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In this work, the sound transmission loss (STL) of a simply supported doubly curved shallow aluminum shell covered by two layers of piezoelectric material, PZT-5H is presented. The study takes into account the presence of uncertain ambient temperature which is shown to significantly affect piezoelectric control of sound transmission. To derive the equations of motion, the assumed mode method combined with the first-order shear deformation theory and Hamilton's principles are employed. The modeling process incorporates the ambient temperature and thoroughly investigates its effects on STL, vibrational displacement, and piezoelectric voltage in terms of thermal strain, piezoelectric constants, and the pyroelectric coefficient uncertainties. Results show that uncertainty in environmental temperature significantly affects STL uncertainty up to 10% and vibrational displacement of the shell to the 15 times of its lowest value. The piezoelectric voltage also fluctuates with the variation in the temperature in a maximum range of 0.12–5.2 Volt. Further, the piezoelectric sensing voltage which accounts for the piezoelectric sensor thickness is observed to be highly sensitive to the temperature uncertainty with a maximum range of 0.65–7.6 Volt, causing depolarization and hysteresis nonlinearity. Thus, environmental temperature variation is considered as one of the main uncertain aspects for robust sound transmission controller. The proposed study provides an insightful investigation for robust piezoelectric control of STL in the presence of thermal uncertainty. [ABSTRACT FROM AUTHOR]

We describe the design and implementation of a control system for testing the performance of single particle tracking (SPT) microscopes with the method of synthetic motion. SPT has become a common and powerful tool in the study of biomolecular transport in cellular biology, providing the ability to track individual biological macromolecules in their native environment. Existing methods for testing SPT techniques rely on physical simulations and there is a clear need for experimental-based schemes for both comparing different approaches and for characterizing the accuracy and precision of techniques on particular experimental setups. Synthetic motion, that is, using an actuator such as a nanopositioning stage to drive a particle along a known ground-truth trajectory, is a means for achieving these ends. However, the resolution, accuracy, and flexibility of this method is limited by the actuator static and dynamic characteristics. In this work, we apply system identification and model inverse feedforward control to increase actuator bandwidth and address some common actuator nonlinearities, develop a set of dimensionless numbers that describe system limitations, and provide a set of guidelines for the practical use of synthetic motion in SPT. [ABSTRACT FROM AUTHOR]

This contribution focuses on force- and stress-tracking of a multi-degree of freedom system by eigenstrain actuation. The example under consideration is an axially excited piezoelectric bar which can be modeled as a lumped parameter system. The piezoelectric effect serves as actuation source and the question is answered how to prescribe the piezoelectric actuation in order to achieve a desired stress distribution, or, in the lumped case, a desired distribution of internal forces. First, the equations of motion are set up in matrix notation where the state vector contains the displacement components. After some basic manipulations, the governing equation can be written in terms of the internal force vector. Now, if one intends to have a certain desired internal force distribution, it is straightforward to find a condition for the piezoelectric control actuation. The developed theory is first verified by using a continuous piezoelectric bar, where the motion of one end is prescribed. Then the theory is experimentally verified: a lumped two-degree of freedom system is investigated and the goal is to reduce the stress or the internal force in order to avoid mechanical damage. The force-controlled configuration is exposed to a sweep-signal excitation between 1000−4900 Hz, running for 22 minutes without any signs of damage. Then the same system is excited by the same excitation but without piezoelectric control. After some seconds the test sample is visibly damaged, going along with a significant reduction of the first eigenfrequency. This gives strong evidence for the appropriateness of the proposed stress or force control methodology.

