Related papers: The vibrations of thin plates
Much of standard galaxy dynamics rests on the implicit assumption that the corresponding N-body problem is (near) integrable. This notion although leading to great simplification is by no means a fact. It is therefore important to develop…
Quantum computation of vibrational properties of molecules is a promising platform to obtain computational advantages for computational chemistry. However, fault-tolerant quantum computations of vibrational properties remain a relatively…
We analyse a system of partial differential equations describing the behaviour of an elastic plate with periodic moduli in the two planar directions, in the asymptotic regime when the period and the plate thickness are of the same order of…
Planetary topography can either be modeled as a load supported by the lithosphere, or as a dynamical effect due to lithospheric flexure caused by mantle convection. In both cases the response of the lithosphere to external forces can be…
We study the dynamics of a droplet moving on an inclined rough surface in the absence of inertial and viscous stress effects. In this case, the dynamics of the droplet is a purely geometric motion in terms of the wetting domain and the…
We provide a road towards obtaining gravitational waveforms from inspiraling material binaries with an accuracy viable for third-generation gravitational wave detectors, without necessarily advancing computational hardware or…
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the…
We present a new particle-based (discrete element) numerical method for the simulation of granular dynamics, with application to motions of particles on small solar system body and planetary surfaces. The method employs the parallel N-body…
We develop the foundations of an effective-one-body (EOB) model for eccentric binary coalescences that includes the conservative dynamics, radiation reaction, and gravitational waveform modes from the inspiral and the merger-ringdown…
Using post-Newtonian equations of motion for fluid bodies valid to the second post-Newtonian order, we derive the equations of motion for binary systems with finite-sized, non-spinning but arbitrarily shaped bodies. In particular we study…
An iterative method is presented for solving the problem of a uniformly rotating, self-gravitating ring without a central body in Newtonian gravity by expanding about the thin ring limit. Using this method, a simple formula relating mass to…
Various many-body models are treated, which describe $N$ points confined to move on a plane circle. Their Newtonian equations of motion ("accelerations equal forces") are integrable, i. e. they allow the explicit exhibition of $N$ constants…
A method to simulate orthotropic behaviour in thin shell finite elements is proposed. The approach is based on the transformation of shape function derivatives, resulting in a new orthogonal basis aligned to a specified preferred direction…
We report experimental and numerical results on the buildup of the energy spectrum in wave turbulence of a vibrating thin elastic plate. Three steps are observed: first a short linear stage, then the turbulent spectrum is constructed by the…
Theoretical and experimental results for in-plane vibrations of a uniform rectangular plate with free boundary conditions are obtained. The experimental setup uses electromagnetic-acoustic transducers and a vector network analyzer. The…
The mechanical model of a thin plate with boundary control and observation is presented as a port-Hamiltonian system (pHs), both in vectorial and tensorial forms: the Kirchhoff-Love model of a plate is described by using a Stokes-Dirac…
(abbreviated) In this paper we develop a consistent WKBJ formalism, together with a formal first order perturbation theory for calculating the properties of the inertial modes of a uniformly rotating coreless body (modelled as a polytrope…
We present example applications of an approach to first-principles calculations of vibrational properties of materials implemented within the Exabyte.io platform. We deploy models based on the Density Functional Perturbation Theory to…
Motivated by recent advances in the inverse design of electromagnetic materials, we develop two methods for manipulating flexural waves on thin elastic plates. Firstly, we derive a technique for determining plate pinning or mass-loading of…
A concise method for following the evolving geometry of a moving surface using Lagrangian coordinates is described. All computations can be done in the fixed geometry of the initial surface despite the evolving complexity of the moving…