M.N. Ichchou

Piano soundboard: structural behavior, numerical and experimental study in the modal range

Abstract The low frequency broadband vibrational behavior of a piano soundboard is considered. Attention is focused on the ability of finite element models and analytical models to predict precisely the behavior of such a complicated structure—especially with its orthotropy and rib effects. In order to validate these abilities, an experimental modal analysis, considered as the reference, is compared first with a numerical calculation and then with an analytical modeling of the modal basis of the same soundboard. The high structural complexity of the soundboard exceeds the analytical capabilities, but agreement is very good for the numerical model, in the frequency domain, and equally in the spatial one. The final aim is to generate a numerical tool for designing and optimizing piano soundboards.

Energetics of axisymmetric fluid-filled pipes up to high frequencies

Abstract The energetics of motions of axisymmetric fluid-filled pipes are presented in this paper, in view of high-frequency modelling. This study deals in particular with derivations of local energy equations well suited for the prediction of averaged response of coupled fluid–structure systems. The derivation of the latter requires special manipulation of the kinematic dynamics based here on the notion of propagation modes. Thus, the focus is on the Donnell–Mushtari cylindrical shell with an internal acoustic fluid, a typical example of waveguides with multiple transmission mechanisms. “Exact” and statistical approaches are developed for this system. A state-space representation is first proposed; it allows the characterization of propagating modes in a general manner. This propagating content then leads to the formulation of the local energy approach for this canonical problem.

Active rubber mounts by means of piezoelectric actuators, experimental work

This paper proposes an experimental mock-up which aims to validate a new concept of a piezo-rubber mount. This new concept is based upon the combination of an electrically-monitored active piezoelectric block with a passive rubber mount. An adaptive control law is then used for an off-line identification and control of the force transmissibility. The new hybrid mount is shown to be very efficient and significantly improves the transfer between disturbances and receiving components.

Wave Finite Element Method Based on Reduced Model for One-Dimensional Periodic Structures

In this paper, an efficient numerical approach is proposed to study free and forced vibration of complex one-dimensional (1D) periodic structures. The proposed method combines the advantages of component mode synthesis (CMS) and wave finite element method. It exploits the periodicity of the structure since only one unit cell is modelled. The model reduction based on CMS improves the computational efficiency of unit cell dynamics, avoiding ill-conditioning issues. The selection of reduced modal basis can reveal the influence of local dynamics on global behavior. The effectiveness of the proposed approach is illustrated via numerical examples.

Flexural waves focusing through shunted piezoelectric patches

In this paper, we designed and analyzed a piezo-lens to focus flexural waves in thin plates. The piezo-lens is comprised of a host plate and piezoelectric arrays bonded on the surfaces of the plate. The piezoelectric patches are shunted with negative capacitance circuits. The effective refractive indexes inside the piezo-lens are designed to fit a hyperbolic secant distribution by tuning the negative capacitance values. A homogenized model of a piezo-mechanical system is adopted in the designing process of the piezo-lens. The wave focusing effect is studied by the finite element method. Numerical results show that the piezo-lens can focus flexural waves by bending their trajectories, and is effective in a large frequency band. The piezo-lens has the ability to focus flexural waves at different locations by tuning the shunting negative capacitance values. The piezo-lens is shown to be effective for flexural waves generated by different types of sources.

Double Panel Partition (AVNC) by Means of Optimized Piezoceramic Structural Boundary Control

Towards low frequencies, the sound reduction of a double panel partition has an efficiency loss. A feasibility study is investigated to improve the sound reduction of a realistic double panel partition by means of piezoelectric elements as structural control actuators between the panel boundary. Finite element modeling of the double glazing window permits an understanding of the physical phenomenon governing the vibroacoustic behavior. In particular, the incidence of the fluid cavity and the boundary conditions effects on the insertion loss factor are analyzed. Hence, an original structural control experiment has been conducted using optimized piezoceramic actuators at the double glazing window boundaries. The performances of the proposed control strategy are evaluated and it is shown that an improvement has been achieved with a simple velocity or a pressure feedback control.

Energy flow analysis for curved beams

This paper presents an energy model for the medium- and high-frequency analysis of Love–Kirchhoff curved beams. This model introduced by Nefske and Sung [Statistical Energy Analysis NCA 3, 47–54 (1987)] for straight beams and investigated further by other authors, is developed for curved rods (tangential or longitudinal waves), and then for curved beams (radial or flexural waves). The exact-energy solution for curved rods or beams is shown to consist of a smooth spatial variation, which the energy model represents, and a spatially oscillating solution, which can be represented by an energy envelope. Finally, a complete energy model is proposed for curved components including both longitudinal and flexural waves. Boundary conditions are also given in this paper. It is shown that this method, which is numerically attractive in the mid- and high-frequency range, predicts the arithmetic mean value of the energy variables.

A Polynomial Chaos Expansion Based Reliability Method for Linear Random Structures

Within the framework of mechanical engineering, reliability assessment is usually involved in the procedure of finite element analysis (FEA) combined with Monte Carlo simulation (MCS). Unfortunately, such approaches require high computational effort. To improve efficiency, we propose a polynomial chaos expansion (PCE) based MCS method for linear random structures, in which the time consuming repeated FEA is avoided in manner of approximating the random response by PCE. However, applications of PCE are always restricted for the first passage problem due to the curse of high dimensionality. To overcome this, we use the convolution form to compute the dynamic response, in which PCE is raised to approximate the modal properties so that the dimension of uncertainties is reduced since only structural random parameters are considered. Four examples are studied to show the effectiveness and relevancy of the proposed method.

Damage Detection in Cylindrical Pipe through Diffusion Matrix in Wave Finite Element Method

This paper addresses the question of damage detection of cylindrical structures using finite element and periodic structure theory. The structure is modeled considering two waveguides connected through a coupling element, simulated as the defect. Wave characteristics in the waveguides are evaluated using a Wave Finite Element method (W.F.E.M) based on the analysis of the anomalies which affect the elastic wave travelling in the structure. Reflection and transmission coefficients of the wave modes which are incident to the coupling element are provided by a diffusion matrix. Then forced response of the pipe with and without transversal defect is predicted using wave decomposition. Numerical examples are given. These concern an isotropic pipe, for which dispersion curves are provided and diffusion coefficients in presence of a transversal and a longitudinal defect are predicted.

Absorption coefficient and energy flow path identification by means of inverse local energy method

Estimation of the single absorption rate and of acoustical power input is currently made in reverberant rooms where a diffuse field is established. In this paper we aim at describing a method dedicated to absorption coefficients and energy flow path identification within all type of acoustic fields in medium and high frequencies, by means of an inverse local energy method. Making use of an energy integral equation with diffuse reflection, an estimator of the wall various absorption rates is built up, while the cavity is excited by a standard spherical acoustic source. A similar formulation is used to characterize a wall continuous excitation. Then it is possible to go through the measurements (pressure, intensity) and supply a detailed analysis of the wall input energy flow. This study also includes a numerical comparison between optimization methods used when trying to match the calculated field and the reference field. Among those methods, the spheric gradient proves to be efficient when compared with e...