A fully-coupled nonlinear thermoelectromechanical model for piezolaminated smart structures

In present engineering applications piezoelectric materials gain increasing importance in the development of smart structures; e.g., for shape and vibration control problems. Such structures exhibit a three-way coupling effect between the mechanical, electrical and thermal quantities. In the majority of papers available in literature this coupling is taken into account only in the constitutive equations. It is however well known that truly coupled analysis should also be based on the interaction of the mechanical, thermal and electrostatic quantities in the field equations. Only in this way many physical effects can be taken into account; e.g., the strain rate dependant change of temperature due to mechanical loading. Furthermore most of the analyses conducted in this area are performed in the linear range of deformations assuming small strains, rotations and temperature changes. However smart technology is generally applied to thin walled structures and in many cases reported in literature the deflections are much larger than the thickness, which results into geometrically nonlinear behaviour, like e.g. the occurrence of stress stiffening which greatly affects the prediction of sensor voltage outputs. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Resonance excitation and mode selection in smart structures with piezoelectric patch actuators

A system of piezoelectric flexible patch actuators bonded to an elastic layered substrate is considered. An integral equation based model for the smart structure under consideration has been developing. The rigorous solution to the patch–substrate dynamic contact problem extends the range of the model's utility far beyond the bounds of conventional simplified models that rely on plate, beam or shell equations for the waveguide part. The developed approach provides the possibility to reveal the effects of resonance energy radiation associated with higher modes that would be inaccessible using models accounting for the fundamental modes only. Algorithms that correctly account for the mutual wave interaction among the actuators via the host medium, for selective mode excitation in a layer as well as for body waves directed to required zones in a half–space, have also been elaborated and implemented in computer code. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear transient FE analysis of piezolaminated smart structures

The presented paper focuses on the modeling and finite element simulation of thin composite structures with integrated piezoelectric layers. Geometrically nonlinear piezolaminated finite elements are based on the Reissner-Mindlin or third-order transverse shear deformation hypotheses and the assumptions of small strains but moderate rotations. The numerical results are compared to results in literature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal actuators placements for the active control of flexible structures

A scheme for the optimal spatial placement of a limited number of sensors and actuators under a minimum energy requirement for the active control of flexible structures is proposed. The method is based on the interpretation of the functional relationship (transfer matrix/conrol influence matrix) between the actuators and modes of the structural system. It is shown that, from the form of the matrix, the controllability and observability of the system with respect to differing locations of the sensors and actuators can be established. The algorithm presented circumvents prevailing problems encountered in contemporary optimal control applications. In particular, and in order to enhance the results presented in this paper, numerical simulation for a prismatic beam subjected to horizontal random wind loads and a simply supported square plate modelled as a single degree of freedom system are given to illustrate the placement strategy.     

Non-linear dynamic contact of thin-walled structures

In many areas of mechanical engineering contact problems of thin–walled structures play a crucial role. Car crash tests and incremental sheet metal forming can be named as examples. But also in civil engineering, for instance when determining the moment–rotation characteristics of a bolted beam–column joint, contact occurs. Effective simulation of these and other contact problems, especially in three–dimensional non–linear implicit structural mechanic is still a challenging task. Modelling of those problems needs a robust method, which takes the thin–walled character and dynamic effects into account. We use a segment–to–segment approach for discretization of the contact and introduce Lagrange Multipliers, which physically represent the contact pressure. The geometric impenetrability condition is formulated in a weak, integral sense. Choosing dual shape functions for the interpolation of the Lagrange Multipliers, we obtain decoupled nodal constraint conditions. Combining this with an active set strategy, an elimination of the Lagrange multipliers is easily possible, so that the size of the resulting system of equations remains constant. Discretization in time is done with the implicit Generalized-α Method and the Generalized Energy–Momentum Method. Using the “Velocity–Update” Method, the total energy is conserved for frictionless contact. Various examples show the performance of the presented strategies. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite deformations of thin shells with piezoelectric sensors and actuators

