NUMERICAL ANALYSIS OF NON-LINEAR VIBRATIONS OF A FRACTIONALLY DAMPED CYLINDRICAL SHELL UNDER THE ADDITIVE COMBINATIONAL INTERNAL RESONANCE

Non-linear damped vibrations of a cylindrical shell subjected to the additive type combinational internal resonance are investigated numerically using two different numerical methods. The damping features of the surrounding medium are described by the fractional derivative Kelvin-Voigt model involving the Riemann-Liouville fractional derivatives. Within the first method, the generalized displacements of a coupled set of nonlinear ordinary differential are estimated using numerical solution of nonlinear multi-term fractional differential equations by the procedure based on the reduction of the problem to a system of fractional differential equations. According to the second method, the amplitudes and phases of nonlinear vibrations are estimated from the governing nonlinear differential equations describing amplitude-and-phase modulations for the case of the additive combinational internal resonance. A good agreement in results is declare

Soliton-Like Solutions in the Problems of Vibrations of Nonlinear Mechanical Systems: Survey

In the given chapter, free vibrations of different nonlinear mechanical systems with one-degree-of-freedom, two-degree-of-freedom, and multiple-degree-of-freedoms are reviewed with the emphasis on the vibratory regimes which could go over into the aperiodic motions under certain conditions. Such unfavorable and even dangerous regimes of vibrations resulting in the irreversible process of energy exchange from its one type to another type are discussed in detail. The solutions describing such processes are found analytically in terms of functions, which are in frequent use in the theory of solitons

PASSIVE AND ACTIVE CONTROL OF THE VIBROACOUSTIC RESPONSE OF A COATED CYLINDRICAL SHELL SUBMERGED IN A HEAVY FLUID

A major source of anthropogenic noise pollution in the marine environment is underwater radiated sound from marine vessels. This thesis investigates sound radiation from a coated cylindrical shell submerged in a heavy fluid. The shell is externally coated with a soft elastic material embedded with a regular distribution of resonant inclusions that are vacuous cavities or hard steel scatterers. The coating is treated as a multilayered equivalent fluid, in which the layers of inclusions are modelled as homogenised layers with effective material and geometric properties. The radiated acoustic pressure is analytically derived by assembling and solving continuity and kinematic conditions at the interfaces between the cylindrical shell, the multilayered coating, and the interior and exterior acoustic domains. Coating designs with different combinations of homogenised layers are examined and physical mechanisms governing acoustic performance of the coating designs are described. The vibroacoustic response of the locally resonant coated shell submerged in water of infinite extent, submerged at a finite depth near a free sea surface, and partially immersed in water is studied. The free sea surface is treated as a pressure release boundary. The image method is employed to capture the interaction between the free surface and the shell submerged at a finite depth. For the semi-immersed coated shell, a partial fluid loading condition is imposed on the wetted coating surface. A hybrid passive-active control system composed of an array of inertial actuators with tuned vibration absorbers is designed to further attenuate sound radiation from a coated shell with cavities. The passive components of the inertial actuators are tuned to shell circumferential resonances. The active component of the inertial actuators, driven using a feedforward linear-quadratic regulator algorithm, is utilised to suppress the spring-mass resonance of the coated shell. Using detailed understanding of the physical system responses, passive and active control of the radiated sound from a submerged coated shell over a broad frequency range is achieved

Fluid-structure interaction modelling of a patient-specific arteriovenous access fistula

This research forms part of an interdisciplinary project that aims to improve the detailed understanding of the haemodynamics and vascular mechanics in arteriovenous shunts that are required for haemodialysis treatments. A combination of new PCMRA imaging and computational modelling of in vivo blood flow aims to determine the haemodynamic conditions that may lead to the high failure rate of vascular access in these circumstances. This thesis focuses on developing a patient-specific fluid-structure interaction (FSI) model of a PC-MRA imaged arteriovenous fistula. The numerical FSI model is developed and simulated within the commercial multiphysics simulation package ANSYS® Academic Research, Release 16. The blood flow is modelled as a Newtonian fluid with the finite-volume method solver ANSYS® Fluent®. A pulsatile mass-flow boundary condition is applied at the artery inlet and a three-element Windkessel model at the artery and vein outlets. ANSYS® Mechanical™, a finite element method solver, is used to model the nonlinear behaviour of the vessel walls. The artery and vein walls are assumed to follow a third-order Yeoh model, and are differentiated by thickness and by material strength characteristics. The staggered FSI model is configured and executed in ANSYS® Workbench™, forming a semi-implicit coupling of the blood flow and vessel wall models. This work shows the effectiveness of combining a number of stabilisation techniques to simultaneously overcome the added-mass effect and optimise the efficiency of the overall model. The PC-MRA data, fluid model, and FSI model show almost identical flow features in the fistula; this applies in particular to a flow recirculation region in the vein that could potentially lead to fistula failure

Accurate approximations for nonlinear vibrations

As global issues such as climate change and overpopulation continue to grow, the role of the engineer is forced to adapt. The general population now places an emphasis not only on the performance of a mechanical system, but also the efficiency with which this can be achieved. In pushing these structures to their maximum efficiency, a number of design and engineering challenges can arise. In particular, the occurrence of geometric nonlinearities can lead to failures in the linear modelling techniques that have traditionally been used. The aim of this thesis is to increase the understanding of a number of widely-used, nonlinear methods, so that they may eventually be used with the same ease and confidence as traditional linear techniques. A key theme throughout this work is the notion that nonlinear behaviour is typically approximated in some way, rather than finding exact solutions. This is not to say that exact solutions cannot be found, but rather that the process of doing so, or the solutions themselves, can be prohibitively complicated. Across the techniques considered, there is a desire to accurately predict the frequency-amplitude relationship, whether this be for the free or forced response of the system. Analytical techniques can be used to produce insight that may be inaccessible through the use of numerical methods, though they require assumptions to be made about the structure. In this thesis, a number of these methods are compared in terms of their accuracy and their usability, so that the influence of the aforementioned assumptions can be understood. Frequency tuning is then used to bring the solutions from three prominent methods in line with one another. The Galerkin method is used to project a continuous beam model into a discrete set of modal equations, as is the traditional method for treating such a system. Motivated by microscale beam structures, an updated approach for incorporating nonlinear boundary conditions is developed. This methodology is then applied to two example structures to demonstrate the importance of this procedure in developing accurate solutions. The discussion is expanded to consider non-intrusive reduced-order modelling techniques, which are typically applied to systems developed with commercial finite element software. By instead applying these methods to an analytical nonlinear system, it is possible to compare the approximated results with exact analytical solutions. This allows a number of observations to be made regarding their application to real structures, noting a number of situations in which the static cases applied or the software itself may influence the solution accuracy