Related papers: A new closed-form model for isotropic elastic sphe…
We develop a new higher order closed-form model for the dynamics of a hyperelastic isotropic 3D cylindrical body. We derive, for the first time, a simple explicit expression for the fundamental frequency.
Higher order closed-form formulation for Neo-Hookean shell is presented. New solution for natural frequency of free vibration of a hemisphere is derived.
The purpose of this work is to calculate the vibrational modes of an elastically anisotropic sphere embedded in an isotropic matrix. This has important application to understanding the spectra of low-frequency Raman scattering from…
Acoustic vibrations of nanoparticles made of materials with anisotropic elasticity and nanoparticles with non-spherical shapes are theoretically investigated using a homogeneous continuum model. Cubic, hexagonal and tetragonal symmetries of…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
This paper discusses the free vibration of elastic spherical structures in the presence of an externally unbounded acoustic medium. In this vibration, damping associated with the radiation of energy from the confined solid medium to the…
The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study in particular the eigenfrequencies of an elastic disc with free boundaries and their connection to…
We derive closed-form solutions for reverberant elastography in anisotropic elastic media by adapting the framework used in electromagnetic theory to treat transverse isotropic materials. Different sample-setup geometries are analyzed,…
In this paper we investigate the deformation of cylindrical linearly elastic shells using the Koiter model. We formulate and solve the relaxed Saint-Venant's problem for thin cylindrical tubes made of isotropic and homogeneous elastic…
This paper presents a mathematical model for an industry-inspired problem of vibration isolation applied to elastic fluid-filled containers. A fundamental problem of suppression of vibrations within a finite-width frequency interval for a…
The buckling instabilities of core-shell systems, comprising an interior elastic sphere, attached to an exterior shell, have been proposed to underlie myriad biological morphologies. To fully discuss such systems, however, it is important…
Vibrational mode frequencies and damping are calculated for an elastic sphere embedded in an infinite, homogeneous, isotropic elastic medium. Anisotropic elasticity of the sphere significantly shifts the frequencies in comparison to…
Linearised relativistic elasticity equations of motion are considered for a rod and a spinning ring encountering a gravitational wave. In the case of the rod, the equations reduce to a wave equation with appropriate boundary conditions.…
The aim of this short note is to give a synthetic presentation of the mathematical elements that are used to solve the elastic wave system of equations in a bounded anisotropic elastic body, in a general framework. In particular, the proof…
This paper presents a three-dimensional analytical study of the intrinsic free vibration of an elastic multilayered hollow sphere interacting with an exterior non-Newtonian fluid medium. The fluid is assumed to be characterized by a…
A dynamical model is proposed for isotropic turbulence driven by steady forcing that yields a viscosity independent dynamics for the small-scale (inertial) regime. This reproduces the Kolmogorov spectrum for the two-point velocity…
It is the aim of the paper to present a new point of view on rotational elasticity in a nonlinear setting using orthogonal matrices. The proposed model, in the linear approximation, can be compared to the well known equilibrium equations of…
In this paper, we derive a series of exact analytical closed expressions to calculate the complex eigenfrequencies and the displacement for the corresponding eigenmodes of a viscoelastic (nano-)sphere in the presence of linear damping.…
We study elasticity-driven morphological transitions of soft spherical core shell structures in which the core can be treated as an isotropic elastic continuum and the surface or shell as a tensionless liquid layer, whose elastic response…
The spectrum of acoustic vibrational modes of an inhomogeneous elastic continuum are analyzed with application to a spherical nanoparticle embedded in an infinite glass block. The relationship of these modes to the discrete vibrational…