Mark Pitman

On the direct determination of the eigenmodes of finite flow-structure systems

A new method for directly determining the eigenmodes of finite flow–structure systems is presented using the classical problem of the interaction of a uniform incompressible flow with a flexible panel, held at both ends, as an exemplar. The method is a hybrid of theoretical analysis and computational modelling. This method is contrasted with Galerkin and travelling-wave methods, which are most often used to study the hydroelasticity of such systems. The new method does not require an a priori approximation of perturbations via a finite sum of modes. Instead, the coupled equations for the wall–flow system are used to derive a single matrix equation for the system that is a second-order differential equation for the panel-displacement variable. This is achieved in this exemplar by applying a combination of boundary-element and finite-element methods to the discretized system. Standard state-space methods are then used to extract the eigenmodes of the system directly. We present the results for the stability of the case of an unsupported flexible plate, elucidating its divergence and flutter characteristics, and the effect of energy dissipation in the structure. We then present the results for the case of a spring-backed flexible plate, showing that its motion is dominated by travelling waves. Finally, we illustrate the versatility of the approach by extracting the stability diagrams and modes for a panel with spatially varying properties and a panel with non-standard boundary conditions. In doing so, we show how spatial inhomogeneity can modify the energy exchanges between flow and structure, thereby introducing a single-mode flutter instability at pre-divergence flow speeds.

A New Method for Determining the Eigenmodes of Finite Flow-Structure Systems

A new method for directly determining the eigenmodes of finite flow-structure systems is presented, using the classical problem of the interaction of a uniform flow with a flexible panel, held at both ends, as an exemplar. The method is a hybrid of theoretical analysis and computational modelling. This new approach is contrasted with the standard Galerkin method that is most often used to study the hydro-elasticity of finite systems. Unlike the Galerkin method, the new method does not require an a priori approximation of perturbations via a finite sum of modes. Instead, the coupled equations for the wall-flow system are cast, using computational methods that, in this exemplar, combine boundary-element and finite-element methods, to yield a single matrix equation for the system that is a second-order differential equation for the panel-displacement variable. Standard state-space methods are then used to extract the eigenmodes of the system directly. We present definitive results for the stability of the case of an unsupported flexible plate, elucidating its divergence and flutter characteristics, and the effect of energy dissipation in the structure. Finally, we present some results for the case of a spring-backed flexible plate that illustrate the complicated dynamics of this type of wall; these dynamics would be poorly modelled by a traditional Galerkin method.© 2006 ASME

Hydroelastic Stability of a Flexible Panel: Eigen-Analysis and Time-Domain Response

A state-space model, based upon computational modeling, is used to investigate the hydroelastic stability of a finite flexible panel interacting with a uniform flow. A merit of this approach is that it allows the fluid-structure system eigenmodes to be found readily when structural inhomogeneity is included or a source of external excitation is present. The system studied herein is two-dimensional although the concepts presented can be readily extended to three dimensions. Two problems are considered. In the first, we solve the initial-value, boundary-value, problem to show how the system response evolves from a source of localized excitation. This problem is deceptively complex and has evidenced some very unusual behaviour as demonstrated by theoretical studies based on the assumption of an infinitely long flexible panel. Our contribution herein is to formulate and illustrate the use of a hybrid of theoretical and computational models that includes the effects of finiteness. In the second problem we solve the boundary-value problem to determine the long-time response and investigate the effects of adding localized structural inhomogeneity on the linear stability of a flexible panel. It is well known that a simple flexible plate first loses its stability to divergence that is replaced by modal-coalescence flutter at higher speeds. Our contribution is to show how the introduction of localized structural inhomogeneity can be used to modify the divergence-onset and flutter-onset critical flow speeds.Copyright

Optimal Swimming Modes of a Homo-Sapien Performing Butterfly-Stroke Kick

This paper outlines the development and application of a computational method that finds the most efficient two-dimensional swimming mode of a human performing fully submerged butterfly-stroke kick at high Reynolds number. The optimal solution of this non-linear problem is found using a Genetic Algorithm (GA) search method where possible solutions compete in a ‘survival of the fittest’ scheme to ‘breed’ the optimal solution. The swimming is modelled using Discrete Vortex Method (DVM) and Boundary Element Method (BEM) computational techniques. The BEM solves for the inviscid flow field around the two-dimensional body while the shedding of vorticies from joints where the curvature is high (ie. knee, waist and ankle joints) generate the vortex structures necessary for propulsion. The motion of the limbs is characterised by a displacement function which includes the possibility for simple harmonic or non-harmonic motion with a ‘rest’ period in the kick. The finite number of joints means that a finite length parameter set can be developed which characterises the motion of the swimming body. This parameter set is fed into the GA to perform the optimisation based on a scoring function. In this case, the scoring function is simply the distance that the body swims in a set amount of time. The objective of the GA is to maximise this score for a set kicking frequency. This method opens a wider possibility for optimisation of a variety of systems that involve fluid-structure interactions, particulary the possibility of optimisation in the non-linear regime of prescribed motion coupled with compliant surfaces (such as rubbery flippers) that could further increase efficiency.Copyright