• Smart Structures and Systems
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• v.5 no.3
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• pp.241-260
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• 2009

Shape control of flexible structures using piezoelectric materials has attracted much attention due to its wide applications in controllable systems such as space and aeronautical engineering. The major work in the field is to find a best control voltage or an optimal placement of the piezoelectric actuators in order to actuate the structure shape as close as possible to the desired one. The current research focus on the investigation of static shape control of intelligent shells using spatially distributed piezoelectric curve beam actuators. The finite element formulation of the piezoelectric model is briefly described. The piezoelectric curve beam element is then integrated into a collocated host shell element by using nodal displacement constraint equations. The linear least square method (LLSM) is employed to get the optimum voltage distributions in the control system so that the desired structure shape can be well matched. Furthermore, to find the optimal placement of the piezoelectric curve beam actuators, a genetic algorithm (GA) is introduced in the computation model as well as the consideration of the different objective functions. Numerical results are given to demonstrate the validity of the theoretical model and numerical algorithm developed.

• Smart Structures and Systems
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• v.11 no.2
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• pp.217-240
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• 2013

In this paper, practical methods to utilize PZT's dual piezoelectric effects (i.e., dynamic strain and electro-mechanical (E/M) impedance responses) for damage detection in beam-type structures are presented. In order to achieve the objective, the following approaches are implemented. Firstly, PZT material's dual piezoelectric characteristics on dynamic strain and E/M impedance are investigated. Secondly, global vibration-based and local impedance-based methods to detect the occurrence and the location of damage are presented. Finally, the vibration-based and impedance-based damage detection methods using the dual piezoelectric responses are evaluated from experiments on a lab-scaled beam for several damage scenarios. Damage detection results from using PZT sensor are compared with those obtained from using accelerometer and electric strain gauge.

• Smart Structures and Systems
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• v.1 no.3
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• pp.283-308
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• 2005

This paper features about the modeling and design of a fast output sampling feedback controller for a smart Timoshenko beam system for a SISO case by considering the first 3 vibratory modes. The beam structure is modeled in state space form using FEM technique and the Timoshenko beam theory by dividing the beam into 4 finite elements and placing the piezoelectric sensor/actuator at one location as a collocated pair, i.e., as surface mounted sensor/actuator, say, at FE position 2. State space models are developed for various aspect ratios by considering the shear effects and the axial displacements. The effects of changing the aspect ratio on the master structure is observed and the performance of the designed FOS controller on the beam system is evaluated for vibration control.

• Structural Engineering and Mechanics
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• v.67 no.2
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• pp.175-183
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• 2018

This research deals with the wave dispersion analysis of functionally graded double-layered nanobeam systems (FG-DNBSs) considering the piezoelectric effect based on nonlocal strain gradient theory. The nanobeam is modeled via Euler-Bernoulli beam theory. Material properties are considered to change gradually along the nanobeams' thickness on the basis of the rule of mixture. By implementing a Hamiltonian approach, the Euler-Lagrange equations of piezoelectric FG-DNBSs are obtained. Furthermore, applying an analytical solution, the dispersion relations of smart FG-DNBSs are derived by solving an eigenvalue problem. The effects of various parameters such as nonlocality, length scale parameter, interlayer stiffness, applied electric voltage, relative motions and gradient index on the wave dispersion characteristics of nanoscale beam have been investigated. Also, validity of reported results is proven in the framework of a diagram showing the convergence of this model's curve with that of a previous published attempt.

• Smart Structures and Systems
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• v.1 no.3
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• pp.309-324
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• 2005

This paper presents an efficient and accurate coupled beam model for piezoelectric bimorphs based on improved first-order shear deformation theory (FSDT). The model combines the equivalent single layer approach for the mechanical displacements and a layerwise modeling for the electric potential. General electric field function is proposed to reasonably approximate the through-the-thickness distribution of the applied and induced electric potentials. Layerwise defined shear correction factor (k) accounting for nonlinear shear strain distribution is introduced into both the shear stress resultant and the electric displacement integration. Analytical solutions for free vibrations and forced response under electromechanical loads are obtained for the simply supported piezoelectric bimorphs with series or parallel arrangement, and the numerical results for various length-to-thickness ratios are compared with the exact two-dimensional piezoelasticity solution. Excellent predictions with low error estimates of local and global responses as well as the modal frequencies are observed.

• Journal of KSNVE
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• v.9 no.1
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• pp.70-76
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• 1999

This paper presents a pseudo-sensor-output-feedback(PSOF) method for the vibration suppression of the flexible piezoelectric smart structures. This method reduces the modeling errors using pseudo sensors in the output equation formulation. It also reduces computation time in practice. since the output equation does not need the state observer required in the state space equation. Experimental works are performed for the validation of theoretical predictions with the piezoelectric sensor and actuator bonded on the cantilever beam. An algorithm based on the sliding mode control theory is developed and analyzed for the robustness to the modeling errors and parameter uncertainties. This study also discusses the characteristics of the active and semi-active systems.

