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Abstract: The present paper considers the problem of realizing an effective targeted energy pumping from a linear oscillator to a set of ungrounded linear resonators attached to it. Theoretical as well as numerical results demonstrate the efficacy of using a complex attachment as a passive absorber of broadband energy injected into the primary structure. The paper unveils also the existence of an instantaneous frequency associated with the master response characterized by intermittency: a rather surprising result for a linear autonomous system. Comparison with nonlinear energy sinks demonstrates that the two systems have some analogies in this respect and that the linear complex attachment is a very efficient energy trap. [Copyright &y& Elsevier]

Abstract: 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 as 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. Some general arguments, supported by the results of numerical experiments, enlightening promoting or inhibiting factors to the reaching of energy equipartition conditions, are given. [Copyright &y& Elsevier]

This paper is concerned with emergence of novel effects in wave propagation in one-dimensional waveguides, when integrated with periodic nonlocalities. The nonlocalities are introduced by a connectivity superimposed to a conventional waveguide and depicted as a graph with trees and leaves, each with its own periodicity. Merging nonlocality and periodicity notions induces a distinction between homogenous and non-homogenous periodic configurations. Specifically, various unconventional phenomena linked to the presence of nonlocalities result in disruption of the energy transmission in such systems, disclosing new opportunities for vibration isolation applications. To demonstrate these effects, simple models of propagation of plane extension/compression waves in a uniform infinite rod equipped with co-axial spring-like elements is used. The homogenous case is analysed by a direct double, space and time, Fourier transform, leading to discussion of unusual dispersion effects, including vanishing and negative group velocity. In the non-homogeneous case, the canonical Floquet theory is used to identify stopbands and control their positions in the frequency domain. The results are compared with eigenfrequency analysis of unit periodicity cells and finite structures. Next, the forcing problem is considered and the insertion losses in a semi-infinite rod with nonlocal spring effects are computed to corroborate predictions of Floquet theory, providing physical explanations of the obtained results. Finally, possibilities to employ the non-local interaction forces in an active control format to generate stopbands at arbitrarily low frequencies are highlighted. [ABSTRACT FROM AUTHOR]

Two statistical techniques are developed to predict the statistical moments of the horizontal motion of a floating moored dock, known as catenary anchor leg mooring (CALM), loaded by hydrodynamic random forces. The dock is represented by a lumped mass, the mooring cables by equivalent nonlinear springs and the hydrodynamic forces are modelled by a modified Morison equation. The model of the floating dock leads to a nonlinear ordinary differential equation. Although the problem could be approached by a direct numerical integration, e.g. by Monte-Carlo simulations, because of the stochastic nature of the excitation, this would imply a large number of runs to produce results of some statistical significance. In the present paper an alternative solution is based on the development of two more efficient techniques to predict the relevant statistical moments of the dock response. The first method, called CPSP (conventional perturbation–statistical perturbation), is based on the application of two subsequent perturbation techniques, the first relying on a classical perturbation method, the second on a statistical perturbation approach. The second method, called SLSP (statistical linearization–statistical perturbation), combines indeed a statistical linearization approach together with a statistical perturbation approach. The procedures allow the linearization of the cables restoring forces as well as of the hydrodynamic load and they can be easily generalized to be applied to different dock configurations or to systems of different physical nature. The results, compared with those obtained by a Monte-Carlo simulations, show, in terms of statistical moments of the dock response, a satisfactory agreement. [Copyright &y& Elsevier]

Abstract: This paper attempts to introduce a new point of view on energy analysis in structural dynamics with particular emphasis to its link with uncertainty and complexity. A linear, elastic system undergoing free vibrations, is considered. The system is subdivided into two subsystems and their respective energies together with the shared energy flow are analysed. First, the ensemble energy average of the two subsystems, assuming uncertain the natural frequencies, is investigated. It is shown how the energy averages follow a simple law when observing the long-term response of the system, obtained by a suitable asymptotic expansion. The second part of the analysis shows how the ensemble energy average of a set of random samples is representative even of the single case if the system is complex enough. The two previous points, combined, produce a result that applies to the energy sharing between two subsystems even independently of uncertainty: for complex systems, a simple energy sharing law is indeed stated. Moreover, in the case of absence of damping, a nonlinear relation between the energy flow and the energy (weighted) difference between the two subsystems is derived; on the other hand, when damping is present, this relationship becomes linear, including two terms: one is proportional to the energy (weighted) difference between the two subsystems, the other being proportional to its time derivative. Therefore, the approach suggests a way for deriving a general approach to energy sharing in vibration with results that, in some cases, are reminiscent of those met in Statistical Energy Analysis. Finally, computational experiments, performed on systems of increasing complexity, validate the theoretical results. [Copyright &y& Elsevier]

Abstract: The problem of an elastic lifting hydrofoil in a randomly perturbed flow is considered. It appears that in these conditions the phenomenon of hydroelastic-induced vibrations is controlled by a stochastic differential operator. By using the theory of stochastic perturbation, a technique of solution for this class of problems is proposed, leading to an effective numerical solution. The fundamentals of the method are given and it is applied to the general problem of hydroelastic vibrations. A numerical application to the case of an elastic control surface for a prototype-high- speed marine vehicle is presented. Comparisons between the results obtained by the Stochastic Perturbation Method (SPM) and those provided by standard Monte Carlo simulations (MCS) show the accuracy of the proposed method and a useful saving in computational time. A method is given for comparing the computational time required by the two methods, for a given statistical accuracy. [Copyright &y& Elsevier]

The aim of this paper is to provide a theoretical and experimental analysis of the response of an elastic system carried on board a wedge-shaped body impacting the water surface. The wedge entering the water has a sudden deceleration with shock characteristics, resulting in a short-time duration and a sharp peak value. On the other hand, the carried system undergoes an oscillatory motion induced by the inertial load generated by the impact. The study of this problem reveals the occurrence of special conditions in the response of the on-board oscillator, depending on the parameters associated with the water entry problem, that lead to large elastic forces. The experiments show that when varying the characteristic natural frequency of the on-board oscillator, critical impact conditions occur characterized by very large amplitudes of the structural response that confirm the theoretical predictions. The analysis, based on the water shock spectral response developed by the authors in some previous papers, is generalized here and validated experimentally. [Copyright &y& Elsevier]

Plane wave interference and space averages play a significant role in the derivation of some vibration conductivity equations that are becoming more and more popular in modelling vibroacoustic problems. Particularly, the thermal approach and the modified vibration conductivity equations are here considered with the aim of establishing similarities and/or differences between them and stating relevant consequences. It is shown by formal developments that the thermal equation is obtained under the assumption of performing appropriate space averages, while the modified vibration conductivity equation does not need, in some cases, this condition. It is discussed, however, that in practical applications the conditions of validity of both approaches are quite similar. [Copyright &y& Elsevier]