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Prof. André PREUMONT
Professor Emeritus of Mechanical Engineering and Robotics, Active Structures Laboratory, Department of Control Engineering and System Analysis, Université Libre de Bruxelles, 50 Av. F.D.Roosevelt CP165/55, B-1050 Brussels, Belgium

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Research Keywords & Expertise

0 Adaptive Optics
0 Structural Dynamics
0 Vibration Control
0 Large space structures
0 Flapping wing robots

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Adaptive Optics
Structural Dynamics
Vibration Control

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Technical note
Published: 07 March 2021 in Actuators
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This paper analyzes the lift-production system in hovering of the flapping wing robot COLIBRI of the size of a hummingbird. The paper first examines the flapping wing mechanism for which a new gear transmission is proposed to reduce the friction and facilitate the assembly. Next, a sensitivity analysis is performed on the wing size. Then, the paper discusses several options for the gearbox, various DC motors and two battery configurations (a single battery or two batteries in series) to minimize the heat generation and increase the flight time. The configuration involving two batteries has been found more effective. The flight time is predicted using Shepherd’s discharge model and it is confirmed by an experiment. The robot sustains an endurance of nearly 5 min to produce a lift force equal to the weight of the robot.

ACS Style

André Preumont; Han Wang; Shengzheng Kang; Kainan Wang; Ali Roshanbin. A Note on the Electromechanical Design of a Robotic Hummingbird. Actuators 2021, 10, 52 .

AMA Style

André Preumont, Han Wang, Shengzheng Kang, Kainan Wang, Ali Roshanbin. A Note on the Electromechanical Design of a Robotic Hummingbird. Actuators. 2021; 10 (3):52.

Chicago/Turabian Style

André Preumont; Han Wang; Shengzheng Kang; Kainan Wang; Ali Roshanbin. 2021. "A Note on the Electromechanical Design of a Robotic Hummingbird." Actuators 10, no. 3: 52.

Journal article
Published: 30 December 2020 in Actuators
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This paper discusses the design and manufacturing of a thin polymer spherical adaptive reflector of diameter D=200 mm, controlled by an array of 25 independent electrodes arranged in a keystone configuration actuating a thin film of PVDF-TrFE in d31-mode. The 5 μm layer of electrostrictive material is spray-coated. The results of the present study confirm that the active material can be modelled by a unidirectional quadratic model and that excellent properties can be achieved if the material is properly annealed. The experimental influence functions of the control electrodes are determined by a quasi-static harmonic technique; they are in good agreement with the numerical simulations and their better circular symmetry indicates a clear improvement in the manufacturing process, as compared to a previous study. The low order optical modes can be reconstructed by combining the 25 influence functions; a regularization technique is used to alleviate the ill-conditioning of the Jacobian and allow to approximate the optical modes with reasonable voltages.

ACS Style

Kainan Wang; Thomas Godfroid; Damien Robert; André Preumont. Adaptive Shell Spherical Reflector Actuated with PVDF-TrFE Thin Film Strain Actuators. Actuators 2020, 10, 7 .

AMA Style

Kainan Wang, Thomas Godfroid, Damien Robert, André Preumont. Adaptive Shell Spherical Reflector Actuated with PVDF-TrFE Thin Film Strain Actuators. Actuators. 2020; 10 (1):7.

Chicago/Turabian Style

Kainan Wang; Thomas Godfroid; Damien Robert; André Preumont. 2020. "Adaptive Shell Spherical Reflector Actuated with PVDF-TrFE Thin Film Strain Actuators." Actuators 10, no. 1: 7.

