G. Tondreau - Academia.edu (original) (raw)

Papers by G. Tondreau

Smart Materials and Structures, 2014

The objective of this paper is to propose an exact closed-form solution to the ∞ H optimization o... more The objective of this paper is to propose an exact closed-form solution to the ∞ H optimization of piezoelectric materials shunted with inductive-resistive passive electrical circuits. Realizing that Den Hartogʼs method which imposes fixed points of equal height in the receptance transfer function is approximate, the parameters of the piezoelectric tuned vibration absorber are calculated through the direct minimization of the maxima of the receptance. The method is applied to a one-degree-of-freedom primary oscillator considering various values of the electromechanical coupling coefficients.

Conference Proceedings of the Society for Experimental Mechanics Series, 2013

MATEC Web of Conferences, 2014

This paper studies linear and nonlinear piezoelectric vibration absorbers that are designed based... more This paper studies linear and nonlinear piezoelectric vibration absorbers that are designed based on the equal-peak method. A comparison between the performance of linear mechanical and electrical tuned vibration absorbers coupled to a linear oscillator is first performed. Nonlinearity is then introduced in the primary oscillator to which a new nonlinear electrical tuned vibration absorber is attached. Despite the frequency-energy dependence of nonlinear oscillations, we show that the nonlinear absorber is capable of effectively mitigating the vibrations of the nonlinear primary system in a large range of forcing amplitudes.

Encyclopedia of Earthquake Engineering, 2014

ABSTRACT This paper investigates the design of a perfect point load actuator based on flat triang... more ABSTRACT This paper investigates the design of a perfect point load actuator based on flat triangular piezoelectric patches. Applying a difference of electric potential between the electrodes of a triangular patch leads to point loads at the tips and distributed moments along the edges of the electrodes. The previously derived analytical expressions of these forces show that they depend on two factors: the width over height (b/l) ratio of the triangle, and the ratio of the in-plane piezoelectric properties () of the active layer of the piezoelectric patch. In this paper, it is shown that by a proper choice of b/l and of the piezoelectric properties, the moments can be cancelled, so that if one side of the triangle is clamped, a perfect point load actuation can be achieved. This requires to be negative, which imposes the use of interdigitated electrodes instead of continuous ones. The design of two transducers with interdigitated electrodes for perfect point load actuation on a clamped plate is verified with finite element calculations. The first design is based on a full piezoelectric ceramic patch and shows superior actuation performance than the second design based on a piezocomposite patch with a volume fraction of fibres of 86%. The results show that both designs lead to perfect point load actuation while the use of an isotropic PZT patch with continuous electrodes gives significantly different results.

The possibility to deduce dynamic strains from acceleration measurements is investigated in this ... more The possibility to deduce dynamic strains from acceleration measurements is investigated in this paper. The classic technique applied on beam-like structures which consists in using vertical accelerations to estimate longitudinal strains with a second order central finite difference is compared with two methods based on horizontal accelerations. Time domain responses of accelerometers and strain sensors installed on a simply supported beam are simulated, and the strains deduced from accelerations are compared with the real strains. The possibility of locating damage with the mode shape obtained with estimated strains is also addressed.

ABSTRACT This work investigates the experimental application of a damage localization technique b... more ABSTRACT This work investigates the experimental application of a damage localization technique based on local modal filters on a 3.78 meters long steel I-beam equipped with 20 piezoelectric (PVDF) sensors, and excited with an electro-dynamic shaker. A small damage responsible of a small shift of the eigenfrequencies (less than 2%) is introduced at different locations by fixing a stiffener. By following the guidelines established in previous numerical studies, the modal filters are applied on five local filters in order to locate damage, and a new feature extraction procedure is proposed. Hotelling T 2 control charts are used to locate automatically all the damage positions correctly. The results obtained with this experimental application of modal filters based on strain measurements confirm the first experimental observations that were previously obtained on a small scale set-up, and show the real interest of this very simple method for output-only non-model based automated damage localization of real structures.

