Insights into the energy equipartition principle in large undamped structures

The question of energy sharing among complex engineering vibrating systems is still an open problem. On the basis of some recent investigations, this paper is addressed to the prediction of the equilibrium energies of interacting conservative resonators and to a better understanding of the principle of energy equipartition for large undamped systems. The analysis explores the field of linear and nonlinear vibrations, the effects of inhomogeneity, the weak or the strong coupling its well as the effect of the initial energy distribution among the subsystems. The principle of energy equipartition is shown to react in a different fashion to these factors. Sonic general arguments, supported by the results of numerical experiments, enlightening promoting or inhibiting factors to the reaching of energy equipartition conditions, are given. (C) 2008 Elsevier Ltd. All rights reserved

Time domain energy response of uncertain structures

The dynamic response characterization of a complex system comprises of multiple heterogeneous substructures remains one of the most challenging problems in structural dynamics. Inherent uncertainties and the high dimensionality of the problem led to develop approaches imported also from other areas of physics and engineering. In this paper a new approach, namely the Time Asymptotic ensemble Energy average (TAE), a statistical method for the prediction of the transient energy sharing among two or more subsystems, for both weak and strong coupling is developed. The originality of this method relies on an asymptotic expansion technique, able to evaluate the energy distribution among the subcomponents of a system in transient and steady state conditions, based on the low order modes response, i.e. at a low computational cost. The method is experimentally validated for and a good agreement with theoretical prediction is found

A new energy approach to the analysis of complex and uncertain system

A new approach for predicting the response of a complex and uncertain structural-acoustic system was developed, namely the Time Asymptotic ensemble Energy Average (TAE). This approach belongs to the class of the energetic methods, since the system dynamic is described in terms of global parameters (the energies of a subset of the system) and a statistical approach is developed by introducing random natural frequencies, whose variability is due to stochastic perturbations of physical and geometrical parameters of the system. The developed method allows the evaluation of the energy sharing among two or more subsystems, for both weak and strong coupling. The originality of this method lies in the development of an asymptotic expansion technique, which permits to evaluate the energy distribution among the subcomponents of a system in both transient and steady state conditions in terms of only few modes of the system and the related marginal probabilities, determined with a low computational cost. The proposed method has been experimentally validated for two different configurations: a twoplate and a three-plate assemblies. The typical experiment consists in a transient excitation on a subcomponent of the structure and a measure of the dynamical responses of the plates at different locations upon all the subsystems, in order to derive a space-average value of the vibrational energies

Hydrodynamic and hydroelastic analyses of a plate excited by the turbulent boundary layer

Recent studies have demonstrated that the characterisation of wall-pressure fluctuations for surface ships is of great interest not only for military applications but also for civil marine vehicles. A ship model towed in a towing tank is used to perform pressure and structural measurements at high Reynolds numbers. This facility provides ideal flow conditions because background turbulence and noise are almost absent. Free surface effects are naturally included in the analysis, although in the particular section chosen for the present study do not have significant consequences on pressure spectra. Scaling laws for the power spectral density are identified providing the possibility to estimate pressure spectra for different flow conditions and in particular for full-scale applications. The range of validity of some theoretical models for the cross-spectral density representation is analysed by direct comparison with experimental data of wall-pressure fluctuations measured in streamwise and spanwise direction. In a second phase, an indirect validation is performed by comparing the measured vibrational response of an elastic plate inserted in the catamaran hull with that obtained numerically using, as a forcing function, the modelled pressure load. In general, marine structures are able to accept energy mainly from the sub-convective components of the pressure field because the typical bending wavenumber values are usually lower than the convective one; thus, a model that gives an accurate description of the phenomenon at low wavenumbers is needed. In this work, it is shown that the use of the Chase model for the description of the pressure field provides a satisfactory agreement between the numerical and the experimental response of the hull plate. These experimental data, although acquired at model scale, represent a significant test case also for the real ship problem