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The accurate dynamic equation of the parabolic shell with variable cross-section is developed in this paper. The geometric nonlinearity is used to amend the expression of the strain. Considering the large overall motion and solar heat flux, the flexible deformations and freedom vibrations of the parabolic shell are analyzed by the proposed method. Meanwhile, the strain rate feedback control law with piezoelectric layer is presented to improve the dynamic performance of the parabolic shell during the motion process. The experiments with parabolic shell are studied to verify the correctness of the proposed method and control strategy. It is found that the results obtained by the proposed method agree very well with the experiments. Furthermore, the numerical results show that high-frequency vibration and flexible deformation can be effectively improved by the Macro Fiber Composite (MFC). And the optimized controller gain coefficient is also discussed at the end of this paper. This paper demonstrates the importance of the piezoelectric layer for the improvement of the dynamic response of flexible parts. [ABSTRACT FROM AUTHOR]

Linear and nonlinear analyses of a piezoelectric-controlled Ziegler's column, endowed with a Van der Pol-like nonlinear damping, are carried out in the present paper. The effects of three linear and passive piezoelectric controllers on the position and on the amplitude of the limit-cycle at the Hopf bifurcation, triggered by the follower force, are investigated. The controllers, previously introduced in the literature and here referred to as Non-Singular Resonant, Singular Non-Resonant, and Tuned Piezoelectric Damper, resemble well-known devices, adopted for controlling both linear and nonlinear oscillations, namely, a large-mass Tuned Mass Damper, a singular Energy Sink, and a classical small-mass Tuned Mass Damper. Numerical simulations on a linearly and uniformly damped column, under different nonlinear damping conditions, are carried out to show the effectiveness of the controllers in reducing the amplitude of the limit-cycle and their behavior with respect to the possible occurrence of the hard loss bifurcation. [ABSTRACT FROM AUTHOR]

Linear and non-linear analyses of a piezoelectric controlled non-linear Ziegler column are carried out in this paper. The aim is to evaluate the effects of a linear piezoelectric element on the Hopf bifurcations of the non-linear mechanical system, triggered by the non-conservative follower force. To this end a linear stability analysis, showing the performances of the controller in shifting forward the critical load of the uncontrolled system, is carried out and the role of the electro-mechanical coupling parameter and of the mechanical damping is investigated. The beneficial effects of the controller on the amplitude of the limit cycle occurring in the post-critical field are also discussed. [ABSTRACT FROM AUTHOR]

The effect of the time delay between the sensor output and actuation is studied on the displacement and velocity feedback control of a cantilever beam. The system consists of a piezoelectric sensor and actuator pair bonded to an Euler-Bernoulli beam to form an actively controlled laminated structure. The effects of Kelvin-Voigt damping are also included in the problem. The piezoelectric actuators and sensors are taken as patches of partial length which leads to a differential equation formulation with discontinuities. The numerical solution is obtained by replacing the original formulation with an integral equation which is solved by expanding the state function in terms of the eigenfunctions of the freely vibrating beam. This approach leads to an infinite set of linear equations which can be solved with a high degree of accuracy by computing the characteristic equation using a small number of terms. Numerical results are given to analyze the control effectiveness in terms of changes in the natural frequencies for various gains, damping coefficients and time delays. [ABSTRACT FROM AUTHOR]

Abstract: The Euler–Bernoulli model of transverse vibrations of a cantilever beam is extended to include viscous and Kelvin–Voigt (strain rate) damping to study active vibration control under damping. The controls are of feedback type with displacement and velocity feedback controls provided by full length or patch piezoelectric actuators and sensors bonded to the top and the bottom of the beam. The resulting partial differential equation which contains discontinuities in a differential equation setting due to patch actuators is solved by formulating the problem in an integral equation setting which eliminates the singularities. The solution is reduced to the solution of a linear system of equations by using an orthonormal set of the eigenfunctions of the freely vibrating beam which provide an accurate approximation to the controlled vibration case. Control effectiveness is investigated in terms of changes in the damped natural frequencies for different gains, damping coefficients, and patch locations. The effect of the displacement and velocity feedback controls and problem parameters on the real and complex parts of the fundamental, second and third order frequencies is discussed with a view towards establishing the damped and oscillatory behaviour of the piezo controlled beams. [Copyright &y& Elsevier]

