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http://hdl.handle.net/10985/8195
Vibroacoustics of the piano soundboard : (Non)linearity and modal properties in the low- and mid-frequency ranges
EGE, Kerem; BOUTILLON, Xavier; REBILLAT, Marc
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 3 kHz 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.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/81952013-01-01T00:00:00ZEGE, KeremBOUTILLON, XavierREBILLAT, MarcThe 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 3 kHz 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.Exponential sine sweeps for the autonomous estimation of nonlinearities and errors assessment by bootstrap Application to thin vibrating structures
http://hdl.handle.net/10985/10369
Exponential sine sweeps for the autonomous estimation of nonlinearities and errors assessment by bootstrap Application to thin vibrating structures
REBILLAT, Marc; EGE, Kerem; GALLO, Maxime; ANTONI, Jérôme
Vibrating structures are generally assumed to behave linearly and in a noise-free environment. This is in practice not perfectly the case. First, nonlinear phenomena such as jump phenomenon, hysteresis or internal resonance appear when the transverse vibration of a bi-dimensional structure exceeds amplitudes in the order of magnitude of its thickness. Secondly, the presence of plant noise is a natural phenomenon that is unavoidable for all experimental measurements. In order to perform reliable measurements of vibrating mechanical structures one should thus keep in mind these two issues and care about them. However, it turns out that they are actually coupled. Indeed, all the noise that is not correctly removed from the measurements could be misinterpreted as nonlinearities, thus polluting measurements. And if nonlinearities are not accurately estimated, they will end up within the noise signal and information about the structure under study will be lost. We thus try here to solve simultaneously both issues. The underlying idea consists in extracting the maximum of available linear and nonlinear deterministic information from measurements without misinterpreting noise. The aim of this talk is thus to provide a methodology that allows for the autonomous estimation of nonlinearities and errors assessment 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 errors are simultaneously assessed using repetitions of the input signal (multi exponential sine sweeps) as the input of a bootstrap procedure. Mathematical foundations and practical implementation of the method are discussed on 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 evolutions of nonlinearities and of signal to noise ratio over a wide range of frequencies and input amplitudes.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/103692015-01-01T00:00:00ZREBILLAT, MarcEGE, KeremGALLO, MaximeANTONI, JérômeVibrating structures are generally assumed to behave linearly and in a noise-free environment. This is in practice not perfectly the case. First, nonlinear phenomena such as jump phenomenon, hysteresis or internal resonance appear when the transverse vibration of a bi-dimensional structure exceeds amplitudes in the order of magnitude of its thickness. Secondly, the presence of plant noise is a natural phenomenon that is unavoidable for all experimental measurements. In order to perform reliable measurements of vibrating mechanical structures one should thus keep in mind these two issues and care about them. However, it turns out that they are actually coupled. Indeed, all the noise that is not correctly removed from the measurements could be misinterpreted as nonlinearities, thus polluting measurements. And if nonlinearities are not accurately estimated, they will end up within the noise signal and information about the structure under study will be lost. We thus try here to solve simultaneously both issues. The underlying idea consists in extracting the maximum of available linear and nonlinear deterministic information from measurements without misinterpreting noise. The aim of this talk is thus to provide a methodology that allows for the autonomous estimation of nonlinearities and errors assessment 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 errors are simultaneously assessed using repetitions of the input signal (multi exponential sine sweeps) as the input of a bootstrap procedure. Mathematical foundations and practical implementation of the method are discussed on 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 evolutions of nonlinearities and of signal to noise ratio over a wide range of frequencies and input amplitudes.Repeated exponential sine sweeps for the autonomous estimation of nonlinearities and bootstrap assessment of uncertainties
http://hdl.handle.net/10985/10522
Repeated exponential sine sweeps for the autonomous estimation of nonlinearities and bootstrap assessment of uncertainties
REBILLAT, Marc; EGE, Kerem; GALLO, Maxime; ANTONI, Jérôme
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.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/105222015-01-01T00:00:00ZREBILLAT, MarcEGE, KeremGALLO, MaximeANTONI, JérômeMeasurements 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.A multi-sine sweep method for the characterization of weak non-linearities ; plant noise and variability estimation.
http://hdl.handle.net/10985/10288
A multi-sine sweep method for the characterization of weak non-linearities ; plant noise and variability estimation.
