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The presented investigation is motivated by the need to uncover connections between underlying rotor fluid-structure interactions and vortex dynamics to fatigue performance and characterization of flexible rotor blades, their hub, and their…
A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy…
This paper aims to quantitatively relate the energy dissipated at a shock wave in a nonlinearly elastic bar to the energy in the oscillations in two related dissipationless, dispersive systems. In contrast to a phase boundary, there is no…
The vortex-induced vibration of multiple spring-mounted bodies free to move in the orthogonal direction of the flow is investigated. In a first step, we derive a Linear Arbitrary Lagrangian Eulerian (L-ALE) method to solve the…
We consider flow along a finite-length collapsible channel driven by a fixed upstream flux, where a section of one wall of a planar rigid channel is replaced by a plane-strain elastic beam subject to uniform external pressure. A modified…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
This study presents the analytical formulation and the finite element solution of fractional order nonlocal plates under both Mindlin and Kirchoff formulations. By employing consistent definitions for fractional-order kinematic relations,…
The fluid flow along the Riga plate with the influence of magnetic force in a rotating system has been investigated numerically. The governing equations have been derived from Navier-Stokes equations. Applying the boundary layer…
In all structural models, the section or fiber response is a relation between the strain measures and the stress resultants. This relation can only be expressed in a simple analytical form when the material response is linear elastic. For…
This paper considers the network flow stabilization problem in power systems and adopts an output regulation viewpoint. Building upon the structure of a heterogeneous port-Hamiltonian model, we integrate network aspects and develop a…
A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
In this paper, I presented the analysis and numerical results for free transverse vibration of thin rectangular plates having arbitrarily varying non-homogeneity with the in-plane coordinates along the two concurrent edges. For finding the…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
We explore the instabilities developed in a fluid in which viscosity depends on temperature. In particular, we consider a dependency that models a very viscous (and thus rather rigid) lithosphere over a convecting mantle. To this end, we…
We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers,…
Three different vortex glass models are studied by examining the energy barrier against vortex motion across the system. In the two-dimensional gauge glass this energy barrier is found to increase logarithmically with system size which is…
We study two closely related, nonlinear models of a viscoplastic solid. These models capture essential features of plasticity over a wide range of strain rates and applied stresses. They exhibit inelastic strain relaxation and steady flow…