In this paper, nonlinear dynamics of Duffing system with fractional order damping is investigated. The four order RungeKutta method and ten order CFE-Euler methods are introduced to simulate the fractional order Duffing equations. The effect of taking fractional order on the system dynamics is investigated using phase diagrams, bifurcation diagrams and Poincare map. The bifurcation diagram is a...

This contribution presents the control of a certain kind of mechanical systems based on energy considerations. The plants under investigation are underactuated lumped and distributed parameter systems, which consist of two masses and an elastic element. After a brief introduction of the used mathematical objects, the proposed controller design method is applied to a simple introductory example ...

An overview of recent advances in computational aeroacoustics (CAA) is presented. CAA algorithms must not be dispersive and dissipative. It should propagate waves supported by the Euler equations with the correct group velocities. Computation domains are inevitably finite in size. To avoid the reflection of acoustic and other outgoing waves at the boundaries of the computation domain, it is req...

A control system is proposed for a low Earth orbit gravity gradient stabilised microsatellite using Z wheel. The microsatellite is 3-axis stabilized using a yaw reaction wheel, with dual redundant 3-axis magnetorquers. Two vector magnetometers and four dual sun sensors are carried in order to determine the full attitude. The attitude was estimated using an Euler angles (small libration version)...

We study a system coupling the incompressible Navier-Stokes equations in a 2D rectangular type domain with a damped Euler-Bernoulli beam equation, where the beam is a part of the upper boundary of the domain occupied by the fluid. Due to the deformation of the beam the fluid domain depends on time. We prove that this system is exponentially stabilizable, locally about the null solution, with an...

We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential equations cannot be directly identified with a set of Euler-Lagrange equations, one can reformulate such a set in an equivalent first-order form which can always...

We have developed a three-dimensional (3D) spectral hydrodynamic code to study vortex dynamics in rotating, shearing, stratified systems (e.g., the atmosphere of gas giant planets, protoplanetary disks around newly forming protostars). The timeindependent background state is stably stratified in the vertical direction and has a unidirectional linear shear flow aligned with one horizontal axis. ...

This paper addresses the model reduction and simulation of a damped Euler–Bernoulli–von Kármán pinned beam excited by distributed force. nonlinear problem is formulated as PDE reformulated well-posed state-space system. The order are derived combining two approaches: Volterra series expansion truncation pseudo-modal defined from eigenbasis linearized problem. interest this approach lies in larg...

In this paper, a closed-form approximate formula for estimating the maximum resonant response of beam bridges on viscoelastic supports (VS) under moving loads is proposed. The methodology based discrete approximation fundamental vertical mode non-proportionally damped Bernoulli–Euler beam, which allows derivation expressions modal characteristics and amplitude free vibration at mid-span VS beam...

We study the energy decay of a damped Euler-Bernoulli beam which is subject to point-wise feedback force representing Shape Memory Alloy (SMA) cable. The problem we consider that paper by [Liu et al. Int. J. Struct. Stab. Dyn. 17 (2017) 1750076] but, for simplicity, our mod-elization does not take into account additional stiffness term they considered. An explicit expression given resolvent und...