An improvement of the modal filters method is proposed to enhance small damages localization, as ... more An improvement of the modal filters method is proposed to enhance small damages localization, as well as to follow their evolution through modal filters updating. The origin of the parameters which govern the sensitivity of the filters to damages is justified by analyzing fundamental equations. The expectations are next verified by considering a FE model of a simply supported beam, where a small damage is introduced (1% of stiffness decrease). Strains are inferred direclty from the nodal curvatures and the filtered frequency responses are computed with the classical FE FRFs. The results obtained confirm previous observations, and allow to suggest a set of rules to design modal filters for a better early damage localization, as well as to update them with respect to the evolution of the damage.

An output-only vibration based method for very small damage localization is proposed and applied ... more An output-only vibration based method for very small damage localization is proposed and applied on a numerical example inspired from the Boirs viaduc near Liège in Belgium. The use of local modal filtering from a network of long-gage fibre-optic strain sensors allows to locate the area where the damage is situated without the need for a numerical model of the structure. The general methodology consists in extracting features from multiple filters and to use multivariate control charts in order to detect a deviation from normal condition in one of the filters, indicating the occurrence of damage in this area. The robustness of the new method for damage localization with respect to noise on sensors and environmental changes is assessed.

Mechanical tuned vibration absorbers (MTVAs) are devices used to mitigate the vibrations of a str... more Mechanical tuned vibration absorbers (MTVAs) are devices used to mitigate the vibrations of a structure around one of its eigenfrequencies. By introducing an additional degree of freedom in the structure, MTVAs allow to split the peak of interest in the frequency response in two peaks with lower amplitudes. The design of MTVAs is usually based on the (approximate) equal-peak method proposed by Den Hartog. A closed-form exact solution was however obtained by Asami and Nishihara, for which the two peaks of the frequency response have exactly the same amplitude. Similarly to MTVAs, piezoelectric tuned vibration absorbers (PTVAs) allow to damp efficiently a specific peak of the frequency response. Although a pole placement technique can be used to design such devices, tuning rules are usually based on approximate equal-peak methods which define the optimum values of the resistor and the inductance of the shunt. Very recently, Asami and Nishihara's exact solution has been extended for the equal-peak method to PTVAs by the authors of the present paper. The first contribution of this paper is to illustrate this new optimum design of a series RL piezoelectric shunt on a realistic example. A clamped-free steel plate excited with two piezoelectric actuators and shunted with two piezoelectric transducers is modelled using plate elements (laminates). Non-linearity is then introduced in the host structure, and a new nonlinear PTVA for mitigating the vibrations of the non-linear host structure is proposed. The improvement of damping performances in the presence of structural non-linearties using a non-linear PTVA is illustrated. * Gilles Tondreau, gilles.tondreau@ulb.ac.be.

Journal of Sound and Vibration, 2014

ABSTRACT This paper deals with the experimental application of modal filters for automated damage... more ABSTRACT This paper deals with the experimental application of modal filters for automated damage localization using dynamic strain measurements. Previously developed for damage detection, the extension of modal filtering to damage localization consists in splitting a very large network of dynamic strain sensors into several independent local sensor networks. An efficient signal processing coupled to control charts allows a fully automated data-based damage localization once the modal filters are initialized. The method is tested experimentally on a small clamped-free steel plate and a 3.78 m long steel I-beam, both instrumented with a network of cheap piezoelectric patches to measure the dynamic strains. A removable damage is introduced at different positions by means of a small removable damage device. For both applications, the method can successfully detect and locate all damage cases considered, showing the potentiality of the method for field applications.

This work investigates the experimental damage detection of a Piper Tomahawk aircraft wing equipp... more This work investigates the experimental damage detection of a Piper Tomahawk aircraft wing equipped with a network of 15 accelerometers, one force transducer and excited with an electro-dynamic shaker. Damage is introduced by replacing inspection panels with damaged panels (panel with a saw cut, panel with one hole, panel with two holes and no panel). We first apply a modified version of the modal filtering technique for the damage detection. Then, we make a principal component analysis on the FRFs as well as on the transmibillities for the same purpose. The damage detection is automated using the multivariate Hotelling T 2 control chart. The three approaches succeed in the damage detection but we illustrate the advantage of using the modal filtering algorithm.

