In questa Nota vengono usati alcuni risultati precedentemente ottenuti - v. [4] e [5] - riguardanti l'urto di un martelletto rigido e di una corda elastica. Da essi possono dedursi le condizioni della corda - deformazione e atto di moto - all'istante in cui essa rimane libera dall'influenza del martelletto. È dunque possibile determinare mediante l'analisi di Fourier, i valori delle energie delle varie armoniche, i quali, com'è ben noto, determinano il timbro del suono emesso dalla corda (timbro...

In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer...

3D-2D asymptotic analysis for thin structures rests on the mastery of scaled gradients $\left({\nabla }_{\alpha }{u}_{\epsilon }|\frac{1}{\epsilon }{\nabla }_3{u}_{\epsilon }\right)$ bounded in $L^p(\Omega ;{ℝ}^9),1\<p\<+\infty .$ Here it is shown that, up to a subsequence, $u_{\epsilon }$ may be decomposed as $w_{\epsilon }+z_{\epsilon },$ where $z_{\epsilon }$ carries all the concentration effects, i.e. $\left\{{\left|\left({\nabla }_{\alpha }{w}_{\epsilon }|\frac{1}{\epsilon }{\nabla }_3{w}_{\epsilon }\right)\right|}^p\right\}$ is equi-integrable, and $w_{\epsilon }$ captures the oscillatory behavior, i.e. $z_{\epsilon }\to 0$ in measure. In addition, if $\left\{u_{\epsilon }\right\}$ is a recovering sequence then $z_{\epsilon }=z_{\epsilon }\left(x_{\alpha }\right)$ nearby $\partial \Omega .$

3D-2D asymptotic analysis for thin structures rests on the mastery of scaled gradients $\left({\nabla }_{\alpha }{u}_{\epsilon }|\frac{1}{\epsilon }{\nabla }_3{u}_{\epsilon }\right)$ bounded in $L^p(\Omega ;{ℝ}^9),1<p<+\infty .$ Here it is shown that, up to a subsequence, $u_{\epsilon }$ may be decomposed as $w_{\epsilon }+z_{\epsilon },$ where $z_{\epsilon }$ carries all the concentration effects, i.e.$\left\{{\left|\left({\nabla }_{\alpha }{w}_{\epsilon }|\frac{1}{\epsilon }{\nabla }_3{w}_{\epsilon }\right)\right|}^p\right\}$ is equi-integrable, and $w_{\epsilon }$ captures the oscillatory behavior, i.e.$z_{\epsilon }\to 0$ in measure. In addition, if $\left\{u_{\epsilon }\right\}$ is a recovering sequence then $z_{\epsilon }=z_{\epsilon }\left(x_{\alpha }\right)$ nearby $\partial \Omega .$

The paper deals with the analysis of generalized von Kármán equations which desribe stability of a thin circular viscoelastic clamped plate of constant thickness under a uniform compressible load which is applied along its edge and depends on a real parameter. The meaning of a solution of the mathematical problem is extended and various equivalent reformulations of the problem are considered. The structural pattern of the generalized von Kármán equations is analyzed from the point of view of nonlinear...

The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrödinger equation, with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in [Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous space, giving a root...

An adaptive strategy for nonlinear finite-element analysis, based on the combination of error estimation and h-remeshing, is presented. Its two main ingredients are a residual-type error estimator and an unstructured quadrilateral mesh generator. The error estimator is based on simple local computations over the elements and the so-called patches. In contrast to other residual estimators, no flux splitting is required. The adaptive strategy is illustrated by means of a complex nonlinear problem:...

The free motion of a thin elastic linear membrane is described, in a simplyfied model, by a second order linear homogeneous hyperbolic system of partial differential equations whose spatial part is the Laplace Beltrami operator acting on a Riemannian 2-dimensional manifold with boundary. We adapt the estimates of the spectrum of the Laplacian obtained in the last years by several authors for compact closed Riemannian manifolds. To make so, we use the standard technique of the doubled manifold to...

This paper is devoted to Eulerian models for incompressible fluid-structure systems. These models are primarily derived for computational purposes as they allow to simulate in a rather straightforward way complex 3D systems. We first analyze the level set model of immersed membranes proposed in [Cottet and Maitre, Math. Models Methods Appl. Sci.16 (2006) 415–438]. We in particular show that this model can be interpreted as a generalization of so-called Korteweg fluids. We then extend this model...

We consider the exact controllability of a hybrid system consisting of an elastic beam, clamped at one end and attached at the other end to a rigid antenna. Such a system is governed by one partial differential equation and two ordinary differential equations. Using the HUM method, we prove that the hybrid system is exactly controllable in an arbitrarily short time in the usual energy space.

We consider the exact controllability of a hybrid system consisting of an elastic beam, clamped at one end and attached at the other end to a rigid antenna. Such a system is governed by one partial differential equation and two ordinary differential equations. Using the HUM method, we prove that the hybrid system is exactly controllable in an arbitrarily short time in the usual energy space.

Exact controllability results for a multilayer plate system are obtained from the method of Carleman estimates. The multilayer plate system is a natural multilayer generalization of a classical three-layer “sandwich plate” system due to Rao and Nakra. The multilayer version involves a number of Lamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controls are assumed to be locally distributed in a neighborhood...

Exact controllability results for a multilayer plate system are obtained from the method of Carleman estimates. The multilayer plate system is a natural multilayer generalization of a classical three-layer “sandwich plate” system due to Rao and Nakra. The multilayer version involves a number of Lamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controls are assumed to be locally distributed in a neighborhood...

We consider the problem of boundary control of an elastic system with coupling to a potential equation. The potential equation represents the linearized motions of an incompressible inviscid fluid in a cavity bounded in part by an elastic membrane. Sufficient control is placed on a portion of the elastic membrane to insure that the uncoupled membrane is exactly controllable. The main result is that if the density of the fluid is sufficiently small, then the coupled system is exactly controllable....

We prove an exact controllability result for thin cups using the Fourier method and recent improvements of Ingham type theorems, given in a previous paper [2].