Related papers: A derivation of the beam equation
Euler's equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler's equation in terms of generalized coordinates. This is…
We derive novel guaranteed lower bounds for eigenvalues of the Euler-Bernoulli beam with variable bending stiffness. While the standard finite element Rayleigh-Ritz method automatically yields upper bounds, we obtain lower bounds by…
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…
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…
A fluid droplet in general deforms, if subject to active driving, such as a finite slip velocity or active tractions on its interface. We show that these deformations and their dynamics can be computed analytically in a perturbation theory…
This paper deals with the introduction of a decomposition of the deformations of curved thin beams, with section of order $\delta$, which takes into account the specific geometry of such beams. A deformation $v$ is split into an elementary…
The paper extends the formulation of a 2D geometrically exact beam element proposed in our previous paper [1] to curved elastic beams. This formulation is based on equilibrium equations in their integrated form, combined with the kinematic…
In view of the fundamental distinction between the force-controlled model and the displacement-controlled model in buckling problems of structures and the complexity of the asymptotic post-buckling analysis traditionally based on the…
"Bernoulli" levitation is the basis of many popular counter-intuitive physics demonstrations. However, few of these lend themselves to a quantitative description without recourse to computational fluid dynamics. Levitation of a flat plate…
We propose a discussion of angular momentum and its Euler equation, with the aim of giving a short outline of their history. This outline can be useful for teaching purposes too, to amend some problems that students can have in learning…
Pre-displaced micromechanical resonators made from high-stress material give rise to new rich static and dynamic behavior. Here, an analytical model is presented to describe the mechanics of such pre-displaced resonators. The bending and…
We derive the Euler equations from quantum dynamics for a class of fermionic many-body systems. We make two types of assumptions. The first type are physical assumptions on the solution of the Euler equations for the given initial data. The…
Consider a fluid flowing through a junction between two pipes with different sections. Its evolution is described by the 2D or 3D Euler equations, whose analytical theory is far from complete and whose numerical treatment may be rather…
A hybrid framework integrating the Virtual Element Method (VEM) with deep learning is presented as an initial step toward developing efficient and flexible numerical models for one-dimensional Euler-Bernoulli beams. The primary aim is to…
The derivation of a linear fractional representation (LFR) model for a flexible, spinning and uniform Euler-Bernoulli beam is accomplished using the {Lagrange} technique, fully capturing the centrifugal force generated by the spinning…
The mathematical model representing the equation of motion of a pendulum is nonlinear. Solutions that satisfy the equation cannot be represented by elementary functions, such as trigonometric functions. To solve such problems, it is common…
The size-dependent bending behavior of nano-beams is investigated by the modified nonlocal strain gradient elasticity theory. According to this model, the bending moment is expressed by integral convolutions of elastic flexural curvature…
Bernoulli's equation, which relates the pressure of an ideal fluid in motion with its velocity and height under certain conditions, is a central topic in General Physics courses for Science and Engineering students. This equation,…
We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form valued 2-forms, and their divergence as a covariant exterior derivative. We review…
This paper provides a new analytical method to obtain Green's functions of linear dispersive partial differential equations. The Euler-Bernoulli beam equation and the one-dimensional heat conduction equation (dissipation equation) under…