Deep Symbolic Regression for Nonlinear Dynamical Systems

From the motion of electrons in an atom to the orbits of celestial bodies in the cosmos, governing equations are essential to the characterisation of dynamical systems. They facilitate an understanding of the physics of a system, which enables the development of useful techniques such as predictive control. An increasingly popular method to...

Tuning graphene dynamics by mechanical strain

Two-dimensional (membrane) materials have been receiving much scientific attention due to their unique material properties that can be used to study the smallest physical phenomena. One such material is graphene, perceived as the holy grail in material physics, due to its unique material properties. Its aspect ratio diminishes the bending...

Output Regulation of Nonlinear Systems in a Koopman Operator Framework

This thesis considers the problem of nonlinear output regulation in a Koopman operator framework. The goal of output regulation is to asymptotically track a reference and/or simultaneously reject a disturbance signal, both generated by some external autonomous system called the exosystem. The nonlinear output regulation problem is solvable if...

Applying Koopman Methods for Nonlinear Reachability Analysis

In this thesis we investigate the possibilities for applying Koopman methods for reachability analysis. Reachability analysis is a verification process used to determine that a dynamical system starting in an initial set X0 cannot reach a certain set of dangerous states D within a time interval [0,T]. Koopman methods seem promising, because they...

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...

Nonlinear dynamics of graphene membranes: Quality factor limits of membranes caused by mode interaction

Graphene is expected to open up a world of new possibilities in the field of micro and nano sensors, due to its outstanding properties. However, graphene membranes suffer from high damping which limit their performance. The physical mechanism behind this damping is still unknown. Therefore, in this work, it is investigated how coupling between...

Study of nonlinear dynamic soil response to harmonic excitation using semi-analytical and numerical methods

The strive for cleaner energy sources is one of the most demanding problems the world faces today. The role of offshore wind in the energy transition is becoming increasingly relevant. One of the areas where the industry expects to reduce conservatism and uncertainty in design is the interaction of the foundations of offshore wind turbines with...

Nonlinear damping in graphene nanodrum resonators

Nanomechanical resonators made from graphene are widely researched for their potential applications due to their high sensitivity. Their atomic scale thickness makes it that these resonators exhibit amplitude-dependent damping at relatively small driving forces. To further increase the performance of these devices, it is essential to understand...

Finite element based analysis and validation for nonlinear structural dynamics

Analysing nonlinear vibrations of any finite element model containing a considerable number of degrees of freedom requires extensive computational resources. For a time-dependent nonlinear analysis, numerous iterations and time increments are required to compute steady statesolutions....

The effect of push-pull rod on the dynamic behavior of movable bridges

In the Netherlands the design of a movable bridge and machinery part is based on the design standard NEN 6786:2001 (2001). When the bridge is in motion the calculations for the machinery part focus on the dynamic loads (torque) generating at the motor shaft. The calculation of these loads is carried out using tabulated formulas of the standard,...

Tip identification in atomic force microscopy using nonlinear dynamics

Since its invention, the Atomic Force Microscope has emerged into one of the most useful tools in<br/>nanotechnology due to its acclaimed abilities in exploring surface topography, micro- and nanoscale manipulation<br/>and characterization. The nonlinear interaction between the cantilever tip and the sample surface<br/>has been studied in great...

A Hamiltonian Reduction Method for Nonlinear Dynamics

Nonlinear analysis of dynamic problems has become important for modern industrial design applications. The increasing pressure on airlines to decrease fuel costs demands the design of more efficient aircraft. This requires aircraft manufacturing companies to design lighter structural components. The result is the need for more realistic and...