In this paper, we consider a vibrating system with piezoelectric patches whose minimum vibration frequency is to be maximized subject to some constraint on the patch geometry. A numerical scheme is constructed based on the integral equation approach for the computation of the corresponding eigenvalue problem and the boundary parametrization optimization technique. Various numerical results are provided for the case of a Plexiglas plate with PVDF sensor and actuator patches. [ABSTRACT FROM AUTHOR]

A camless engine proof-of-concept prototype was completed on the basis of the use of piezoelectric control of a hydraulic actuator. This novel approach was taken in an attempt to enhance earlier solenoid-based camless engine prototypes, several of which are reviewed as an introduction to camless engine technology. Following a historical review, an overview of the piezoelectrically-controlled camless engine actuator is discussed. The prototype system is capable of displacing an engine valve up to 12.4 mm, and valve actuation frequencies of up to 500 Hz have been obtained. The proof of concept can be considered successful, as it demonstrates the potential of piezoelectric control of hydraulics for use as an internal combustion engine valve actuator. Furthermore, in conjunction with variable timing, the piezoelectric control based pilot allows for direct regulation of other engine valve parameters including variable lift and seating velocity. [ABSTRACT FROM AUTHOR]

An analysis of existing models for hydraulic servo valves is presented for use in simulations of a camless engine actuator. Because of the limitations of the accepted models, a new servo valve model is derived, presented and verified. The updated model allows for more complex internal geometry, including new port shapes and port lapping parameters. Comparative results are presented, outlining the significant improvement in valve lift versus time simulation of the newly derived model. The improved model results allow for better simulations and control system design for camless engine valve actuators. [ABSTRACT FROM AUTHOR]

The effect of axial force in the vibration control of beams is studied by means of an integral equation formulation, which facilitates the numerical solution of the problem of finding the eigenfrequencies and eigenfunctions of a freely vibrating beam controlled by piezo patch sensors and actuators. The basic formulation of the problem is given in terms of a differential equation which is converted to an equivalent integral equation formulation by introducing an explicit Green’s function. After approximating the kernel of the integral equation in terms of Fourier series based on the eigenfrequencies of the host structure, a method of solution is outlined which consists of expressing the integral equation as an infinite series of linear equations and using a finite of number of these equations in the numerical solution. Numerical results are obtained for different values of the gain, the axial load and for three patch sizes. The first three vibration frequencies of the controlled and uncontrolled beam are given. The tip deflections of the beam for different axial loads are also plotted to compare transient behaviour. [Copyright &y& Elsevier]

Formulation of the problem for the feedback displacement control of a vibrating laminated plate with orthotropic piezoelectric sensors and actuators is given in terms of an integral equation. The objective is to develop a formulation which facilitates the numerical solution to obtain the eigenfrequencies and eigenfunctions of the piezo-controlled plate. The control is carried out via piezoelectric sensors and actuators which are of orthorhombic crystal class mm2 with poling in the z direction. The initial formulation of the problem is given in terms of a differential equation which is the conventional formulation most often used in the literature. The conversion to an integral equation formulation is achieved by introducing an explicit Green’s function. Explicit expressions for the kernel of the integral equation are given and the method of solution using the new formulation is outlined. The solution technique involves approximating the integral equation with an infinite system of linear equations and using a finite number of these equations to obtain the numerical results. [Copyright &y& Elsevier]

A critical review of three paradoxical phenomena, occurring in the dynamic stability of finite-dimensional autonomous mechanical systems, is carried out. In particular, the well-known destabilization paradoxes of Ziegler, due to damping, and Nicolai, due to follower torque, and the less well known failure of the so-called 'principle of similarity', as a control strategy in piezo-electro-mechanical systems, are discussed. Some examples concerning the uncontrolled and controlled Ziegler column and the Nicolai beam are discussed, both in linear and nonlinear regimes. The paper aims to discuss in depth the reasons of paradoxes in the linear behavior, sometimes by looking at these problems in a new perspective with respect to the existing literature. Moreover, it represents a first attempt to investigate also the post-critical regime.