Related papers: Vibration modes of the Euler-Bernoulli beam equati…
We study a class of linear ordinary differential equations (ODE)s with distributional coefficients. These equations are defined using an {\it intrinsic} multiplicative product of Schwartz distributions which is an extension of the…
We consider non-stationary localized oscillations of an infinite Bernoulli-Euler beam. The beam lies on the Winkler foundation with a point inhomogeneity (a concentrated spring with negative time-varying stiffness). In such a system with…
We study the initial-boundary value problem for an Euler-Bernoulli beam model with discontinuous bending stiffness laying on a viscoelastic foundation and subjected to an axial force and an external load both of Dirac-type. The…
We study existence and uniqueness of distributional solutions to the differential equation of the Euler-Bernoulli rod with discontinuous coefficients and right-hand side. Upon checking the validity of a solution the occurring products of…
In this paper, the vibration model of an elastic beam, governed by the damped Euler-Bernoulli equation $\rho(x)u_{tt}+\mu(x)u_{t}$$+\left(r(x)u_{xx}\right)_{xx}=0$, subject to the clamped boundary conditions $u(0,t)=u_x(0,t)=0$ at $x=0$,…
In this work we investigate a very weak solution to the initial-boundary value problem of an Euler-Bernoulli beam model. We allow for bending stiffness, axial- and transversal forces as well as for initial conditions to be irregular…
Stochastic flexural vibrations of small-scale Bernoulli-Euler beams with external damping are investigated by stress-driven nonlocal mechanics. Damping effects are simulated considering viscous interactions between beam and surrounding…
In this paper, we consider an Euler-Bernoulli beam equation with time-varying internal fluid. We assume that the fluid is moving with non-constant velocity and dynamical boundary conditions are satisfied. We prove the existence and…
A system of partial differential equations describing the spatial oscillations of an Euler-Bernoulli beam with a tip mass is considered. The linear system considered is actuated by two independent controls and separated into a pair of…
This paper is concerned with the study of regularity and stability properties of two Euler-Bernoulli beam equations with localized singular damping. Under suitable regularity assumptions on the damping coefficient, we establish Gevrey…
This paper provides a qualitative analysis of a non-uniform Euler-Bernoulli beam with degenerate flexural rigidity, subjected to axial force and boundary control with time delay $\tau > 0$. By reformulating the system as an abstract…
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…
A generalization of the Euler's elastic problem, i.e., finding a stationary configuration (planar elastica) of the Bernoulli's thin ideal elastic rod with boundary conditions defined through fixed endpoints and/or tangents at the endpoints,…
This paper addresses the analysis of a boundary feedback system involving a non-homogeneous Euler-Bernoulli beam governed by the equation $m(x)u_{tt}+\mu(x)u_{t}$$+\left(r(x)u_{xx}\right)_{xx}=0$, subject to the initial $u(x,0)=u_0(x)$,…
We propose and analyze the numerical approximation for a viscoelastic Euler-Bernoulli beam model containing a nonlinear strong damping coefficient. The finite difference method is used for spatial discretization, while the backward Euler…
This paper is devoted to the study of periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients. Such mathematical model may be described the infinitesimal, free, undamped in-plane bending vibrations of a…
We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable. The underlying variational model relies on the…
This work investigates the global exponential stabilization of a degenerate Euler-Bernoulli beam subjected to a non uniform axial force and a delayed feedback control. First, we address the well-posedness of the system by constructing an…
A new approach to the Euler-Bernoulli beam based on an inhomogeneous matrix string problem is presented. Three ramifications of the approach are developed: (1) motivated by an analogy with the Camassa-Holm equation a class of isospectral…
This paper introduces a modeling framework that is suitable to resolve singularities of impact phenomena encountered in applications. The method involves an exact transformation that turns the continuum, often partial differential equation…