Slow Effects of Fast Harmonic Excitation for Elastic Structures

High-frequency excitation may affect the slow behavior of a dynamical system. For example, equilibria may move, disappear, or gain or loose stability. We consider such slow effects of fast excitation for a simple mechanical system that incorporates features of many engineering structures. The study is intended to contribute to the general understanding of periodically excited linear and nonlinear systems, as well as to the current attempts to utilize high-frequency excitation for altering the low-frequency properties of structures.     

Force transmissibility versus displacement transmissibility

It is well-known that when a single-degree-of-freedom (sdof) system is excited by a continuous motion of the foundation, the force transmissibility, relating the force transmitted to the foundation to the applied force, equals the displacement transmissibility. Recent developments in the generalization of the transmissibility to multiple-degree-of-freedom (mdof) systems have shown that similar simple and direct relations between both types of transmissibility do not appear naturally from the definitions, as happens in the sdof case.     

Nonlinear dynamics and chaos of a finite-degree-of-freedom model of a buckled rod

The simple example of a mechanical system expressively exhibiting unpredictable and chaotic motions is a rod compressed by a supercritical force and subjected to a time-dependent transverse loading. Dynamics of this system can be analyzed either through modal analysis or through another lumped parameter modelling, for example, by discretization of the rod into an ensemble of segments. The paper is aimed to present the latter formulation of the problem and to discuss numerical results obtained in this framework.

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Sommario Un semplice esempio di sistema meccanico in grado di esibire in modo espressivo comportamenti dinamici non predicibili e caotici è rappresentato da una trave compressa in regime supercritico e soggetta ad un carico trasversale dipendente dal tempo. La dinamica di questo sistema può essere analizzata tramite approssimazioni modali, ovvero attraverso una modellazione a parametri concentrati, ad esempio discretizzando la trave in elementi rigidi con deformabilità localizzate. Il lavoro presenta quest'ultima formulazione del problema e ne discute i relativi risultati numerici.

     

Chain-length dependent nematic ordering of conjugated polymers in a liquid crystal solvent

In this communication we demonstrate the dependence of the solute order parameter on the solute molecular weight for polymer solutes dissolved in liquid crystalline solvents. Using ensemble absorption polarization spectroscopy together with single molecule fluorescence polarization measurements, we have determined the order parameter of the conjugated polymer MEH-PPV (poly[2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene vinylene]) in the liquid crystal 5CB (4-cyano-4-n-pentylbiphenyl) as a function of polymer chain length. Ensemble absorption polarization measurements agree well with results obtained by single molecule fluorescence polarization spectroscopy, indicating a large-scale ordering of the MEH-PPV solute in 5CB. These results demonstrate that the increasing number of defects for larger polymer weights inherently limits the alignment of the polymer solute.