This research was done to develop tools to predict parametric roll motion of ships in regular and irregular sea and provide guidelines to avoid parametric roll during initial design stage. A post Panamax hull form (modified C11 Hull form, Courtesy of MARIN) was used to study parametric roll in ships. The approach of the study has been to simplify the roll equation of motion to a single degree of freedom equation so as to utilize the tools available to analyze the system retaining the non-linear character of the system. The Hill’ equation is used to develop highly accurate stability boundaries in the Ince-Strutt Diagram. The effect of non-linear damping has also been incorporated into the chart for the first time providing a simple method to predict the bounded roll motion amplitude. Floquet theory is also extended to predict parametric roll motion amplitude. Forward speed of the vessel has been treated as a bifurcation parameter and its effects studied both in head and following sea condition. In the second half of the research, parametric roll of the vessel in irregular sea is investigated using the Volterra Quadratic model. GM variation in irregular sea was obtained using transfer functions of the Volterra model. Heave and pitch coupling to roll motion was also studied using this approach. Sensitivity studies of spectral peak period and significant wave height on roll motion amplitude were also carried out. Forward speed effects were also evaluated using the Volterra approach. Based on the study, the Hill’s equation approach was found to give more accurate prediction of parametric roll in regular sea. The boundaries in the stability chart were more accurately defined by the Hill’s equation. The inclusion of non-linear damping in the stability chart gave reasonably accurate bounded motion amplitude prediction. The Volterra approach was found to be a good analytical prediction tool for parametric roll motion in irregular sea. Using the Volterra model, it was found that there is a high probability of parametric roll when the spectral modal period is close to twice the natural period of roll.

Cette thèse porte sur l'étude de l'amortissement des structures assemblées, et plus précisément de la contribution des assemblages sous sollicitations vibratoires. Le mémoire est composé de cinq chapitres traitant la problématique tant du point de vue analytique qu'expérimental. Un banc d'étude académique est proposé afin d'étudier des assemblages sous sollicitation normale constante (statique) et sous sollicitations tangentielles liées aux vibrations de la structure (dynamique). Le facteur de perte caractérisant l'amortissement de la structure est obtenu, dans un premier temps par une étude locale quasi-statique. Puis une fonction de dissipation est définie, permettant d'affiner la modélisation de l'amortissement par une étude dynamique globale. Au regard des résultats obtenus par la modélisation, une analyse expérimentale est menée. Cela afin d'isoler la contribution, à l'amortissement de la structure, des glissements partiels dans les assemblages. Pour cela, deux structures géométriquement identiques, l'une monolithique et l'autre assemblée sont étudiées. Les effets des interfaces sont analysés puis comparés aux résultats analytiques. Afin de simuler plus précisément ces effets, une modélisation prenant en compte les défauts de forme des surfaces en contact est menée / This thesis presents a study of damping in assembled structures, or, more precisely, a study of the vibrations of assemblies under external excitations. The paper contains five chapters examining this problem from both analytical and experimental viewpoints. An academic investigation is presented as a foundation in order to study assemblies both under constant normal stresses (static), and under tangential stresses linked to the structural vibrations (dynamic). The loss factor that characterizes the damping of the structure is obtained through a quasi-static local study. Then, a dissipation function is given, which allows the refinement of the damping model through a global dynamic study. An experimental analysis is undertaken to examine the results obtained by the modeling. The objective of this analysis is to isolate the effects, at the structural damping, of partial sliding in the assemblies. To isolate these effects, two structures identical in shape and material, one assembled and one uniform, are studied. The data collected from the interfaces are analyzed, and then compared to the analytical results. In order to simulate these effects with greater precision, a modeling is undertaken that takes into account the defects of form for the surfaces in contact

PMM testing is a method used to identify the added mass and damping coefficients used in the equations of motion of a vehicle by attempting to decouple the forces on a body due to velocity and acceleration as a result of creating "hydrodynamically pure" velocities and accelerations. This makes it possible to use quasi-steady state models with terms independent of both velocity and acceleration. This paper explores the ability of simple damping models (solely a function of velocity) with added mass terms (solely a function of acceleration) to simulate the heave force of an 8:1 ellipsoid undergoing PMM testing. In order to help explain the complexity of the flow during PMM tests, a flow analysis of the 8:1 spheroid is provided, which discusses the flow topology of spheroids at steady angle of attack, validity of quasi-steady models, and some other basic flow features seen in PMM testing. In this paper, a simple proportionality relationship between a linear and quadratic damping model is revealed. It is also shown that variations in the heave force response during PMM tests are most heavily influenced by viscous effects, especially cross flow separation. Finally, it is shown where these models break down, owing to the increasing nonlinearity of the flow induced by the harsher motions of large amplitude and/or large frequency tests. / Master of Science