Journal article
Published: 17 July 2020 in Actuators
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This paper presents the technology to control the shape of thin polymer doubly curved shell structures with a unimorph layer of strain actuators to achieve high quality, light-weight, foldable space reflectors. The selected active material is PVDF-TrFE deposited by spin coating; it is electrostrictive, isotropic and enjoys an excellent piezoelectric coefficient d 31 ≃ 15 pC/N when properly annealed, but has a nonlinear, quadratic behavior. The strain actuation is controlled by an array of segmented electrodes. The purpose of this study is to evaluate the material properties achieved in the manufacturing process. A simple, unidirectional model of electrostrictive material is considered and the material constants (electrostrictive constant Q 33 , piezoelectric constant d 31 , spontaneous polarization P s and poling strain S P ) are estimated from various static and dynamic experiments. The final part of the paper illustrates the control authority on a small demonstrator with seven independent electrodes and compares the experimental results with numerical finite element simulations.

ACS Style

Kainan Wang; Thomas Godfroid; Damien Robert; André Preumont. Electrostrictive PVDF-TrFE Thin Film Actuators for the Control of Adaptive Thin Shell Reflectors. Actuators 2020, 9, 53 .

AMA Style

Kainan Wang, Thomas Godfroid, Damien Robert, André Preumont. Electrostrictive PVDF-TrFE Thin Film Actuators for the Control of Adaptive Thin Shell Reflectors. Actuators. 2020; 9 (3):53.

Chicago/Turabian Style

Kainan Wang; Thomas Godfroid; Damien Robert; André Preumont. 2020. "Electrostrictive PVDF-TrFE Thin Film Actuators for the Control of Adaptive Thin Shell Reflectors." Actuators 9, no. 3: 53.

Journal article
Published: 01 November 2019 in Actuators
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Piezoelectric unimorph deformable mirrors offer a cheap solution to adaptive optics, with mass production capability. However, standard solutions have significant drawbacks: (i) the static shape is sensitive to the temperature, and (ii) the low structural damping limits the control bandwidth, because of the interaction between the shape control and the vibration modes of the mirror. This paper discusses how these two problems may be alleviated by using a mirror covered with an array of actuators working in d31 mode on the back side and a ring of transducers (actuators and sensors) on the front side, outside the pupil of the mirror.

ACS Style

Kainan Wang; David Alaluf; André Preumont. Thermal Balance and Active Damping of a Piezoelectric Deformable Mirror for Adaptive Optics. Actuators 2019, 8, 75 .

AMA Style

Kainan Wang, David Alaluf, André Preumont. Thermal Balance and Active Damping of a Piezoelectric Deformable Mirror for Adaptive Optics. Actuators. 2019; 8 (4):75.

Chicago/Turabian Style

Kainan Wang; David Alaluf; André Preumont. 2019. "Thermal Balance and Active Damping of a Piezoelectric Deformable Mirror for Adaptive Optics." Actuators 8, no. 4: 75.

Journal article
Published: 01 February 2019 in Applied Optics
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This paper discusses the field stabilization control of the M5 unit under wind disturbances. The first part is a literature survey of the spectral content of the wind disturbance. Next, a simplified model of a tip/tilt mirror control system is used to analyze the conditions for control-structure interaction. The influence of the asymptotic decay rate of the wind tilt disturbance on the magnitude and spectral content of the control torques is pointed out. A full telescope model is developed to justify a decoupled tip/tilt control design and to analyze the response of the primary mirror M1 to the disturbance generated by the control torques of the M5 unit.

ACS Style

Kainan Wang; André Preumont. Field stabilization control of the European Extremely Large Telescope under wind disturbance. Applied Optics 2019, 58, 1174 -1184.

AMA Style

Kainan Wang, André Preumont. Field stabilization control of the European Extremely Large Telescope under wind disturbance. Applied Optics. 2019; 58 (4):1174-1184.

Chicago/Turabian Style

Kainan Wang; André Preumont. 2019. "Field stabilization control of the European Extremely Large Telescope under wind disturbance." Applied Optics 58, no. 4: 1174-1184.