• Smart Structures and Systems
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• v.19 no.5
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• pp.567-576
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• 2017

Design of piezoelectric energy harvester for a wide operating frequency range is a challenging problem and is currently being investigated by many researchers. Widening the operating frequency is required, as the energy is harvested from ambient source of vibration which consists of spectrum of frequency. This paper presents a new technique to increase the operating frequency range which is achieved by designing a harvester featured by a propped cantilever beam with variable over hang length. The proposed piezoelectric energy harvester is modeled analytically using Euler Bernoulli beam theory and the effectiveness of the harvester is demonstrated through experimentation. The results from analytical model and from experimentation reveal that the proposed energy harvester generates an open circuit output voltage ranging from 36.43 V to 11.94 V for the frequency range of 27.24 Hz to 48.47 Hz. The proposed harvester produces continuously varying output voltage and power in the broadened operating frequency range.

• Smart Structures and Systems
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• v.12 no.5
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• pp.501-521
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• 2013

This paper is concerned with static and dynamic shape control of a laminated Bernoulli-Euler beam hosting a uniformly distributed array of resistively interconnected piezoelectric patches. We present an analytical one-dimensional model for a laminated piezoelectric beam with material discontinuities within the framework of Bernoulli-Euler and extent the model by a network of resistors which are connected to several piezoelectric patch actuators. The voltage of only one piezoelectric patch is prescribed: we answer the question how to design the interconnected resistive electric network in order to annihilate lateral vibrations of a cantilever. As a practical example, a cantilever with eight patch actuators under the influence of a tip-force is studied. It is found that the deflection at eight arbitrary points along the beam axis may be controlled independently, if the local action of the piezoelectric patches is equal in magnitude, but opposite in sign, to the external load. This is achieved by the proper design of the resistive network and a suitable choice of the input voltage signal. The validity of our method is exact in the static case for a Bernoulli-Euler beam, but it also gives satisfactory results at higher frequencies and for transient excitations. As long as a certain non-dimensional parameter, involving the number of the piezoelectric patches, the sum of the resistances in the electric network and the excitation frequency, is small, the proposed shape control method is approximately fulfilled for dynamic load excitations. We evaluate the feasibility of the proposed shape control method with a more refined model, by comparing the results of our one-dimensional calculations based on the extended Bernoulli-Euler equations to three-dimensional electromechanically coupled finite element results in ANSYS 12.0. The results with the simple Bernoulli-Euler model agree well with the three-dimensional finite element results.

• Smart Structures and Systems
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• v.18 no.2
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• pp.355-374
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• 2016

This paper presents and compares a one-dimensional (1D) bending theory for piezoelectric thin beam-type structures with resistive-inductive electrodes to ANSYS$^{(R)}$ three-dimensional (3D) finite element (FE) analysis. In particular, the lateral deflections and vibrations of slender piezoelectric beams are considered. The peculiarity of the piezoelectric beam model is the modeling of electrodes in such a manner that is does not fulfill the equipotential area condition. The case of ideal, perfectly conductive electrodes is a special case of our 1D model. Two-coupled partial differential equations are obtained for the lateral deflection and for the voltage distribution along the electrodes: the first one is an extended Bernoulli-Euler beam equation (second-order in time, forth order in space) and the second one the so-called Telegrapher's equation (second-order in time and space). Analytical results of our theory are validated by 3D electromechanically coupled FE simulations with ANSYS$^{(R)}$. A clamped-hinged beam is considered with various types of electrodes for the piezoelectric layers, which can be either resistive and/or inductive. A natural frequency analysis as well as quasi-static and dynamic simulations are performed. A good agreement between the extended beam theory and the FE results is found. Finally, the practical relevance of this type of electrodes is shown. It is found that the damping capability of properly tuned resistive or resistive-inductive electrodes exceeds the damping performance of beams, where the electrodes are simply linked to an optimized impedance.

• Structural Engineering and Mechanics
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• v.91 no.1
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• pp.87-102
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• 2024

In recent years, the focus on vibration analysis of multilayer smart structures has attracted considerable attention in many engineering applications. In this work, vibration analysis of a three-layer microporous beam with a core amplified by a composite material reinforced with graphene platelets and two piezoelectric thin films is discussed. It is assumed that piezoelectric layers with a thickness of 0.01 core are very thin and the properties of the matrix and reinforcement vary in the thickness directions. The governing equations of motion are obtained using an energy approach and the method of numerical differential quadrature to solve them. The results of this work are compared to other research and there is good agreement between them. The influences of the volumetric weight fraction of graphene wafers, different graphene platelets distributions, porosity distribution, mass scale parameters and thin ratio of graphene platelets take into account the natural dimensionless frequencies of the micro-beam. The results of this study show that the symmetric distribution of graphene platelets based on the symmetric porosity distribution has a great influence on the natural frequencies without basic dimension of the micro-beam, while the shape ratios of graphene platelets do not have a significant influence on natural frequency changes.