This Thesis comprises of two parts containing similar studies of Nonlinear Localization induced Base Isolation of structural systems. The present method of base isolation,like other nonlinear vibration isolation methods, enjoys certain merits like capability of absorbing broad band vibrations, attenuating heavy shocks etc. The research in this thesis is an extension of this base isolation strategy first proposed by Vakakis and co-author. The strategy involves augmenting an appendage referred to as the secondary system with the main structural unit or the primary system, which we want to isolate from disturbances at the base. The primary system is coupled to the secondary system through a stiffness element. Both the primary and secondary systems have nonlinear dynamic behavior. It is seen that for certain choice of values of the coupling element, steady state vibration of very small magnitude is induced in the primary system. This result was established by considering a general discrete nonlinear system with viscous damping. Now it is a well known fact that viscous damping, though being widely used in literature as well as in practice doesn't turn out to be accurate enough to capture structural damping behaviors. Moreover, the actual damping mechanism if governed by some nonlinear function of the system variables, may influence the physics governing the nonlinear localization phenomenon in a manner rendering the present method not suitable for structural systems at the very outset. So in the present study we focus our attention in establishing the robustness and hence utility of the method by considering technically more defensible models of structural damping. These models efficiently capture certain complex phenomena which structures are known to exhibit. The occurrence of localization induced vibration isolation in structural systems in the presence of these damping models is taken as a proof of the efficacy of the method and its applicability to a wide range of situations. The present study establishes existence of localization through relevant analytical and numerical exercises. In the first part of the thesis we take up the study of nonlinear localization induced base isolation of a three degrees of freedom system having cubic nonlinearities under sinusoidal base excitation. The damping forces in the system are hysteretic in nature. In the present setting this is captured by Bouc-Wen model of hysteresis. Bouc-Wen model is one of the most widely used phenomenological model of hysteresis to have a ready-to-use mathematical description of hysteretic patterns appearing in structural engineering systems. The nature of responses of the different degrees of freedom as excitation frequency varies is a better way of analyzing the performance of the vibration isolation system. We adopt this line of approach for the present study. Normally Harmonic Balance Method (HBM) serves this purpose very well but in the present case as the hysteretic variable is not explicitly related to the system variables, HBM cannot be straightway implemented. Moreover, the hysteretic variable is related to other state variables through a relation which contains non-smooth terms. As a result, Incremental Harmonic Balance (IHB) method is used to obtain amplitude frequency relationship of the system response. The stability analysis of the solution branches is done by using Floquet Theory. Direct numerical simulation is then made use of to support our results that are obtained from this approximate numeric-analytic estimate of the amplitudefrequency relationships of the system, which helps us to analyze the efficacy of this method of base isolation for a broad class of systems. In the next part we consider a similar system where the damping forces in the system are described by functions of fractional derivative of the instantaneous displacements. Fractional Derivative based damping model has been found to be very effective in describing structural damping. We adopt half-order fractional derivative for our study, which can capture damping behavior of polymeric material very well. Typically linear and quadratic damping is considered separately as these are the two most relevant representations of structural damping. Under the assumption of smallness of certain system parameters and nonlinear terms an approximate estimate of the response at each degree of freedom of the system is obtained using Method of Multiple Scales. We then consider a situation where the nonlinear terms and certain other system parameters are no longer small. For the case where asymptotic methods are no longer valid, the assessment of performance of the vibration isolation system is made from amplitude-frequency relations. As a result, we take recourse to the Harmonic Balance Method in conjunction with arc length based continuation technique for obtaining the frequency amplitude plot for linear damping and Incremental Harmonic Balance method for quadratic damping, each of which is validated against results obtained from direct numerical simulation of the system. It needs to be appreciated that base isolation obtained this way has no counterpart in the linear theory.