Research article
Published: 01 January 2019 in International Journal of Advanced Robotic Systems
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This study describes the design, development, and flight tests of a novel control mechanism to generate yaw control torque of a hovering robotic hummingbird (known as Colibri). The proposed method generates yaw torque by modifying the wing kinematics while minimizing its influence on roll and pitch torques. To achieve this, two different architectures of series and parallel mechanisms are investigated; they are mathematically analyzed to investigate their behavior with respect to cross-coupling effects. The analysis is verified by measuring the control torque characteristics. The efficacy of the proposed method is also explored by flight experiments.

ACS Style

Ali Roshanbin; André Preumont. Yaw control torque generation for a hovering robotic hummingbird. International Journal of Advanced Robotic Systems 2019, 16, 1 .

AMA Style

Ali Roshanbin, André Preumont. Yaw control torque generation for a hovering robotic hummingbird. International Journal of Advanced Robotic Systems. 2019; 16 (1):1.

Chicago/Turabian Style

Ali Roshanbin; André Preumont. 2019. "Yaw control torque generation for a hovering robotic hummingbird." International Journal of Advanced Robotic Systems 16, no. 1: 1.

Journal article
Published: 07 September 2018 in Sensors
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This paper considers a Hilbert marginal spectrum-based approach to health monitoring of active suspension bridge hangers. The paper proposes to takes advantage of the presence of active cables and use them as an excitation mean of the bridge, while they are used for active damping. The Hilbert–Huang transform is used to calculate the Hilbert marginal spectrum and establish a damage index for each hanger of the suspension bridge. The paper aims to investigate the method experimentally, through a series of damage scenarios, on a laboratory suspension bridge mock-up equipped with four active cables; each active cable is made of a displacement actuator collocated with a force sensor. Different locations and levels of damage severity are implemented. For the first time, the investigation demonstrates experimentally the effectiveness of the technique, as well as its limitations, to detect and locate the damage in hangers of a suspension bridge.

ACS Style

Fanhao Meng; Bilal Mokrani; David Alaluf; Jingjun Yu; André Preumont. Damage Detection in Active Suspension Bridges: An Experimental Investigation. Sensors 2018, 18, 3002 .

AMA Style

Fanhao Meng, Bilal Mokrani, David Alaluf, Jingjun Yu, André Preumont. Damage Detection in Active Suspension Bridges: An Experimental Investigation. Sensors. 2018; 18 (9):3002.

Chicago/Turabian Style

Fanhao Meng; Bilal Mokrani; David Alaluf; Jingjun Yu; André Preumont. 2018. "Damage Detection in Active Suspension Bridges: An Experimental Investigation." Sensors 18, no. 9: 3002.

Journal article
Published: 19 July 2018 in Actuators
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This paper considers the piezoelectric resistive and inductive RL shunt damping applied to rotationally periodic structures equipped with an array of regularly spaced piezoelectric patches. A method for simplifying the hardware, by reducing the size of the inductors and eliminating the use of synthetic inductors, is described. The paper compares two different ways of using the piezoelectric array: independent loops and parallel loops. It shows that, if a specific mode with n nodal diameters is targeted, mounting 4n piezoelectric patches in two parallel loops is as efficient as mounting them in 4n independent loops, while considerably reducing the demand on the inductors, L, (by 4n2). The method takes advantage of the mode shapes of rotationally periodic structures. The proposed method is validated numerically and experimentally on a rotationally periodic circular plate (nearly axisymmetric). The proposed technique is aimed at turbomachinery applications.

ACS Style

Bilal Mokrani; Renaud Bastaits; Iulian Romanescu; Mihaita Horodinca; Ioan Burda; André Preumont. Passive Damping of Rotationally Periodic Structures with Tuned Piezoelectric Inductive Shunt. Actuators 2018, 7, 41 .

AMA Style

Bilal Mokrani, Renaud Bastaits, Iulian Romanescu, Mihaita Horodinca, Ioan Burda, André Preumont. Passive Damping of Rotationally Periodic Structures with Tuned Piezoelectric Inductive Shunt. Actuators. 2018; 7 (3):41.