Mechanical Systems and Signal Processing, 2013

The Journal of the Acoustical Society of America, 2011

When a voltage is applied across the electrodes of a flat piezoelectric transducer attached to a ... more When a voltage is applied across the electrodes of a flat piezoelectric transducer attached to a thin plate structure, the transducer acts as equivalent loads applied to the host plate structure. In this paper, analytical expressions of these equivalent loads are derived for the general case of an orthotropic piezoelectric actuator using Hamilton's principle and two different mathematical approaches leading to the same results: Green's theorem and derivation using the theory of distributions. The equivalent loads are a function of the material properties as well as the normal to the contour of the transducer. Examples of applications to simple geometric shapes (triangle, rectangle, and circle) are given.

Journal of Sound and Vibration, 2014

ABSTRACT Modal parameters of structures are often used as inputs for finite element model updatin... more ABSTRACT Modal parameters of structures are often used as inputs for finite element model updating, vibration control, structural design or structural health monitoring (SHM). In order to test the robustness of these methods, it is a common practice to introduce uncertainty on the eigenfrequencies and modal damping coefficients under the form of a Gaussian perturbation, while the uncertainty on the mode shapes is modeled in the form of independent Gaussian noise at each measured location. A more rigorous approach consists however in adding uncorrelated noise on the time domain responses at each sensor before proceeding to an operational modal analysis. In this paper, we study in detail the resulting uncertainty when modal analysis is performed using the stochastic subspace identification method. A Monte-Carlo simulation is performed on a simply supported beam, and the uncertainty on a set of 5000 modal parameters identified with the stochastic subspace identification method is discussed. Next, 4000 experimental modal identifications of a small clamped–free steel plate equipped with 8 piezoelectric patches are performed in order to confirm the conclusions drawn in the numerical case study. In particular, the results point out that the uncertainty on eigenfrequencies and modal damping coefficients may exhibit a non-normal distribution, and that there is a non-negligible spatial correlation between the uncertainty on mode shapes at sensors of different locations.

Smart Materials and Structures, 2014

The objective of this paper is to propose an exact closed-form solution to the ∞ H optimization o... more The objective of this paper is to propose an exact closed-form solution to the ∞ H optimization of piezoelectric materials shunted with inductive-resistive passive electrical circuits. Realizing that Den Hartogʼs method which imposes fixed points of equal height in the receptance transfer function is approximate, the parameters of the piezoelectric tuned vibration absorber are calculated through the direct minimization of the maxima of the receptance. The method is applied to a one-degree-of-freedom primary oscillator considering various values of the electromechanical coupling coefficients.

Conference Proceedings of the Society for Experimental Mechanics Series, 2013

MATEC Web of Conferences, 2014

This paper studies linear and nonlinear piezoelectric vibration absorbers that are designed based... more This paper studies linear and nonlinear piezoelectric vibration absorbers that are designed based on the equal-peak method. A comparison between the performance of linear mechanical and electrical tuned vibration absorbers coupled to a linear oscillator is first performed. Nonlinearity is then introduced in the primary oscillator to which a new nonlinear electrical tuned vibration absorber is attached. Despite the frequency-energy dependence of nonlinear oscillations, we show that the nonlinear absorber is capable of effectively mitigating the vibrations of the nonlinear primary system in a large range of forcing amplitudes.

Encyclopedia of Earthquake Engineering, 2014

ABSTRACT This paper investigates the design of a perfect point load actuator based on flat triang... more ABSTRACT This paper investigates the design of a perfect point load actuator based on flat triangular piezoelectric patches. Applying a difference of electric potential between the electrodes of a triangular patch leads to point loads at the tips and distributed moments along the edges of the electrodes. The previously derived analytical expressions of these forces show that they depend on two factors: the width over height (b/l) ratio of the triangle, and the ratio of the in-plane piezoelectric properties () of the active layer of the piezoelectric patch. In this paper, it is shown that by a proper choice of b/l and of the piezoelectric properties, the moments can be cancelled, so that if one side of the triangle is clamped, a perfect point load actuation can be achieved. This requires to be negative, which imposes the use of interdigitated electrodes instead of continuous ones. The design of two transducers with interdigitated electrodes for perfect point load actuation on a clamped plate is verified with finite element calculations. The first design is based on a full piezoelectric ceramic patch and shows superior actuation performance than the second design based on a piezocomposite patch with a volume fraction of fibres of 86%. The results show that both designs lead to perfect point load actuation while the use of an isotropic PZT patch with continuous electrodes gives significantly different results.

