Related papers: The (small) vibrations of thin plates
We describe the equations of motion of an incompressible elastic body $\Omega$ in 3-space acted on by an external pressure force, and the Newton iteration scheme that proves the well-posedness of the resulting initial value problem for its…
We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling…
The goal of this paper is to obtain an approximate solution of the restricted three-body problem in the case of small perturbations in the vicinity of, but not in exact resonance. In this paper, we study the restricted threebody problem…
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…
This paper aims to study the convergence of solutions in three-dimensional nonlinear elastodynamics for a thin rod as its cross section shrinks to zero for displacements that are comparable to the small radius of the rod. Assuming the…
Equations of motion are derived for (visco)elastic, self-gravitating, and variably-rotating planets. The equations are written using a decomposition of the elastic motion that separates the body's elastic deformation from its net…
The aim of this paper is to develop a virtual element method (VEM) for the vibration problem of thin plates on polygonal meshes. We consider a variational formulation relying only on the transverse displacement of the plate and propose an…
Recent developments on three body systems have revealed that dynamics of trajectories passing through collinear configurations can be easily adopted. We analyse the reduction procedure in order to detect the points where collinear…
The transmission coefficient for vibrational waves crossing an abrupt junction between two thin elastic plates of different widths is calculated. These calculations are relevant to ballistic phonon thermal transport at low temperatures in…
The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values…
In this paper we present the validation of our recently published mathematical model for the dynamics of Cosserat elastic plates. The validation is based on the comparison with the exact solution of the 3-dimensional Cosserat…
Using dimensionally reduced models for the numerical simulation of thin objects is highly attractive as this reduces the computational work substantially. The case of narrow thin elastic bands is considered and a convergent finite element…
In this paper, I presented the analysis and numerical results for free transverse vibration of thin rectangular plates having arbitrarily varying non-homogeneity with the in-plane coordinates along the two concurrent edges. For finding the…
After a brief introduction to several variational problems in the study of shapes of thin thickness structures, we deal with variational problems on 2-dimensional surface in 3-dimensional Euclidian space by using exterior differential…
We adopt a truncated version of two-body dynamics by neglecting three-body correlations, as is supported by microscopic numerical calculations. Introducing orthogonal channel correlations for the pp- and the ph-channel and integrating the…
An approach is developed to find approximate solutions to the restricted circular three body problem. The solution is useful in approximately describing the position vectors of three spherically symmetric masses, one of which has a much…
We present a method to determine the equilibrium geometry of large atomistic systems with linear scaling. It is based on a separate treatment of long and short wavelength components of the forces. While the rapidly varying part is handled…
We show that solutions for a specifically scaled nonlinear wave equation of nonlinear elasticity converge to solutions of a linear Euler-Bernoulli beam system. We construct an approximation of the solution, using a suitable asymptotic…
Several N-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (``acceleration equal force;'' in most cases, the forces are velocity-dependent) and are amenable to exact…
We consider the steady-state analysis of a pinned elastic plate lying on the free surface of a thin viscous fluid, forced by the motion of a bottom substrate moving at constant speed. A mathematical model incorporating elasticity,…