Chicago/Turabian Style

Bilal Mokrani; Renaud Bastaits; Iulian Romanescu; Mihaita Horodinca; Ioan Burda; André Preumont. 2018. "Passive Damping of Rotationally Periodic Structures with Tuned Piezoelectric Inductive Shunt." Actuators 7, no. 3: 41.

Chapter
Published: 11 February 2018 in Internal Variables in Thermoelasticity
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This chapter addresses the problem of vibration isolation; the excitation may be harmonic or wide band. The chapter begins with the single-axis passive isolation: linear viscous isolator and relaxation isolator; an electromagnetic realization of the relaxation isolator is discussed. Next, the active isolation is considered: the celebrated single-axis sky-hook damper and its Integral Force Feedback (IFF) implementation. The difference between the two implementations when applied to flexible structures is highlighted, and the superiority (due to built-in stability properties) of the IFF is pointed out. Next, after a brief discussion of the payload isolation in spacecraft, the six-axis isolation is considered with a Gough–Stewart platform; the passive isolation when the legs consist of relaxation isolators and the active isolation when the legs are controlled according to the IFF are discussed and compared. The influence of the modal spread on performance is analyzed, as well as the parasitic stiffness of the spherical joints of the Stewart platform. Finally, a quarter-car model of a vehicle suspension is briefly analyzed. The chapter concludes with a short list of references and a set of problems.

ACS Style

André Preumont. Vibration Isolation. Internal Variables in Thermoelasticity 2018, 165 -197.

AMA Style

André Preumont. Vibration Isolation. Internal Variables in Thermoelasticity. 2018; ():165-197.

Chicago/Turabian Style

André Preumont. 2018. "Vibration Isolation." Internal Variables in Thermoelasticity , no. : 165-197.

Chapter
Published: 11 February 2018 in Solid Mechanics
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This chapter generalizes the concepts introduced in Chap. 9 to multi-input multi-output systems. It begins with the Linear Quadratic Regulator (LQR), deterministic and stochastic. A procedure is described which allows to prescribe a minimum degree of stability (alpha-shift). Next, the state reconstruction is discussed through the full state observer and the Kalman Filter, leading to the Linear Quadratic Gaussian (LQG). The duality between the LQR and the Kalman Filter is stressed. A discussion of the spillover follows; this phenomenon is typical of large lightly damped systems: the modes which are not included in the controller (residual modes) and which have a small stability margin (due to natural damping) tend to be destabilized by the state feedback controller. Finally, the integral control and more generally the frequency shaping of the LQG is discussed. The chapter concludes with a short list of references and a set of problems.

ACS Style

André Preumont. Optimal Control. Solid Mechanics 2018, 259 -287.

AMA Style

André Preumont. Optimal Control. Solid Mechanics. 2018; ():259-287.

Chicago/Turabian Style

André Preumont. 2018. "Optimal Control." Solid Mechanics , no. : 259-287.

Chapter
Published: 11 February 2018 in Internal Variables in Thermoelasticity
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This chapter begins with a brief discussion of the Nyquist stability criterion and recalling the important concepts of gain and phase margins. Next, the feedback specification for single-input single-output system is discussed, together with various representations of the unstructured uncertainty, robust performance, and robust stability. It is followed by a discussion of Bode’s gain–phase relationships (Bode integrals) and how they can be used in design (Bode Ideal Cutoff). Next, the penalty associated with a non-minimum phase system is examined, followed by a brief discussion of usual compensators (Lead, PI, PID). Finally, the discussion is extended to multi-input multi-output system; the small gain theorem allows to derive sufficient conditions for stability. These robustness tests are useful to evaluate a lower bound to the stability margin with respect to spillover (when the high order dynamics is neglected). The chapter concludes with a short list of references and a set of problems.

ACS Style

André Preumont. Analysis and Synthesis in the Frequency Domain. Internal Variables in Thermoelasticity 2018, 227 -257.