The possibility to deduce dynamic strains from acceleration measurements is investigated in this ... more The possibility to deduce dynamic strains from acceleration measurements is investigated in this paper. The classic technique applied on beam-like structures which consists in using vertical accelerations to estimate longitudinal strains with a second order central finite difference is compared with two methods based on horizontal accelerations. Time domain responses of accelerometers and strain sensors installed on a simply supported beam are simulated, and the strains deduced from accelerations are compared with the real strains. The possibility of locating damage with the mode shape obtained with estimated strains is also addressed.

ABSTRACT This work investigates the experimental application of a damage localization technique b... more ABSTRACT This work investigates the experimental application of a damage localization technique based on local modal filters on a 3.78 meters long steel I-beam equipped with 20 piezoelectric (PVDF) sensors, and excited with an electro-dynamic shaker. A small damage responsible of a small shift of the eigenfrequencies (less than 2%) is introduced at different locations by fixing a stiffener. By following the guidelines established in previous numerical studies, the modal filters are applied on five local filters in order to locate damage, and a new feature extraction procedure is proposed. Hotelling T 2 control charts are used to locate automatically all the damage positions correctly. The results obtained with this experimental application of modal filters based on strain measurements confirm the first experimental observations that were previously obtained on a small scale set-up, and show the real interest of this very simple method for output-only non-model based automated damage localization of real structures.

An improvement of the modal filters method is proposed to enhance small damages localization, as ... more An improvement of the modal filters method is proposed to enhance small damages localization, as well as to follow their evolution through modal filters updating. The origin of the parameters which govern the sensitivity of the filters to damages is justified by analyzing fundamental equations. The expectations are next verified by considering a FE model of a simply supported beam, where a small damage is introduced (1% of stiffness decrease). Strains are inferred direclty from the nodal curvatures and the filtered frequency responses are computed with the classical FE FRFs. The results obtained confirm previous observations, and allow to suggest a set of rules to design modal filters for a better early damage localization, as well as to update them with respect to the evolution of the damage.

An output-only vibration based method for very small damage localization is proposed and applied ... more An output-only vibration based method for very small damage localization is proposed and applied on a numerical example inspired from the Boirs viaduc near Liège in Belgium. The use of local modal filtering from a network of long-gage fibre-optic strain sensors allows to locate the area where the damage is situated without the need for a numerical model of the structure. The general methodology consists in extracting features from multiple filters and to use multivariate control charts in order to detect a deviation from normal condition in one of the filters, indicating the occurrence of damage in this area. The robustness of the new method for damage localization with respect to noise on sensors and environmental changes is assessed.

Mechanical tuned vibration absorbers (MTVAs) are devices used to mitigate the vibrations of a str... more Mechanical tuned vibration absorbers (MTVAs) are devices used to mitigate the vibrations of a structure around one of its eigenfrequencies. By introducing an additional degree of freedom in the structure, MTVAs allow to split the peak of interest in the frequency response in two peaks with lower amplitudes. The design of MTVAs is usually based on the (approximate) equal-peak method proposed by Den Hartog. A closed-form exact solution was however obtained by Asami and Nishihara, for which the two peaks of the frequency response have exactly the same amplitude. Similarly to MTVAs, piezoelectric tuned vibration absorbers (PTVAs) allow to damp efficiently a specific peak of the frequency response. Although a pole placement technique can be used to design such devices, tuning rules are usually based on approximate equal-peak methods which define the optimum values of the resistor and the inductance of the shunt. Very recently, Asami and Nishihara's exact solution has been extended for the equal-peak method to PTVAs by the authors of the present paper. The first contribution of this paper is to illustrate this new optimum design of a series RL piezoelectric shunt on a realistic example. A clamped-free steel plate excited with two piezoelectric actuators and shunted with two piezoelectric transducers is modelled using plate elements (laminates). Non-linearity is then introduced in the host structure, and a new nonlinear PTVA for mitigating the vibrations of the non-linear host structure is proposed. The improvement of damping performances in the presence of structural non-linearties using a non-linear PTVA is illustrated. * Gilles Tondreau, gilles.tondreau@ulb.ac.be.

