MODELLING SMART STRUCTURES WITH SEGMENTED PIEZOELECTRIC SENSORS AND ACTUATORS

doi:10.1006/jsvi.2000.2944

Journal of Sound and Vibration

Volume 235, Issue 3, 17 August 2000, Pages 495-520

https://doi.org/10.1006/jsvi.2000.2944 Get rights and content

Abstract

In this paper, a number of finite element models have been developed for comprehensive modelling of smart structures with segmented piezoelectric sensing and actuating patches. These include an eight-node solid-shell element for modelling homogeneous and laminated host structures as well as an eight-node solid-shell and a four-node piezoelectric membrane elements for modelling surface bonded piezoelectric sensing and actuating patches. To resolve the locking problems in these elements and improve their accuracy, assumed natural strain and hybrid stress formulations are employed. Furthermore, piezoelectric patches are often coated with metallization. The concept of electric nodes is introduced that can eliminate the burden of constraining the equality of the electric potential for physical nodes lying on the same metallization. A number of problems are studied by the developed finite element models and comparisons with other ad hoc element models are presented.

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A novel three dimensional underwater smart piezo-sandwich spherical shell cloak is designed and analyzed based on the hybrid active/semi-active distributed structural acoustic control strategy. The sandwich configuration consists of series- or parallel-connected piezoelectric (PZT) bimorph actuator skin layers collocated with a semi-active electro-rheological fluid (ERF) core layer. Two separate coupled elasto-acoustic formulations are systematically developed. The first model is based on the variational principle of structural mechanics and the approximate Kirchhoff-Love thin shell theory while the standard sliding mode control (SMC) scheme is utilized to activate the acoustic scattering extinction capability of the hybrid structure. The second model is built on the exact linear theory of 3D piezoelasticity and the classical state-space transfer matrix approach along with the active damping control (ADC) strategy. Extensive numerical simulations reveal that the best broadband backscattering cancellation performance can effectively be achieved with the smart hybrid active/semi-active bimorph piezo-sandwich spherical shell cloak operating in parallel connection. To quantify the overall cloaking performance of the proposed design, the percentage error $(% Err)$ of the external cloaked field relative to the background incident pressure field is calculated at selected dominant structural resonance frequencies within eight designated frequency bands (regions I to VIII). The remarkable (near-perfect) cloaking performance of the parallel-connected thick-walled hybrid bimorph piezo-sandwich shell $(25 % shell cloak)$ is demonstrated in the intermediate to high frequency regions (i.e., below 1.5% error in regions I, and III to VIII). This excellent invisibility performance is somewhat degraded in a narrow low frequency band (i.e., up to 8% error in region II) which is primarily linked to the elasto-acoustic resonances due to the coherent coupling of various types of highly interacting fluid- and shell-borne peripheral waves. On the other hand, the superior cloaking performance of the parallel-connected thin-walled hybrid bimorph piezo-sandwich shell $(7 % shell cloak)$ is observed predominantly in the low frequency range (i.e., below 1.5% error in regions I and II), while this exceptional performance is gradually degraded as the incident wave frequency is increased (i.e., up to 6.5% error in regions III to VIII), where partial or directional cancellation of the scattered field mostly occurs. Also, some important practical issues and limitations regarding the experimental implementation of proposed hybrid active/semi-active acoustic cloaking device are briefly discussed.
An efficient facet shell element with layerwise mechanics for coupled electromechanical response of piezolaminated smart shells
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In this work, an efficient four-node facet shell element is presented for analysis of doubly curved multilayered piezoelectric shells, based on an electromechanically coupled third order zigzag theory. It is motivated by the excellent performance of the shell element developed earlier by the authors for elastic laminated shells. The laminate theory not only incorporates a layerwise description of the inplane displacements but also accounts for the layerwise normal deformation due to the $d_{33}$ -effect of the piezoelectric layers. The number of primary displacement variables is, however, the same as for the smeared third order theory (TOT). A quadratic variation of the electric potential across the piezoelectric layers is assumed, while satisfying the equipotential condition of electroded piezoelectric surfaces using the concept of electric nodes. The performance of the element is assessed for the stress analysis under mechanical and electric potential loads, and for the free vibration response of hybrid piezolaminated deep shells in comparison with the three dimensional piezoelasticity based analytical and finite element solutions. The comparison shows excellent accuracy of the present element for the deflection, stresses, sensory potential, electric displacement and natural frequencies of hybrid shells made of composite as well as the highly inhomogenous soft-core sandwich laminates, for which the smeared TOT is shown to produce highly erroneous results. It is also shown to yield better accuracy than the other available elements of similar computational efficiency for hybrid composite shells.
Geometrically nonlinear FE analysis of piezoelectric laminated composite structures under strong driving electric field
2017, Composite Structures
To give a precise prediction of piezolaminated smart structures under strong electric field resulting in large displacements and rotations, the paper develops various geometrically nonlinear models with taking into account the electroelastic material nonlinear effect. The present nonlinear FE formulations are derived based on the first-order shear deformation theory (FSDT) with taking into account various geometric nonlinearities, which include von Kármán type nonlinearity, moderate rotation nonlinearity, and large rotation nonlinearity. The constitutive equations with consideration of piezoelectric material nonlinearity are integrated into the present FE formulations. The proposed nonlinear FE models are first validated by experimental and numerical examples in the literature, and later on implemented into numerical analysis for piezolaminated smart plates and shells with applied strong electric field.
Simultaneous optimization of photostrictive actuator locations, numbers and light intensities for structural shape control using hierarchical genetic algorithm
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The present paper introduces an investigation into simultaneous optimization of the PbLaZrTi-based actuator configuration and corresponding applied light intensity for morphing beam structural shapes. A finite element formulation for multiphysics analysis of coupled opto-electro-thermo-mechanical fields in PbLaZrTi ceramics is derived and verified with the theoretical solution and the commercial software ANSYS. This element is then used to simulate beam bending shape control using the orthotropic PbLaZrTi actuators and the simultaneous optimization. In this procedure, the controlling and geometrical variables are simultaneously optimized via a hierarchical genetic algorithm. A bi-coded chromosome is proposed in a hierarchical mode, which consists of some control genes (i.e. actuator location and number) and parametric genes (i.e. applied light intensity). Whether the parametric gene is activated or not is managed by the value of the first-grade control genes. The numerical results demonstrate that the achieved beam bending shapes correlate remarkably well with the expected ones and the simultaneous optimization of photostrictive actuator locations, numbers and light intensities can result in optimal actuator layout with less PbLaZrTi actuators and irradiated light energy. The simulation results also show that the hierarchical genetic algorithm has more superior performance over the conventional real-coded genetic algorithm.
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Citation Excerpt :
Finally, the present coupled dynamic FE model is validated by one benchmark problem, and later applied to analyze piezoelectric integrated composite plates and shells. Additionally, the results obtained by the present large rotation theory are compared to those obtained by simplified nonlinear shell theories, as well as those reported in the literature [41,57,58]. To avoid shear locking effects, the uniformly reduced integration (URI) scheme is adopted in the following computations.
A geometrically nonlinear finite element (FE) model based on large rotation shell theory is developed for static and dynamic analysis of piezoelectric integrated thin-walled structures with cross-ply or angle-ply laminates. The implemented large rotation theory has six kinematic parameters expressed by five nodal degrees of freedom (DOFs) based on first-order shear deformation (FOSD) hypothesis. An eight-node shell element with five mechanical DOFs and one electrical DOF is employed. Due to the assumption of small strains and weak electric potential, linear constitutive equations and constant electric field through the thickness are considered. The large rotation piezoelectric coupled FE model is validated by one static benchmark problem and afterwards applied to the static and dynamic analysis of piezoelectric integrated smart plates and shells composed of cross-ply or angle-ply laminates.
Large rotation theory for static analysis of composite and piezoelectric laminated thin-walled structures
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Citation Excerpt :
This requires models which are able to predict the static behavior of smart structures precisely. In contrast to three-dimensional (3-D) FE methods, see [1–7] among many others, which give very precise FE models but with large size of system matrices, one-dimensional (1-D) and two-dimensional (2-D) FE methods based on various hypotheses are much more frequently used, due to small model size and relative high accuracy. The majority of papers in the literature proposed geometrically linear 1-D or 2-D FE models for static or dynamic analysis of electro-mechanically coupled problems based on various hypotheses, e.g. Bernoulli beam theory [8,9], Timoshenko beam theory [10], Kirchhoff-Love plate/shell theory which yields the so-called classical plate/shell theory [11–17], or Reissner–Mindlin plate/shell theory known as FOSD theory, see [18–25] among many others.
A fully geometrically nonlinear finite element (FE) model is developed using large rotation shell theory for static analysis of composite and piezoelectric laminated thin-walled structures. The proposed large rotation theory is based on the first-order shear deformation (FOSD) hypothesis. It has six independent kinematic parameters which are expressed by five mechanical nodal degrees of freedom (DOFs). Linear electro-mechanically coupled constitutive equations with a constant electric field distribution through the thickness of each smart material layer are considered. Eight-node quadrilateral plate/shell elements with five mechanical DOFs per node and one electrical DOF per smart material layer are employed in the FE modeling. The present large rotation FE model is implemented into static analysis of both composite and piezoelectric laminated plates and shells. The equilibrium equation is solved by Newton–Raphson algorithm with system matrices updated in every iteration. The results are compared with those presented in the literature and others calculated by various simplified nonlinear shell theories. They indicate that large rotation theory has to be considered for the calculation of displacements and sensor output voltages of smart structures undergoing large deflections, since other simplified nonlinear theories fail to predict the static response precisely in many cases.

