Related papers: The vibrations of thin plates
In the real world, we often come across soft objects having spatially varying stiffness, such as human palm or a wart on the skin. In this paper, we propose a novel approach to render thin, deformable objects having spatially varying…
Nematic elastomers and glasses are solids that display spontaneous distortion under external stimuli. Recent advances in the synthesis of sheets with controlled heterogeneities have enabled their actuation into non-trivial shapes with…
We present an O(N) algorithm to study the vibrational properties of amorphous silicon within the framework of tight-binding approach. The dynamical matrix elements have been evaluated numerically in the harmonic approximation exploiting the…
Odd elasticity encompasses active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new anti-symmetric (odd) components…
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…
Wave turbulence in a thin elastic plate is experimentally investigated. By using a Fourier transform profilometry technique, the deformation field of the plate surface is measured simultaneously in time and space. This enables us to compute…
The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…
We study an experimental system of hard granular squares in two dimensions, energized by vibration. The interplay of order in the orientations and positions of anisotropic particles allows for a rich set of phases. We measure the structure…
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…
In the cutting process, machine-tools vibrations are generally a real problem when the amplitude crosses the limits of dimensional or surface quality workpiece precision required. It is necessary to develop models taking into account the…
The problem of acquiring elastic properties of a composite material from the data of the vibrational testing is considered. The specimen is considered to abide by the linear elasticity laws and subject to viscoelastic damping. The BVP for…
We propose three iterative methods for solving the Moser-Veselov equation, which arises in the discretization of the Euler-Arnold differential equations governing the motion of a generalized rigid body. We start by formulating the problem…
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…
We investigate the motion of point vortices on the Mobius band and Klein bottle. Since these are non-orientable surfaces, the standard Hamiltonian approach does not apply. We therefore begin by establishing a modified Hamiltonian approach…
Molecular rotation, vibration, internal rotation, isomerization, tunneling, intermolecular dynamics of weakly and strongly interacting systems, intra-to-inter-molecular energy transfer, hindered rotation and hindered translation over…
In this work, the propagation of an ultrasonic pulse in a thin plate is computed solving the differential equations modeling this problem. To solve these equations finite differences are used to discretize the temporal variable, while…
We consider a single Abelian Higgs vortex on a surface {\Sigma} whose Gaussian curvature K is small relative to the size of the vortex, and analyse vortex motion by using geodesics on the moduli space of static solutions. The moduli space…
In this second paper we define a Post-Minkowskian (PM) weak field approximation leading to a linearization of the Hamilton equations of ADM tetrad gravity in the York canonical basis in a family of non-harmonic 3-orthogonal Schwinger time…
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…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…