Kerem Ege

Vibroacoustics of the piano soundboard: (Non)linearity and modal properties in the low- and mid-frequency ranges

Abstract The piano soundboard transforms the string vibration into sound and therefore, its vibrations are of primary importance for the sound characteristics of the instrument. An original vibro-acoustical method is presented to isolate the soundboard nonlinearity from that of the exciting device (here: a loudspeaker) and to measure it. The nonlinear part of the soundboard response to an external excitation is quantitatively estimated for the first time, at ≈ − 40 dB below the linear part at the ff nuance. Given this essentially linear response, a modal identification is performed up to 3xa0kHz by means of a novel high resolution modal analysis technique [K. Ege, X. Boutillon, B. David, High-resolution modal analysis, Journal of Sound and Vibration 325 (4–5) (2009) 852–869]. Modal dampings (which, so far, were unknown for the piano in this frequency range) are determined in the mid-frequency domain where FFT-based methods fail to evaluate them with an acceptable precision. They turn out to be close to those imposed by wood. A finite-element modelling of the soundboard is also presented. The low-order modal shapes and the comparison between the corresponding experimental and numerical modal frequencies suggest that the boundary conditions can be considered as blocked, except at very low frequencies. The frequency-dependency of the estimated modal densities and the observation of modal shapes reveal two well-separated regimes. Below ≈ 1 kHz , the soundboard vibrates more or less like a homogeneous plate. Above that limit, the structural waves are confined by ribs, as already noticed by several authors, and localised in restricted areas (one or a few inter-rib spaces), presumably due to a slightly irregular spacing of the ribs across the soundboard.

Vibroacoustics of the piano soundboard: Reduced models, mobility synthesis, and acoustical radiation regime

Abstract In string musical instruments, the sound is radiated by the soundboard, subject to the strings excitation. This vibration of this rather complex structure is described here with models which need only a small number of parameters. Predictions of the models are compared with the results of experiments that have been presented in Ege et al. [Vibroacoustics of the piano soundboard: (non)linearity and modal properties in the low- and mid-frequency ranges, Journal of Sound and Vibration 332 (5) (2013) 1288–1305]. The apparent modal density of the soundboard of an upright piano in playing condition, as seen from various points of the structure, exhibits two well-separated regimes, below and above a frequency f lim that is determined by the wood characteristics and by the distance between ribs. Above f lim , most modes appear to be localised, presumably due to the irregularity of the spacing and height of the ribs. The low-frequency regime is predicted by a model which consists of coupled sub-structures: the two ribbed areas split by the main bridge and, in most cases, one or two so-called cut-off corners. In order to assess the dynamical properties of each of the subplates (considered here as homogeneous plates), we propose a derivation of the (low-frequency) modal density of an orthotropic homogeneous plate which accounts for the boundary conditions on an arbitrary geometry. Above f lim , the soundboard, as seen from a given excitation point, is modelled as a set of three structural wave-guides, namely the three inter-rib spacings surrounding the excitation point. Based on these low- and high-frequency models, computations of the point-mobility and of the apparent modal densities seen at several excitation points match published measurements. The dispersion curve of the wave-guide model displays an acoustical radiation scheme which differs significantly from that of a thin homogeneous plate. It appears that piano dimensioning is such that the subsonic regime of acoustical radiation extends over a much wider frequency range than it would be for a homogeneous plate with the same low-frequency vibration. One problem in piano manufacturing is examined in relationship with the possible radiation schemes induced by the models.

Repeated exponential sine sweeps for the autonomous estimation of nonlinearities and bootstrap assessment of uncertainties

Measurements on vibrating structures has been a topic of interest for decades. Vibrating structures are however generally assumed to behave linearly and in a noise-free environment, which is not the case in practice. This paper provides a methodology that allows for the autonomous estimation of nonlinearities and assessment of uncertainties by bootstrap on a given vibrating structure. Nonlinearities are estimated by means of a block-oriented nonlinear model approach based on parallel Hammerstein models and on exponential sine sweeps. Estimation uncertainties are simultaneously assessed using repetitions of the input signal (multi-sine sweeps) as the input of a bootstrap procedure. Mathematical foundations and a practical implementation of the method are discussed using an experimental example. The experiment chosen here consists in exciting a steel plate under various boundary conditions with exponential sine sweeps and at different levels in order to assess the evolution of nonlinearities and uncertainties over a wide range of frequencies and input amplitudes.

Non resonant transmission modelling with statistical modal energy distribution analysis

Statistical modal Energy distribution Analysis (SmEdA) can be used as an alternative to Statistical Energy Analysis for describing subsystems with low modal overlap. In its original form, SmEdA predicts the power flow exchanged between the resonant modes of different subsystems. In the case of sound transmission through a thin structure, it is well-known that the non resonant response of the structure plays a significant role in transmission below the critical frequency. In this paper, we present an extension of SmEdA that takes into account the contributions of the non resonant modes of a thin structure. The dual modal formulation (DMF) is used to describe the behaviour of two acoustic cavities separated by a thin structure, with prior knowledge of the modal basis of each subsystem. Condensation in the DMF equations is achieved on the amplitudes of the non resonant modes and a new coupling scheme between the resonant modes of the three subsystems is obtained after several simplifications. We show that the contribution of the non resonant panel mode results in coupling the cavity modes of stiffness type, characterised by the mode shapes of both the cavities and the structure. Comparisons with reference results demonstrate that the present approach can take into account the non resonant contributions of the structure in the evaluation of the transmission loss.