AMA Style

André Preumont. Analysis and Synthesis in the Frequency Domain. Internal Variables in Thermoelasticity. 2018; ():227-257.

Chicago/Turabian Style

André Preumont. 2018. "Analysis and Synthesis in the Frequency Domain." Internal Variables in Thermoelasticity , no. : 227-257.

Chapter
Published: 11 February 2018 in Solid Mechanics
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This chapter focuses on collocated systems. The property of alternating poles and zeros is used to develop single-input single-output active damping schemes with guaranteed stability for various actuator and sensor types. The following controller are examined: Lead controller, Direct Velocity Feedback (DVF), Positive Position Feedback (PPF), Integral Force Feedback (IFF). The duality between the Lead and the IFF controller is discussed and the formula for the maximum achievable damping is demonstrated. The results are later generalized to the decentralized control of multi-input multi-output structures with collocated pairs. The chapter concludes with a short list of references and a set of problems.

ACS Style

André Preumont. Active Damping with Collocated System. Solid Mechanics 2018, 139 -163.

AMA Style

André Preumont. Active Damping with Collocated System. Solid Mechanics. 2018; ():139-163.

Chicago/Turabian Style

André Preumont. 2018. "Active Damping with Collocated System." Solid Mechanics , no. : 139-163.

Chapter
Published: 11 February 2018 in Solid Mechanics
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This chapter analyzes the constitutive equations of discrete electromechanical transducers. It begins with the voice coil transducer which can be used as sensor as well as actuator; it is followed by applications to modelling of the proof-mass actuator and the geophone sensor. The single axis gyrostabilizer is briefly discussed next. The second part of the chapter is devoted to the constitutive equations and the modelling of a discrete, single axis piezoelectric transducer. The physical meaning of the electromechanical coupling factor is discussed as well as its measurement. The chapter concludes with a short list of references and a set of problems.

ACS Style

André Preumont. Electromagnetic and Piezoelectric Transducers. Solid Mechanics 2018, 47 -66.

AMA Style

André Preumont. Electromagnetic and Piezoelectric Transducers. Solid Mechanics. 2018; ():47-66.

Chicago/Turabian Style

André Preumont. 2018. "Electromagnetic and Piezoelectric Transducers." Solid Mechanics , no. : 47-66.

Chapter
Published: 11 February 2018 in Internal Variables in Thermoelasticity
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This chapter summarizes a few projects which have been conducted in the early days of the Active Structures Laboratory of ULB (mostly before 2002) in various fields including active damping, precision positioning, and vibroacoustics; all of them include numerical and experimental results. After a few words about digital control, the chapter begins with the active damping of a truss structure, followed by a six-axis piezoelectric Stewart platform that is proposed as generic damping interface (it can also be used for precision positioning). Next, the active damping of a piezoelectric plate is considered, with an experiment flown in 1995. It is followed by the active damping of a stiff beam using acceleration feedback and a proof-mass actuator. The next section, on HAC/LAC control, shows how embedding a collocated active damping loop in a non-collocated precision control may be effective in increasing the control bandwidth. The next section is devoted to the development of a sound radiation sensor for active structural acoustic control; the starting point is a discrete array of piezoelectric sensors; finally, a distributed sensor forming a porous electrode is developed successfully, all computations being confirmed by experiments. The chapter concludes with a short list of references and a set of problems.

ACS Style

André Preumont. Applications. Internal Variables in Thermoelasticity 2018, 333 -375.

AMA Style

André Preumont. Applications. Internal Variables in Thermoelasticity. 2018; ():333-375.

Chicago/Turabian Style

André Preumont. 2018. "Applications." Internal Variables in Thermoelasticity , no. : 333-375.