GALLO, Maxime; EGE, Kerem; REBILLAT, Marc; ANTONI, Jérôme
Weak non-linearities in vibrating structures can be characterized by a signal-model approach based on cascade of Hammerstein models. The experiment consists in exciting a device with a sine sweep at different levels, in order to assess the evolutions of non linearities on a wide frequency range. A method developed previously, based on exponential sine sweep, is able to give an approximative identification of the Hammerstein models, but cannot make the distinction between nonlinear distortion and stationary plant noise. Therefore, this paper proposes improvements on the method that provide a more precise estimation of the Hammerstein models through the cancellation of the plant noise: it relies on the repetition of the signal on a certain amount of periods (multi-sine sweeps) and then on the consideration of the synchronous average out of the different periods from the resulting signal. Mathematical foundations and practical implementation of the method are discussed. The second main point of improvement concerning the study of the vibrating device is the use of the Bootstrap analysis. By considering some periods randomly chosen among the multisine sweep, one can study the variability of the experiments. The method becomes more robust.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/102882015-01-01T00:00:00ZGALLO, MaximeEGE, KeremREBILLAT, MarcANTONI, JérômeWeak non-linearities in vibrating structures can be characterized by a signal-model approach based on cascade of Hammerstein models. The experiment consists in exciting a device with a sine sweep at different levels, in order to assess the evolutions of non linearities on a wide frequency range. A method developed previously, based on exponential sine sweep, is able to give an approximative identification of the Hammerstein models, but cannot make the distinction between nonlinear distortion and stationary plant noise. Therefore, this paper proposes improvements on the method that provide a more precise estimation of the Hammerstein models through the cancellation of the plant noise: it relies on the repetition of the signal on a certain amount of periods (multi-sine sweeps) and then on the consideration of the synchronous average out of the different periods from the resulting signal. Mathematical foundations and practical implementation of the method are discussed. The second main point of improvement concerning the study of the vibrating device is the use of the Bootstrap analysis. By considering some periods randomly chosen among the multisine sweep, one can study the variability of the experiments. The method becomes more robust.Repeated exponential sine sweeps for the autonomous estimation of nonlinearities and bootstrap assessment of uncertainties
http://hdl.handle.net/10985/10780
Repeated exponential sine sweeps for the autonomous estimation of nonlinearities and bootstrap assessment of uncertainties
REBILLAT, Marc; EGE, Kerem; ANTONI, Jérôme; MECHBAL, Nazih
Systems and structures are generally assumed to behave linearly and in a noise-free environment. This is in practice not perfectly the case. First, nonlinear phenomena can appear and second, the presence of noise is unavoidable for all experimental measurements. Nonlinearities can be considered as a deterministic process in the sense that in the absence of noise the output signal depends only on the input signal. Noise is purely stochastic: in the absence of an input signal, the output signal is not null and cannot be predicted at any arbitrary instant. It turns out that these two issues are coupled: all the noise that is not correctly removed from the measurements could be misinterpreted as nonlinearities, and if nonlinearities are not accurately estimated, they will end up within the noise signal and information about the system under study will be lost. The underlying idea consists here in extracting the maximum of available linear and nonlinear deterministic information from measurements without misinterpreting noise.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/107802016-01-01T00:00:00ZREBILLAT, MarcEGE, KeremANTONI, JérômeMECHBAL, NazihSystems and structures are generally assumed to behave linearly and in a noise-free environment. This is in practice not perfectly the case. First, nonlinear phenomena can appear and second, the presence of noise is unavoidable for all experimental measurements. Nonlinearities can be considered as a deterministic process in the sense that in the absence of noise the output signal depends only on the input signal. Noise is purely stochastic: in the absence of an input signal, the output signal is not null and cannot be predicted at any arbitrary instant. It turns out that these two issues are coupled: all the noise that is not correctly removed from the measurements could be misinterpreted as nonlinearities, and if nonlinearities are not accurately estimated, they will end up within the noise signal and information about the system under study will be lost. The underlying idea consists here in extracting the maximum of available linear and nonlinear deterministic information from measurements without misinterpreting noise.