SmEdA Vibro-Acoustic Modeling of a Trimmed Truck Cab in the Mid-Frequency Range

The City Lightweight and Innovative Cab (CLIC) project was a scientific collaboration gathering public and private organizations. The aim was to propose an innovative lighten truck cab, where a high strength steel was used. As long as it could affect directly the acoustic environment of the cab, it was necessary to be able to simulate the vibroacoustic behavior of the truck cab in the mid frequency range. The dissipative treatments used for noise and vibration control such as viscoelastic patches and acoustic absorbing materials must then be taken into account in the problem. A process based on the SmEdA (Statistical modal Energy distribution Analysis) method was developed and is presented in this paper. SmEdA allows us substructuring the global problem, to study the interaction between the floor and the interior cavity. The process consists in building finite element models (FEM) of each subsystem (floor, internal cavity), including the dissipative material (damping layer, poroelastic material). Standard modal FEM calculations are then performed for each uncoupled subsystem. From the spatial mode shapes, and the modal strain -kinetic energies, the modal loss factors of both subsystems are estimated. Finally, the pressure levels inside the cavity are deduced from the resolution of the SmEdA equations. To validate this process, a truck cabin has been excited mechanically on a rail of the floor and the pressure levels at different positions inside the cabin were measured for different configurations of dissipative treatment. Comparisons between SmEdA and experimental results allows us to assess the accuracy of the proposed method.

New architecture of MEMS microphone for enhanced performances

This paper describes the conception, designs consideration and fabrication process of a novel MEMS microphone. The presented microphone not only uses a new architecture, the sensitive part being beams moving within the plane of the substrate, but also uses an innovative detection means with Silicon piezo-resistive nanogauges. Modelization will consider acoustic and mechanical interactions. Besides, at MEMS scale, accurate simulation of the sensor must take into account thermal and viscous boundary layers in acoustics, and we will show that the presented sensor takes benefit from these short scale effects, which leads to achieve theoretical resolution as low as 24dB.

Spatial Patterning of the Viscoelastic Core Layer of a Hybrid Sandwich Composite Material to Trigger Its Vibro-Acoustic Performances

With the aim of decreasing CO2 emissions, car producers’ efforts are focused, among others, on reducing the weight of vehicles yet preserving the overall vibrational comfort. To do so, new lightweight materials combining high stiffness and high (passive) damping are sought. For panels essentially loaded in bending, sandwich composites made of two external metallic stiff layers (skins) and an inner polymeric (i.e. absorbing) core are broadly used. Now aiming at creating materials by design with a better control of the final performance of the part, the tuning of the local material properties is pursued. To this end, the present work focuses on controlling the spatial in-plane viscoelastic properties of the polymeric core of such sandwich structures. The spatial patterning is achieved using a recently developed UV irradiation selective technique of Room Temperature Vulcanization (RTV) silicone elastomeric membrane, in which the ultraviolet (UV) irradiation dose, curing time and temperature are the process parameters controlling the viscoelastic properties of the polymeric membrane. Finally, a protocol for the realization of architected aluminum - silicone - aluminum composite sandwich panels is proposed. The influence of UV irradiation selective technique is demonstrated by Dynamic Mechanical Analysis (DMA) measurements on the silicone core itself and by the Corrected Force Analysis Technique (CFAT) to measure the equivalent Young’s modulus and damping of the sandwich structure over a large frequency band. As a first demonstration application, sandwich beams with different core patterns (homogeneous and heterogeneous) are designed and tested. Furthermore, the analytical formalism developed by Guyader et al. is used to model the vibro-acoustic performances of the homogenous sandwich beams and fair model-experiments comparisons are obtained. The spatial patterning of the polymer layer is found to successfully affect the local properties of the composite heterogeneous beam as evidenced by the CFAT method. Finally, this work permits the enunciation of guidelines for designing complex architectured systems with further control of the vibro-acoustics performances.

Vibro-Acoustic Modeling of a Trimmed Truck Cabin in Low Frequency Range to Tackle the Challenge of Weight Reduction

In the challenge of reducing the weight of the vehicle structures, a particular focus has to be done on the interior noise. Indeed, the weight reduction of the structure often implies an increase of the noise in the cabin. nTo maintain a constant acoustic performance, acoustic packages often have to be added, the challenge being that the weight of the acoustic materials added remains lower than the weight saved in the structure. nIn today’s engineering world, numerical simulation is the primary tool to assess the vibro-acoustic behavior of the vehicle during the design phase. To tackle the challenge of weight reduction, it is necessary to simulate accurately the vibro-acoustic response of the structure including the acoustic treatments. nThis paper presents the validation of a simulation method for the vibro-acoustic response of a truck cabin, taking into account the effect of acoustic treatments, in the frequency range [0-200 Hz]. nThe method combined a modal scheme for the structure and the cavity with a physical scheme for the acoustic treatment (porous materials). nThe model consists in a truck cabin with its cavity and five acoustic treatments (three floormats, the headliner and the rear trim panel). A measurement campaign is performed to get reference NTFs, VTFs and local inertances. The model without any treatments is first correlated. The noise reduction given by each treatment alone as well as grouped together is simulated. The comparisons between the simulated and measured results show good agreement both in term of spectrum and amplitude. Although some discrepancies in the low frequency range remain unexplained, the method is considered as validated

Vibroacoutsic Modelling of Piano Soundboards through Analytical Approaches in Frequency and Time Domains

The vibratory behavior and radiation of complex structures are a real challenge for many industrial domains. The increasing requirements of users and manufacturers justify the interest of the scientific community about this subject, particularly about ribbed structures. Initially, the design of such a structure is led by structural reasons and offers in the same time the possibility to reduce the weight and to reinforce the conception. Thus, they are common in many industrial domains, but also building and crafting sector. Among them, mention automotive, shipbuilding and aerospace industries or musical instruments too (see Fig. 8.1).