相关论文: Convergence of Thin Vibrating Rods to a Linear Bea…
We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the…
We derive exact dispersion relations for axial and flexural elastic wave motion in a rod and a beam under finite deformation. For axial motion we consider a simple rod model, and for flexural motion we employ the Euler-Bernoulli kinematic…
We consider {\it small solutions} of a vibrating mechanical system with smooth non-linearities for which we provide an approximate solution by using a triple scale analysis; a rigorous proof of convergence of the triple scale method is…
The problem of measuring the best linear approximation of a nonlinear system by means of multilevel excitation sequences is analyzed. A comparison between different types of sequences applied at the input of Wiener systems is provided by…
We propose and analyze the numerical approximation for a viscoelastic Euler-Bernoulli beam model containing a nonlinear strong damping coefficient. The finite difference method is used for spatial discretization, while the backward Euler…
We study long nonlinear longitudinal bulk strain waves in a hyperelastic rod of circular cross section within the scope of the general weakly-nonlinear elasticity leading to a model with quadratic and cubic nonlinearities. We systematically…
Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity…
A mathematical model of a simply supported Euler-Bernoulli beam with attached spring-mass system is considered. The model is controlled by distributed piezo actuators and lumped force. We address the issue of asymptotic behavior of…
To obtain new types of exact travelling wave solutions to nonlinear partial differential equations, a number of approximate methods are known in the literature. In this study, we extend the class of auxiliary equations of Fibonnacci&Lucas…
Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…
Flexible fibers at the microscopic scale, such as flagella and cilia, play essential roles in biological and synthetic systems. The dynamics of these slender filaments in viscous flows involve intricate interactions between their mechanical…
This paper presents a study of nonlinear superpositions of Riemann wave solutions admitted by quasilinear hyperbolic first-order systems of partial differential equations. In particular, we focus on the Euler system and non-elastic wave…
We present a geometrically exact nonlinear analysis of elastic in-plane beams in the context of finite but small strain theory. The formulation utilizes the full beam metric and obtains the complete analytic elastic constitutive model by…
A system of partial differential equations describing the spatial oscillations of an Euler-Bernoulli beam with a tip mass is considered. The linear system considered is actuated by two independent controls and separated into a pair of…
We describe the equations of motion of elastodynamic bounded bodies in 3-space, and their linearizations at a stationary point. Using the latter as an approximation to model small motions, we develop a scheme to find numerical solutions of…
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…
We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin's-Voigt's rheology where the viscosity stress tensor complies with the principle of time-continuous frame-indifference.…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
We consider a nonlocal linear elastic wave model. We approximate the model using a spectral Galerkin method in space and analyze error in such an approximation. We perform some numerical experiments to demonstrate the scheme.
We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which allows for the modeling of the dynamics of interfaces between…