One may produce the qth harmonic of a string of length π by applying the 'correct touch' at the node $\pi /q$ during a simultaneous pluck or bow. This notion was made precise by a model of Bamberger, Rauch and Taylor. Their 'touch' is a damper of magnitude b concentrated at $\pi /q$. The 'correct touch' is that b for which the modes, that do not vanish at $\pi /q$, are maximally damped. We here examine the associated spectral problem. We find the spectrum to be periodic and determined by a polynomial of degree $q-1$....

This paper presents a derivation of the Rayleigh- Betti reciprocity relation for layered curved composite beams with interlayer slip. The principle of minimum of potential energy is also formulated for two-layer curved composite beams and its applications are illustrated by numerical examples. The solution of the presented problems are obtained by the Ritz method. The applications of the Rayleigh-Betti reciprocity relation proven are illustrated by some examples.

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...

One of the main question arising in Extended Thermodynamics concerns the physical meaning of the temperature far from equilibrium. Some authors define thermodynamic temperature $T_{th}$ the inverse of the coefficient linking the entropy flux with the heat flux. Other authors, instead, define non-equilibrium temperature $\theta$ the inverse of the partial derivative of entropy with respect to energy, at density and heat flux constant. The aim of this paper is to determine the expression of entropy flux in some...

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...

Si dà una presentazione della formulazione delle equazioni di bilancio della Meccanica dei Continui tramite l'approccio insiemistico (flussi e interazioni di Cauchy) e quello distribuzionale (potenze virtuali), illustrando i progressi ottenuti nell'indebolimento delle ipotesi, fino a comprendere campi tensoriali a divergenza misura. Si mostra poi come l'approccio attraverso il Principio delle potenze virtuali permetta di individuare il tensore degli sforzi anche nel caso di un corpo continuo dotato...

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 $\partial \Omega .$

We present equivalent conditions and asymptotic models for the diffraction problem of elastic and acoustic waves in a solid medium surrounded by a thin layer of fluid medium. Due to the thinness of the layer with respect to the wavelength, this problem is well suited for the notion of equivalent conditions and the effect of the fluid medium on the solid is as a first approximation local. We derive and validate equivalent conditions up to the fourth order for the elastic displacement. These conditions...

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...