Journal of Sound and Vibration, 2014

ABSTRACT This paper deals with the experimental application of modal filters for automated damage... more ABSTRACT This paper deals with the experimental application of modal filters for automated damage localization using dynamic strain measurements. Previously developed for damage detection, the extension of modal filtering to damage localization consists in splitting a very large network of dynamic strain sensors into several independent local sensor networks. An efficient signal processing coupled to control charts allows a fully automated data-based damage localization once the modal filters are initialized. The method is tested experimentally on a small clamped-free steel plate and a 3.78 m long steel I-beam, both instrumented with a network of cheap piezoelectric patches to measure the dynamic strains. A removable damage is introduced at different positions by means of a small removable damage device. For both applications, the method can successfully detect and locate all damage cases considered, showing the potentiality of the method for field applications.

This work investigates the experimental damage detection of a Piper Tomahawk aircraft wing equipp... more This work investigates the experimental damage detection of a Piper Tomahawk aircraft wing equipped with a network of 15 accelerometers, one force transducer and excited with an electro-dynamic shaker. Damage is introduced by replacing inspection panels with damaged panels (panel with a saw cut, panel with one hole, panel with two holes and no panel). We first apply a modified version of the modal filtering technique for the damage detection. Then, we make a principal component analysis on the FRFs as well as on the transmibillities for the same purpose. The damage detection is automated using the multivariate Hotelling T 2 control chart. The three approaches succeed in the damage detection but we illustrate the advantage of using the modal filtering algorithm.

Mechanical Systems and Signal Processing, 2013

The Journal of the Acoustical Society of America, 2011

When a voltage is applied across the electrodes of a flat piezoelectric transducer attached to a ... more When a voltage is applied across the electrodes of a flat piezoelectric transducer attached to a thin plate structure, the transducer acts as equivalent loads applied to the host plate structure. In this paper, analytical expressions of these equivalent loads are derived for the general case of an orthotropic piezoelectric actuator using Hamilton's principle and two different mathematical approaches leading to the same results: Green's theorem and derivation using the theory of distributions. The equivalent loads are a function of the material properties as well as the normal to the contour of the transducer. Examples of applications to simple geometric shapes (triangle, rectangle, and circle) are given.

Journal of Sound and Vibration, 2014

ABSTRACT Modal parameters of structures are often used as inputs for finite element model updatin... more ABSTRACT Modal parameters of structures are often used as inputs for finite element model updating, vibration control, structural design or structural health monitoring (SHM). In order to test the robustness of these methods, it is a common practice to introduce uncertainty on the eigenfrequencies and modal damping coefficients under the form of a Gaussian perturbation, while the uncertainty on the mode shapes is modeled in the form of independent Gaussian noise at each measured location. A more rigorous approach consists however in adding uncorrelated noise on the time domain responses at each sensor before proceeding to an operational modal analysis. In this paper, we study in detail the resulting uncertainty when modal analysis is performed using the stochastic subspace identification method. A Monte-Carlo simulation is performed on a simply supported beam, and the uncertainty on a set of 5000 modal parameters identified with the stochastic subspace identification method is discussed. Next, 4000 experimental modal identifications of a small clamped–free steel plate equipped with 8 piezoelectric patches are performed in order to confirm the conclusions drawn in the numerical case study. In particular, the results point out that the uncertainty on eigenfrequencies and modal damping coefficients may exhibit a non-normal distribution, and that there is a non-negligible spatial correlation between the uncertainty on mode shapes at sensors of different locations.