We treat coupled electromechanical problem of finite deformations of piezoelectric shells with the help of the direct approach. A shell is considered as a material surface with mechanical degrees of freedom of particles and with an additional field variable, namely electric potential on the electrodes. This results both in the nonlinear system of equations of piezoelectric shells and in the appropriate numerical scheme. Application of the direct approach is preceded with the three-dimensional asymptotic analysis of a linear electromechanical problem for a non-homogeneous piezoelectric plate, which provides the constitutive relations for the nonlinear theory. As a sample problem, we present finite element analysis of deformation and local buckling of cylindrical panel, equipped with piezoelectric sensors. The latter influence the mechanical behavior and produce signals, which can be interpreted in terms of structural entities. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hybrid optimization procedure applied to optimal location finding for piezoelectric actuators and sensors for active vibration control

This paper presents an efficient hybrid optimization approach using a new coupling technique for solving the constrained optimization problems. This methodology is based on genetic algorithm, sequential quadratic programming and particle swarm optimization combined with a projected gradient techniques in order to correct the solutions out of domain and send them to the domain’s border. The established procedures have been successfully tested with some well known mathematical and engineering optimization problems, also the obtained results are compared with the existing approaches. It is clearly demonstrated that the solutions obtained by the proposed approach are superior to those of existing best solutions reported in the literature. The main application of this procedure is the location optimization of piezoelectric sensors and actuators for active control, the vibration of plates with some piezoelectric patches is considered. Optimization criteria ensuring good observability and controllability based on some main eigenmodes and residual ones are considered. Various rectangular piezoelectric actuators and sensors are used and two optimization variables are considered for each piezoelectric device: the location of its center and shape orientation. The applicability and effectiveness of the present methodological approach are demonstrated and the location optimization of multiple sensors and actuators are successfully obtained with some main modes and residual ones. The shape orientation optimization of sensors observing various modes as well as the local optimization of multiple sensors and actuators are numerically investigated. The effect of residual modes and the spillover reduction can be easily analyzed for a large number of modes and multiple actuators and sensors.     

Finite volume analysis of adaptive beams with piezoelectric sensors and actuators

This paper presents a finite volume (FV) formulation for the free vibration analysis and active vibration control of the smart beams with piezoelectric sensors and actuators. The governing equations based on Timoshenko beam theory are discretized using the finite volume method. For the purpose of forced vibration control of beam structures, the negative velocity feedback controller is designed for the single-input, single-output system. To achieve the best effect, the piezoelectric sensors and actuators are coupled with the host structure in different positions and then the performance of the designed control system is evaluated for each position. In the test examples, first the shear locking free feature of the present formulation is demonstrated. This has been performed by doing static and natural frequency analysis of some reference models. Then, the capability of the proposed method for the prediction of uncontrolled forced vibration response and active vibration control of a beam structure is studied.     

Nonlinear analysis of elastic thin-walled shell structures

Theoretical principles, methodology and algorithms presented herein are to analyze and design the elastic thin-walled engineering structures and components, with emphasis on the important nonlinear behavior. The methodology of the consequent analysis of single-parametric nonlinear problems is applied to structural syntheses. The numerical algorithm for this analysis is based on the parameter continuation methods and the “control parameter subspace changing”. The effectiveness of the proposed approach is illustrated through several examples in thin-walled structures.     

Optimal feedback control laws using nonlinear programming

A procedure of parametrizing feedback controls when solving the optimal control problem using nonlinear programming is considered. The maximum principle is utilized to determine the forms of the parametrized feedback control. Applications are demonstrated by numerical examples.     

Distributed parameter control of nonlinear flexible structures with linear finite-dimensional controllers

In many applications, mechanically flexible structures must be actively controlled to improve their performance. These structures are distributed parameter systems but they must be controlled by on-line computers and a few control actuators and sensors. A variety of controllers based on reduced-order linearized models of the structure may be designed to satisfy a given set of performance requirements. In actual operation, any such controller operates on the total structure and not the model. This paper determines bounds on the controller interaction with the unmodeled part of the structure; such bounds can be used to guarantee the successful operation of the linearly controlled structure even in the presence of nonlinear interactions.     

