined stretched string

In this thesis the dynamics of inclined stretched strings has been studied. These elastic strings are suspended between a fixed support and a vibrating support. Longitudinal vibrations and transversal (in- and out-of-plane) vibrations of the strings have both been considered. In this thesis it has been assumed that the excitation-forces applied...

Mathematical models for rain-wind induced vibrations of simple structures

A mathematical analysis of a belt system with a low and time-varying velocity

In this thesis a mathematical analysis has been given for model which describes the transversal vibrations of belt systems. The belt speed is assumed to be time-varying and to be small compared to the wave speed. Not only linear string-like or beam-like models but also nonlinear models have been studied. In all cases initial-boundary value...

On asymptotic approximations of first integrals for a class of nonlinear oscillators

In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for the nonlinear differential equations are constructed by using the recently developed perturbation method based on integrating vectors. The existence and the stability of time-periodic solutions can be determined from these...

On the Influence of Boundery Damping for 1-D Wave Equations

Weakly Nonlinear Beam Equations: An Asymptotic Analysis