Related papers: Large Deflection of Cantilever Rod Pulled by Cable
The paper provides an exact analytical solution for equilibrium configurations of cantilever rod subject to inclined force and torque acting on its free end. The solution is given in terms of Jacobi elliptical functions and illustrated by…
The large deflections of cantilevered beams and plates are modeled and discussed. Traditional nonlinear elastic models (e.g., that of von Karman) employ elastic restoring forces based on the effect of stretching on bending, and these are…
We consider pure traction problems and we show that incompressible linearized elasticity can be obtained as variational limit of incompressible finite elasticity under suitable conditions on external loads.
Mechanical instabilities can be exploited to design innovative structures, able to change their shape in the presence of external stimuli. In this work, we derive a mathematical model of an elastic beam subjected to an axial force and…
We study the dynamics of an inclined tensioned, heavy cable traveling with a constant speed in the vertical plane. The cable is modeled as a beam resisting bending and shear. The governing equation for the transverse in-plane vibrations of…
The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…
Many mechanical structures, both engineered and biological, combine heavy rigid elements such as bones and beams with lightweight flexible ones such as cables and membranes. These are referred to as tensegrities, reflecting that cables can…
Equations of motion and dynamics of a quadrotor transporting a load with a flexible cable modeled as a chain pendulum is obtained using Euler-Lagrange equations by taking variations on manifolds. An arbitrary number of links considered in a…
In this paper, we consider rods whose thickness vary linearly between $\eps$ and $\eps^2$. Our aim is to study the asymptotic behavior of these rods in the framework of the linear elasticity. We use a decomposition method of the…
The design of compliant mechanisms is crucial in several technologies and relies on the availability of solutions for nonlinear structural problems. One of these solutions is given and experimentally validated in the present article for a…
An elastic double pendulum subject to a force acting along a fixed straight line, the so-called "Reut's column problem", is a structure exhibiting flutter and divergence instability, which was never realized in practice and thus debated…
The equilibrium of magneto-elastic rods, formed of an elastic matrix containing a uniform distribution of paramagnetic particles, that are subject to terminal loads and are immersed in a uniform magnetic field, is studied. The deduced…
The final purpose of this paper is to show that, by inserting a convexity constraint on the cables of a suspension bridge, the torsional instability of the deck appears at lower energy thresholds. Since this constraint is suggested by the…
It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…
Recent equations of motion for the large deflections of a cantilevered elastic beam are analyzed. In the traditional theory of beam (and plate) large deflections, nonlinear restoring forces are due to the effect of stretching on bending;…
The distribution of string tension on the contact line between an ideal string and a massive pulley is a frequently-discussed but incompletely-posed problem that confronts students in introductory mechanics. We highlight ambiguities in the…
This paper is focused on the dynamics and control of arbitrary number of quadrotor UAVs transporting a rigid body payload. The rigid body payload is connected to quadrotors via flexible cables where each flexible cable is modeled as a…
We consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the linearization of our problem has nontrivial solutions. In fact our…
When an inextensible elastic rod is 'injected' through a sliding sleeve against a fixed constraint, configurational forces are developed, deeply influencing the mechanical response. This effect, which is a consequence of the change in…
The study of slender elastic structures is an archetypical problem in continuum mechanics, dynamical systems and bifurcation theory, with a rich history dating back to Euler's seminal work in the 18th century. These filamentary elastic…