In this article, we study the stabilization of an Euler-Bernoulli beam equation with variable coefficients where boundary observation is subject to a time delay. To resolve the mathematical complexity of variable coefficients, we design an observer-predictor based on the well-posed open-loop system: the state of system is estimated with available observation and then predicted without observati...

A flexible system described by Euler-Bernoulli beam equation is considered. The beam is clamped at one end, and is free at the other end. Boundary control force and torque inputs are applied at the free end of the beam. The transfer functions of the controllers are marginally stable and may contain some poles on the imaginary axis. Various stability results are shown and the application of the ...

The classical Helmholtz problem is applied for modelling the axisymmetric inviscid cusp-ended separated flow around a sphere. Two coordinate systems are employed: polar for initial calculations and parabolic the latter being more suitable for investigation of infinitely long stagnation zones. Scaled coordinates are introduced and difference schemes for the free-stream equation and the Bernoulli...

We study the exact controllability of a nonlinear plate equation by the means of a control which acts on an internal region of the plate. The main result asserts that this system is locally exactly controllable if the associated linear Euler-Bernoulli system is exactly controllable. In particular, for rectangular domains we obtain that the Berger system is locally exactly controllable in arbitr...

The purpose of this work is the derivation of closed form expressions for the linear vibration modes of catenary-shaped slender structures. The dynamic behaviour of the structure is described using the Euler–Bernoulli beam formulation with variable tension and angle terms. The desired expressions are obtained by treating the governing fourth-order partial differential equation of dynamic equili...

We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves discontinuous, and even distributional, coefficients and right-hand side. The general problem is solved by application of functional analytic techniques to obt...

We are concerned with the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as the following second-order nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential φ : Ω ⊂ R → R: ...

in this article, vibration analysis of an euler-bernoulli beam resting on a pasternak-type foundation is studied. the governing equation is solved by using a spectral finite element model (sfem). the solution involves calculating wave and time responses of the beam. the fast fourier transform function is used for temporal discretization of the governing partial differential equation into a set ...

A Timoshenko beam equation with boundary feedback control is considered. By an abstract result on the Riesz basis generation for the discrete operators in the Hilbert spaces, we show that the closed-loop system is a Riesz system, that is, the sequence of generalized eigenvectors of the closed-loop system forms a Riesz basis in the state Hilbert space. 1. Introduction. The boundary feedback stab...

Abstract The principles of the energy variation method are commonly utilized in mechanics. Energy is a scalar variable, so these more convenient and simple to establish equilibrium equations compared vector-based approaches (i.e. using forces displacements). present article applied theorem order set for various complicated problems. Four examples applying include differential equation Euler – B...