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^†: On leave from Department of Mechanics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China.

^f1: [email protected]

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Regular ArticleMODELLING SMART STRUCTURES WITH SEGMENTED PIEZOELECTRIC SENSORS AND ACTUATORS

Abstract

Finite Elements in Analysis and Design

Finite Elements in Analysis and Design

Finite elements in analysis and design

Finite Elements in Analysis & Design

Journal Sound and Vibration

Finite element analysis of composite structures containing distributed piezoelectric sensors and actuators

American Institute of Aeronautics and Astronautics Journal

Active vibration control of laminated composite plates using piezoelectric devices: a finite element approach

Journal of Intelligent Material Systems & Structures

Finite element modelling of piezoelectric sensors and actuators

American Institute of Aeronautics and Astronautics Journal

Analysis of distributed thermopiezoelectric sensors and actuators in advanced intelligent structures

American Institute of Aeronautics and Astronautics Journal

Analysis of piezoelectric structures with laminated piezoelectric triangle shell elements

American Institute of Aeronautics and Astronautics Journal

Finite element modelling of structures including piezoelectric active devices

International Journal of Numerical Methods in Engineering

Electro-mechanical dynamics of a coupled piezoelectric/mechanical system applied to vibration control and distributed sensing

Ph.D. dissertation, University of Kentucky, Lexington, Ky. July

An explicit hybrid-stabilized eighteen-node solid element for thin shell analysis

International Journal of Numerical Methods in Engineering

Regular Article
MODELLING SMART STRUCTURES WITH SEGMENTED PIEZOELECTRIC SENSORS AND ACTUATORS