Analysis of the scaling laws for the turbulence driven panel responses

The high computational costs, associated to the numerical solution of the fluctuating pressure field generated at the wall by the turbulent boundary layer and of the induced structural response, push for the exploration of alternative methodologies of analysis. Wall pressure fluctuations spectra are often modeled using semi-empirical expressions based on the experimental evidence and on the identification of universal scaling laws. In this work the possibility to adopt a dimensionless representation, able to provide a universal expression for the structural response of plates under turbulent boundary layer excitations, is investigated with the help of pressure fluctuations and acceleration experimental data sets. The test article is a plane thin plate wetted by a fluid over one face, the boundary layer is fully developed and pressure gradient effects are negligible. The attention is devoted to the investigation and the definition of a normalization of the required axes: the excitation frequency and the power spectral density of the structural response. The analysis is initially based on analytical models for the structural response under turbulent boundary layer excitations. The proposed scaling laws are successively and successfully applied to four data sets measured in different conditions both in wind tunnels and in a towing tank

SENSITIVITY OF THE PREDICTIVE STRUCTURAL MODELS UNDER STOCHASTIC AND CONVECTIVE EXCITATION

The quality of the predictive response of a structural domain, under a random and convective load, is here analyzed by discussing each step of the numerical procedure. The structural response, due to a wall pressure distribution, is derived in modal coordinates according to a finite element scheme. The modal basis can include the dry or wet (aeroelastic) structural mode shapes: in the present analysis only the in vacuum eigenvectors are used. For such a problem one of the most critical points is the transformation of the pressure distribution into discrete locations. In fact, this step depends on (i) the assumed TBL model, (ii) the integration scheme and (iii) the frequency range. These three points are the goals of the present work where the specific sensitivity to each of them is investigated. The transformation of the pressure distribution into discrete locations can be computationally expensive for the desired level of the required numerical approximation. The use of consistent formulation in the finite element scheme can be unfeasible. Moreover the approximations, in expressing the pressure field, can have a different influence on the structural responses according to the chosen TBL models. This is another key aspect of the present work

A DIMENSIONLESS REPRESENTATION OF THE TURBULENCE DRIVEN PANEL RESPONSE

In this paper a summary is presented concerning several experiences in predicting and measuring the structural response under turbulent boundary layer excitations. The theoretical, numerical and experimental evaluations involved both wind tunnel and towing tank (water) tests in which a flow wetted a plane plate over one face. A critical review of all these sets is presented together with the possibility to adopt a dimensionless representation for the response. This is done in order to tentatively compare measurement sets and/or predictive results obtained in nominally different conditions. Specifically, the attention is devoted to the definition of the possible normalisation of the required axes: the excitation frequency and the response metric. To this aim relations suggested by the dimensional analysis are applied to four distinct data sets finding the best choice of dimensionless parameters that allow the collapse of the different curves in a single one. The functional relations between these parameters are discussed and an analytical expression for the dimensionless plate response is obtained

WIND TUNNEL MEASUREMENTS OF PRESSURE FLUCTUATIONS AND STRUCTURAL RESPONSE INDUCED BY THE TURBULENT BOUNDARY LAYER AT HIGH MACH NUMBER, PART 2: COMPARISONS BETWEEN EXPERIMENTAL AND NUMERICAL DATA FOR THE STRUCTURAL RESPONSE

Measurements of the acceleration response of typical homogeneous and composite aeronautical panels with different lay-up to turbulent boundary layer excitation have been performed in a transonic wind tunnel for Mach number values ranging between 0.4 and 0.9. Artificial boundary layers of different thickness have been generated using the setup described in PART 1. Aim of this experimental campaign was the understanding of the influence of different materials and geometrical properties on the response of aeronautical panels to random convective loads as a starting point for a following acoustical optimization. Numerical simulations of the panel response have been performed by FEM and in house codes using, as a forcing function, the modeled pressure field and have been validated by comparisons with measured acceleration data. The numerical determination of the structural response is also fundamental to understand how and when the theoretical models developed for the representation of wall pressure fluctuation spectra can be considered predictive thus, independent on the particular flow conditions

New concepts in damping generation and control: theoretical formulation and industrial applications

These notes are finalized to a particular study of the damping mechanism in Hamiltonian systems, characterized indeed by the absence of any energy dissipation effect. In facr, a clear distinction emerges between the two previous concepts, that indeed seem to be, at a first glance, somehow contradictory. This leads to the wrong expectation that the motion of any part of a disspation-free system maintains a sort of constant amplitude response. It is indeed true the converse: even in the absence of any energy dissipation mechanisms, mechanical systems can exhibit damping, i.e. a decay amplitude motion. This fact is theoretically investigated and applied to cenceive new and high efficient dampers for engineering industrial use