Chapter
Published: 11 February 2018 in Internal Variables in Thermoelasticity
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This chapter begins with a brief description of the requirements for image quality, the measurement of the wavefront aberration with a Shack–Hartmann (SH) sensor and its decomposition in a set of orthogonal functions named the Zernike modes. Next, the Kolmogorov turbulence model is used, together with the assumption of frozen turbulence shape transported by the wind to evaluate the RMS value of the phase error, the image quality, and the power spectral density of the various Zernike modes. The next section discusses the main features of deformable mirrors for adaptive optics, with a special attention to the bimorph piezoelectric mirrors in various actuator configurations (keystone and honeycomb). The following section is devoted to the feedback control using a frequency-shaped singular value decomposition (SVD) controller and assuming a quasi-static response of the deformable mirror; the closed-loop response of the various Zernike modes and the RMS phase error is evaluated as a function of the control bandwidth. Next, a dynamical model of the mirror is used and the control-structure interaction is analyzed, leading to spillover; the importance of the structural damping of the vibration modes is pointed out. The damping augmentation via passive piezo shunt and active damping using modal filtering is then analyzed. The chapter concludes with some remarks on manufacturing and a list of references.

ACS Style

André Preumont. Active Control of Large Telescopes: Adaptive Optics. Internal Variables in Thermoelasticity 2018, 417 -448.

AMA Style

André Preumont. Active Control of Large Telescopes: Adaptive Optics. Internal Variables in Thermoelasticity. 2018; ():417-448.

Chicago/Turabian Style

André Preumont. 2018. "Active Control of Large Telescopes: Adaptive Optics." Internal Variables in Thermoelasticity , no. : 417-448.

Chapter
Published: 11 February 2018 in Internal Variables in Thermoelasticity
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This chapter begins with a general discussion of the future needs for large space reflectors (lighter, larger, foldable), leading to the concept of adaptive thin polymer shell reflector. Next, a comparison between an adaptive plate covered with a layer of piezoelectric material and a similar spherical shell is conducted to point out the fundamental difference of behavior of a shell with double curvature (because of the large hoop stiffness). A multi-electrode spherical shell is considered, and the relationship between the surface figure error and the electrode size, the shell curvature and thickness is derived (for various Zernike modes). Then, the control of adaptive shell involving a very large number (thousands) of independent electrodes is examined and, based on Saint-Venant’s principle, a hierarchical control approach is derived to solve the ill-conditioning of the Jacobian. Finally, petal configurations are considered as a way to increase the controllability and improve the folding capability. The chapter concludes with a reference list.

ACS Style

André Preumont. Adaptive Thin Shell Space Reflectors. Internal Variables in Thermoelasticity 2018, 469 -485.

AMA Style

André Preumont. Adaptive Thin Shell Space Reflectors. Internal Variables in Thermoelasticity. 2018; ():469-485.

Chicago/Turabian Style

André Preumont. 2018. "Adaptive Thin Shell Space Reflectors." Internal Variables in Thermoelasticity , no. : 469-485.

Chapter
Published: 11 February 2018 in Internal Variables in Thermoelasticity
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This chapter deals with the control of the primary mirror of large telescopes in order to compensate the deformation due to manufacturing errors, the thermal gradients, and the changing gravity loads. The case of a monolithic mirror is considered first, followed by that of segmented mirrors (all telescopes with a primary mirror larger than 8 m will be segmented). The control strategy is based on a quasi-static model between the actuator inputs and the sensor outputs (Jacobian); the feedback loop uses a singular value decomposition (SVD) controller shaped in the frequency domain. Next, the dynamic response of the telescope is considered and its possible interaction with the SVD controller is analyzed. A stability robustness test is used to evaluate the stability margin and derive guidelines on the control bandwidth, natural frequency, and structural damping of the telescope structure to avoid spillover instability. The final section discusses some important scaling rules for telescopes of increasing size. The chapter concludes with a reference list.

ACS Style

André Preumont. Active Control of Large Telescopes: Active Optics. Internal Variables in Thermoelasticity 2018, 449 -468.

