Elisabetta Manconi

Wave motion and dispersion phenomena: veering, locking and strong coupling effects.

The dispersion curves describe wave propagation in a structure, each branch representing a wave mode. As frequency varies the wavenumbers change and a number of dispersion phenomena may occur. This paper characterizes, analyzes, and quantifies these phenomena in general terms and illustrates them with examples. Two classes of phenomena occur. Weak coupling phenomena-veering and locking-arise when branches of the dispersion curves interact. These occur in the vicinity of the frequency at which, for undamped waveguides, the dispersion curves in the uncoupled waveguides would cross: if two dispersion curves (representing either propagating or evanescent waves) come close together as frequency increases then the curves either veer apart or lock together, forming a pair of attenuating oscillatory waves, which may later unlock into a pair of either propagating or evanescent waves. Which phenomenon occurs depends on the product of the gradients of the dispersion curves. The wave mode shapes which describe the deformation of the structure under the passage of a wave change rapidly around this critical frequency. These phenomena also occur in damped systems unless the levels of damping of the uncoupled waveguides are sufficiently different. Other phenomena can be attributed to strong coupling effects, where arbitrarily light stiffness or gyroscopic coupling changes the qualitative nature of the dispersion curves.

Wave characterization of cylindrical and curved panels using a finite element method.

This paper describes a wave finite element method for the numerical prediction of wave characteristics of cylindrical and curved panels. The method combines conventional finite elements and the theory of wave propagation in periodic structures. The mass and stiffness matrices of a small segment of the structure, which is typically modeled using either a single shell element or, especially for laminated structures, a stack of solid elements meshed through the cross-section, are postprocessed using periodicity conditions. The matrices are typically found using a commercial FE package. The solutions of the resulting eigenproblem provide the frequency evolution of the wavenumber and the wave modes. For cylindrical geometries, the circumferential order of the wave can be specified in order to define the phase change that a wave experiences as it propagates across the element in the circumferential direction. The method is described and illustrated by application to cylinders and curved panels of different constructions. These include isotropic, orthotropic, and laminated sandwich constructions. The application of the method is seen to be straightforward even in the complicated case of laminated sandwich panels. Accurate predictions of the dispersion curves are found at negligible computational cost.

Numerical and Experimental Investigation of Stop-Bands in Finite and Infinite Periodic One-Dimensional Structures

Adding periodicity to structures leads to wavemode interaction, which generates pass- and stop-bands. The frequencies at which stop-bands occur are related to the periodic nature of the structure. Thus structural periodicity can be shaped in order to design vibro-acoustic filters for reducing vibration and noise transmission. The aim of this paper is to investigate, numerically and experimentally, stop-bands in periodic one-dimensional structures. Two methods for predicting stop-bands are described: the first method applies to infinite periodic structures using a wave approach; the second method deals with the evaluation of a vibration level difference (VLD) in a finite periodic structure embedded within an infinite one-dimensional waveguide. This VLD is defined to predict the performance in terms of noise and vibration insulation of periodic cells embedded in an otherwise uniform structure. Numerical examples are presented, and results are discussed and validated experimentally. Very good agreement between the numerical and experimental models in terms of stop-bands is shown. In particular, the results show that the stop-bands obtained using a wave approach (applied to a single cell of the structure) predict those obtained from the VLD of the corresponding finite periodic structure.

Modal tests on buildings: correlating large amounts of acquisitions with different space–time collocations

This article deals with a method for the time and space superposition of data acquired in the dynamical testing of large structures. The method permits two procedures comprising the integration of sets of measurements taken at different times and the integration of sets of measurements taken at different places. The latter is a very useful feature when dealing with huge structures, such as big buildings comprising a number of different architectural details. The validation of this method is a case study consisting of many dynamical tests performed on an ancient castle.

Frequency response coupling technique for the estimation of the power transmission in multi-point-connected structures

This article presents a frequency response coupling technique for the prediction of the complex mechanical power in multi-point-connected structures. The motivation of this study originates from a real industrial application case concerning the evaluation of the power transmission from a large machine (source) to a flexible structure (cabin/receiver) when only forces and response data of the decoupled substructures (source, receiver, and connectors) can be measured and only acceleration/velocity response data of the whole coupled structure in operation are available. The predicted power can then be used as the input for further investigation on the vibro-acoustic behaviour of the receiver and for design optimisation in terms of noise and vibration reduction. The method is illustrated for a dynamic case representing many real situations of two flexible structures connected through multiple points. Comparison between experimental and numerical results, obtained in the case of a simplified assembled structure consisting of two coupled beams, is investigated.

Prediction of the Coupled Impedance from Frequency Response Data

This work deals with the common case of large mechanical systems which can be modelled considering two main sub-structures: a source structure, corresponding for example to the engine, and a receiving structure, as the accommodation area/cabin in these machines. Numerical models are highly desired for predicting the vibroacoustic behaviour of the receiver at a design stage and for design optimisation. In many cases the mechanical systems must be studied using sub-structuring techniques

Evaluation of Stop Bands in Periodic and Semi-Periodic Structures by Experimental and Numerical Approaches

Adding periodicity in structures leads to wavemode interaction, which generates pass- and stop-bands. Stop-bands are related to the periodic nature of the structure. Thus structural periodicity can be shaped in order to design vibro-acoustic filters to reduce vibration and noise transmission. The aim of this paper is to investigate numerically and experimentally stop-bands in periodic one-dimensional structures. Two methods for predicting stop-bands are described: the first applies to infinite structures using a wave approach; the second deals with the evaluation of a structural transmission loss coefficient. Numerical examples concerning periodic beams are presented. Results are discussed and validated experimentally. Very good agreement between the numerical and experimental models in terms of stop-bands is showed.

A Finite Element Method for Modelling Waves in Laminated Structures

The generality and complexity of laminated structures raises issues regarding modelling their dynamics and optimising their design. In this paper, a wave and finite element (WFE) method for modelling the dynamic behaviour of plane and axisymmetric laminated structures is described. A small segment of the structure is modelled using conventional finite element (FE) methods, typically using a commercial package. The mass and stiffness matrices are found, periodicity conditions are applied, and an eigenvalue problem is formulated and solved to find the dispersion relations. The frequency dependence of viscoelastic material properties and pre-stress can be taken into account straightforwardly. A hybrid FE/WFE approach for determining transmission characteristics of joints is described. Numerical examples are presented, including anisotropic, plane and cylindrical foam-cored laminated sandwich constructions with pre-stress. The method is simple in application, provides accurate results at low computational cost and is a valuable tool for evaluating the vibro-acoustic behaviour of multi-layer panels and optimising their design.