The Mathematical Analysis of Problems Describing the Dynamics of Pipes Conveying Fluids

In this Masters thesis, the dynamics of pipes conveying pulsating flow are investigated. The initial-boundary value problem associated with the linear beam equations of motions governing the pipe system is derived using the principles of Lagrangian mechanics. In this thesis, the fluid flow is assumed to have a small velocity with harmonic time...

Modelling Fluid-structure Interaction in Offshore Photovoltaics

The main aim of the research presented in this report is investigating analytical methods to model fluid-structure interaction in large-scale offshore floating photovoltaics. The model that was attempted to be solved analytically is based on a model presented by Pengpeng Xu (2022).<br/>The dimensions in the equations were removed. Applying a...

On the Influence of Constant Vertical Wind Speed on the Classical Ekman Spiral

The Ekman spiral is described by a coupled system of differential equations originally discussed by Walfrid Ekman (Ekman, 1905). This system is a simplified version of the Navier­Stokes equations. The differential equations, as discussed in Ekman’s paper, concern the currents of the ocean. However, it is also possible to interpret these...

Reflections of waves in infinite strings due to mass-spring-damper attachments

In this paper, it is analysed how an infinite cable behaves when a wave from the right hits a TMD system attached to it. The TMD system consists of a mass M1, a spring with stiffness K, a damper with coefficient C and a second mass M2. The cable has a tension T. Then it is investigated what happens when a wave goes through the cable and hits...

Wave reflections in a semi infinite string due to nonlinear energy sinks at the boundary

Vibrations or oscillations can be caused in overhead cable lines or bridge cables due to strong rain and winds, making the structure unstable.These vibrations can be mathematically described as a string like initial boundary value problem with non-classical boundary conditions. In this thesis, we consider a nonlinear attachment at the boundary...

Analysis of the response of a simply supported microbeam subject to an electric actuation

In this research a study of the response of a simply supported microbeam subject to an electric actuation is presented. A perturbation method called the method of multiple scales is explained and used to solve our problem. A model concerning the mid-plane stretching and an electric force with a direct and alternating current component is...

Limit cycles in mass-spring systems with snap-through mechanisms

Mass-spring systems are commonly used in structural components. Understanding their characteristics and pitfalls is an important issue, combining physics and mathematics to prevent such systems from resonating and causing structures to weaken or collapse. This way, suitable solutions can be found such as the use of dampers with the right...

A cascade of autoresonances in an accelerating elevator cable system

In this project the transversal vibrations of an accelerating elevator cable system are studied, with the aim to find the resonance times, the resonance duration and the resonance amplitude. The elevator cable is modelled as an axially moving string, with length given by l(t) = l0 + 1/2 at2, with a the acceleration and t the...

Analysis of an actuated microbeam

Faculty EEMCS (Mathematical Physics) and Applied Sciences (Quantum Nanoscience). - In this project, we study the governing differential equation for a supported microbeam which is electrostatically actuated. The differential equation has been derived using a Hamiltonian principle and Kirchoff's approximation. Our questions on this differential...

Linear stability and bifurcations of periodic Lagrange orbits in the Elliptic Restricted 3-Body Problem: An investigation at L1/L2 in the Earth-Moon system

The Three Body Problem (3BP) has been one of the main celestial mechanics problems in the past few centuries, for a long time studied by both engineers and mathematicians. Its practical purpose is to describe the motion of three particles only under their mutual gravitational interaction, thus it actually represents a ‘model’ of the real...

On Longitudinal Vibrations in the Hoist Cables of the Pieter Schelte

On rain-wind induced vibrations of an oscillator with a time-varying mass

This report will study an oscillator with time-varying mass under the influence of rain-wind induced vibrations. The vibrations will satisfy an initial value problem with a nonlinear ordinary differential equation. The multiple time-scale perturbation method is used to solve the initial value problem. As the mass is set periodic in time with...

Fast iterative methods for solving the incompressible Navier-Stokes equations

This thesis approaches the solution of the linearized finite element discretization of the Navier-Stokes operator matrix via the use of Krylov subspace methods preconditioned by SIMPLE-type pre conditioners aided by deflation. It includes an explanation of the theoretical setting of the problem as well as a collection of numerical experiments...

Eigenvalue analysis of the Timoshenko beam theory with a damped boundary condition

In this report an attempt is made to analyse how a damped Timoshenko beam is affected by an external force.

Oscillations and stability of a mass-varying system

In this paper the stability properties of the vibrations of a singular degree of freedom oscillator with a periodically and multi-stepwise time-varying mass are studied. The free vibrations and the vibrations due to two types of forcing are investigated.

On the determination of approximations of first integrals for few-body gravitational problems: With applications to capture trajectories

On the determination of approximations of first integrals using the method of integrating vectors for ODE systems, as applied to few-body gravitational problems. Considers the Jacobi 3-body problem, the circular restricted 3-body problem and a 4-body model for ballistic lunar capture. Also discusses the application of these techniques to...

On the integral-conservative numerical solution of few-body gravitational problems: With applications to capture trajectories

On the design and implementation of integral-conservative numerical integration schemes for few-body problems in astrodynamics. Focuses on exact and approximate energy and angular-momentum integrals in the Jacobi 3-body problem, and related Jacobi-type integrals in the circular restricted 3-body problem and a 4-body model for ballistic lunar...