AMA Style

André Preumont. Active Control of Large Telescopes: Active Optics. Internal Variables in Thermoelasticity. 2018; ():449-468.

Chicago/Turabian Style

André Preumont. 2018. "Active Control of Large Telescopes: Active Optics." Internal Variables in Thermoelasticity , no. : 449-468.

Chapter
Published: 11 February 2018 in Solid Mechanics
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This chapter begins with a discussion of the constitutive equations of a general piezoelectric material and of the various actuation and sensing modes. Next, Hamilton’s principle is applied to the piezoelectric Euler–Bernoulli beam, leading to the definition of the piezoelectric loads associated with the various electrode shapes when used as actuator (voltage driven) and a discussion of the laminar sensors (when associated with a charge amplifier); the duality is highlighted, and various modal filters are discussed. The model is applied to a collocated piezoelectric beam, leading to alternating poles and zeros, and a special attention is drawn on the influence of modal truncation on the location of the zeros. Next, the attention is given to the two-dimensional constitutive equations of a piezoelectric laminate and the Kirchhoff plate theory (this work is implemented in a finite element code SAMCEF); the equivalent piezoelectric loads and sensor output are defined, and the duality is pointed out. The beam theory and the plate theory are compared, and the limitations of the beam model for a collocated structure are explained. The chapter ends with the modelling of a piezoelectric truss where one or several bars have been replaced by active struts consisting of a collocated linear piezoelectric actuator and a force sensor. The chapter concludes with a short list of references and a set of problems, including Rosen’s piezoelectric transformer.

ACS Style

André Preumont. Piezoelectric Beam, Plate and Truss. Solid Mechanics 2018, 67 -106.

AMA Style

André Preumont. Piezoelectric Beam, Plate and Truss. Solid Mechanics. 2018; ():67-106.

Chicago/Turabian Style

André Preumont. 2018. "Piezoelectric Beam, Plate and Truss." Solid Mechanics , no. : 67-106.

Chapter
Published: 11 February 2018 in Internal Variables in Thermoelasticity
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This chapter analyzes the basic principle of passive damping with shunted piezoelectric transducers. Resistive shunting and inductive shunting are examined successively. The various ways of tuning the inductor (maximum stability and equal peak design) are carefully reviewed, and the robustness with respect to the shunt parameters is discussed. Next, the switch shunt is analyzed, leading to the technique known as synchronized switch damping on inductor (SSDI); the performances of the various shunting modes are compared. The chapter concludes with a short list of references and a set of problems.

ACS Style

André Preumont. Passive Damping with Piezoelectric Transducers. Internal Variables in Thermoelasticity 2018, 107 -123.

AMA Style

André Preumont. Passive Damping with Piezoelectric Transducers. Internal Variables in Thermoelasticity. 2018; ():107-123.

Chicago/Turabian Style

André Preumont. 2018. "Passive Damping with Piezoelectric Transducers." Internal Variables in Thermoelasticity , no. : 107-123.

Chapter
Published: 11 February 2018 in Solid Mechanics
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This chapter is devoted to the analysis of the controllability and the observability. The goal pursued is to derive quantitative rather than qualitative measures which can be used in actuator and sensor placement. The chapter reviews some concepts which have been proposed to this end. The controllability and observability Gramians are introduced and a coordinate transformation is performed to define a set of internally balanced coordinates that can be used in model reduction. For the particular case of lightly damped flexible structures considered here, if modal coordinates are used, it turns out that the static gains of the various modes constitute a valuable aggregate information regarding the contribution of a mode to the input–output relationship, and can therefore be used in model reduction. The chapter concludes with a short list of references and a set of problems.

ACS Style

André Preumont. Controllability and Observability. Solid Mechanics 2018, 289 -312.

AMA Style

André Preumont. Controllability and Observability. Solid Mechanics. 2018; ():289-312.

Chicago/Turabian Style

André Preumont. 2018. "Controllability and Observability." Solid Mechanics , no. : 289-312.