Interaction of acoustic waves and piezoelectric structures

In the paper, we investigate the basic transmission problems arising in the model of fluid‐solid acoustic interaction when a piezo‐ceramic elastic body ( Ω ⁺ ) is embedded in an unbounded fluid domain ( Ω ^? ). The corresponding physical process is described by boundary‐transmission problems for second order partial differential equations. In particular, in the bounded domain Ω ⁺ , we have 4 × 4 dimensional matrix strongly elliptic second order partial differential equation, while in the unbounded complement domain Ω ^? , we have a scalar Helmholtz equation describing acoustic wave propagation. The physical kinematic and dynamic relations mathematically are described by appropriate boundary and transmission conditions. With the help of the potential method and theory of pseudodifferential equations, the uniqueness and existence theorems are proved in Sobolev–Slobodetskii spaces. Copyright © 2014 John Wiley & Sons, Ltd.     

Reliable control for nonlinear systems with stochastic actuators fault and random delays through a T-S fuzzy model approach

This paper considers the reliable control design for T-S fuzzy systems with probabilistic actuators faults and random time-varying delays. The faults of each actuator occurs randomly and its failure rates are governed by a set of unrelated random variables satisfying certain probabilistic distribution. In terms of the probabilistic failures of each actuator and time-varying random delays, new fault model is proposed. Based on the new fuzzy model, reliable controller is designed and sufficient conditions for the exponentially mean square stability (EMSS) of T-S fuzzy systems are derived by using Lyapunov functional method and linear matrix inequality (LMI) technique. It should be noted that the obtained criteria depend on not only the size of the delay, but also the probability distribution of it. Finally, a numerical example is given to show the effectiveness of the proposed method.     

Shape sensitivity analysis of thin-shell structures

This paper presents explicit formulas for shape sensitivity analysis of thin shell structures. The curvature distribution is the design to be determined. The thin-shell theory employed is the general Koiter model in the Cartesian coordinates. For the shape sensitivity formulation, both the direct differentiation method and the material derivative concept have been used. The two formulations are shown to be equivalent. A computer program based on these formulations has been developed and applied to examples. The shape sensitivity results obtained have been compared to those obtained by finite differencing.     

Stabilization of nonlinear switched systems using control Lyapunov functions

In this paper, we study the stabilization of general nonlinear switched systems by using control Lyapunov functions. The concept of control Lyapunov function for nonlinear control systems is generalized to switched control systems. The first part of our contribution provides a necessary and sufficient condition of stabilization. The main idea is to use a common control Lyapunov function; this is achieved with the converse Lyapunov theorem dedicated to switched systems. In the second part, an explicit construction of a common control Lyapunov function is addressed with respect to a finite family of switched systems. The approach uses a family of control Lyapunov functions attached to the subsystems.     

Compressive and thermal postbuckling behaviors of laminated plates with piezoelectric fiber reinforced composite actuators

This paper studied compressive postbuckling under thermal environments and thermal postbuckling due to a uniform temperature rise for a shear deformable laminated plate with piezoelectric fiber reinforced composite (PFRC) actuators based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. The material properties are assumed to be temperature-dependent and the initial geometric imperfection of the plate is considered. The compressive and thermal postbuckling behaviors of perfect, imperfect, symmetric cross-ply and antisymmetric angle-ply laminated plates with fully covered or embedded PFRC actuators are conducted under different sets of thermal and electric loading conditions. The results reveal that, the applied voltage usually has a small effect on the postbuckling load–deflection relationship of the plate with PFRC actuators in the compressive buckling case, whereas the effect of applied voltage is more pronounced for the plate with PFRC actuators, compared to the results of the same plate with monolithic piezoelectric actuators.     

Genetic algorithm based wireless vibration control of multiple modal for a beam by using photostrictive actuators

The lanthanum-modified lead zirconate titanate (PLZT) actuator, which are capable of converting photonic energy to mechanical motion, have great potential in applications of remote structural vibration control of smart structures and machines. In this paper, a novel genetic algorithm based controlling algorithm for multi-modal vibration control of beam structures via photostrictive actuators is proposed. Two pairs of photostrictive actuators are laminated with the beams and the alternation of light irradiation is in accordance with the changing of the corresponding modal velocity direction. The modal force indexes for beams with different boundary conditions are derived and a binary-coded GA is used to optimize the locations and sizes of photostrictive actuators to maximize the modal force index and guarantee the overall modal force index induced by two pairs of photostrictive actuators is positive. The control effect of multiple vibration modes of beams under irradiation of set/variable light intensity is analyzed. Numerical results demonstrate that the method is robust and efficient, and the use of strategically positioned actuator patches can effectively control the first two bending modes that dominate the structural vibration.