The analysis of inter-laminar stress and electric potential for a laminated piezoelectric plate with interfacial damage

2011 ◽  
Vol 16 (8) ◽  
pp. 793-811 ◽  
Author(s):  
Fu Yiming ◽  
Li Sheng
Keyword(s):  
Electric Potential ◽  
Degrees Of Freedom ◽  
Piezoelectric Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Variation Principle ◽  
Interfacial Damage ◽  
Load Models ◽  
Non Linear ◽  
Piezoelectric Plates

This paper presents a non-linear model for laminated piezoelectric plates with inter-laminar mechanical and electrical damage. The model is based on the general six-degrees-of-freedom plate theory, and the discontinuity of displacement and electric potential on the interfaces are depicted by three shape functions. By using the variation principle, the three-dimensional non-linear equilibrium differential equations of simply supported laminated piezoelectric plates with interfacial damage are derived. Then, an analytical solution is presented by using the finite difference method. In numerical examples, the effects of different damage values, load models, and electric boundary conditions on the inter-laminar stress and electric potential profile of a laminated piezoelectric plate with interfacial imperfections are investigated.

A Non-Linear Numerical Method for the Simulation of Parametric Roll Resonance in Regular Waves

2008 ◽  
Author(s):  
T. M. Ahmed ◽  
E. J. Ballard ◽  
D. A. Hudson ◽  
P. Temarel
Keyword(s):  
Numerical Method ◽  
Potential Flow ◽  
Degrees Of Freedom ◽  
Linear Time ◽  
Three Dimensional ◽  
Regular Waves ◽  
Time Step ◽  
Parametric Roll ◽  
Non Linear ◽  
Parametric Roll Resonance

In this paper, a non-linear time-domain method is used for the prediction of parametric roll resonance in regular waves, assuming the ship to be a system with three degrees of freedom in heave, pitch and roll. Coupled heave and pitch motions are obtained using a three-dimensional frequency-domain potential flow method which also provides the requisite hydrodynamic data of the ship in roll i.e. the potential flow based added inertia and damping. Periodic changes in the underwater hull geometry due to heave, pitch and the wave profile are calculated as a function of the instantaneous breadth. This is carried out using a two-dimensional approach i.e. for sections along the ship and at each time step. This formulation leads to a mathematical model that represents the roll equation of motion with third order non-linearities in the parametric excitation terms. Non-linearities in the roll damping and restoring terms are also accounted for. This method has been applied to two different hull forms, a post-Panamax C11 class containership and a transom stern Trawler, both travelling in regular waves. Special attention is focused on the influence of different operational aspects on parametric roll. Obtained results demonstrate that this numerical method succeeds in producing results similar to those available in the literature, both numerical and experimental.

scholarly journals Three-Dimensional Semianalytical Solutions for Piezoelectric Laminates Subjected to Underwater Shocks

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Xu Liang ◽  
Wenbin Lu ◽  
Ronghua Zhu ◽  
Changpeng Ye ◽  
Guohua Liu
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Electric Potential ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Laminated Plates ◽  
Inversion Method ◽  
Variation Principle ◽  
The Laplace Transform

In this study, a piezoelectric laminate is analyzed by applying the Laplace transform and its numerical inversion, Fourier transform, differential quadrature method (DQM), and state space method. Based on the modified variation principle for the piezoelectric laminate, the fundamental equations for dynamic problems are derived. The solutions for the displacement, stress, electric potential, and dielectric displacement are obtained using the proposed method. Durbin’s inversion method for the Laplace transform is adopted. Four boundary conditions are discussed through the DQM. The proposed method is validated by comparing the results with those of the finite element method (FEM). Moreover, this semianalytical method is further extended to describe the dynamic response of piezoelectric laminated plates subjected to underwater shocks by introducing Taylor’s fluid-structure interaction algorithm. Both air-backed and water-backed laminated plates are investigated, and the effect of the fluid is examined. In the time domain, the electric potential and displacements of sample points are calculated under four boundary conditions. The present method is shown to be accurate and can be a useful method to calculate the dynamic response of underwater laminated sensors.

Benchmark solutions for the free vibration of layered piezoelectric plates based on a variational formulation

2017 ◽  
Vol 28 (19) ◽  
pp. 2688-2704 ◽  
Author(s):  
Gennady M Kulikov ◽  
Svetlana V Plotnikova
Keyword(s):  
Free Vibration ◽  
Variational Formulation ◽  
Piezoelectric Plate ◽  
Three Dimensional ◽  
Middle Surface ◽  
Field Vector ◽  
Lagrange Polynomials ◽  
Electric Potentials ◽  
Benchmark Solutions ◽  
Piezoelectric Plates

This article focuses on the implementation of the sampling surfaces method for the three-dimensional vibration analysis of layered piezoelectric plates. The sampling surfaces method is based on choosing inside the layers not equally spaced sampling surfaces parallel to the middle surface in order to introduce the displacements and electric potentials of these surfaces as basic plate variables. Such choice of unknowns with the consequent use of Lagrange polynomials in the assumed distributions of displacements, strains, electric potential, and electric field vector through the thicknesses of layers leads to the robust piezoelectric plate formulation. The sampling surfaces are located inside each layer at Chebyshev polynomial nodes that makes it possible to minimize uniformly the error due to the Lagrange interpolation. Therefore, the sampling surfaces formulation can be applied efficiently to the obtaining of benchmark solutions for the free vibration of layered piezoelectric plates, which asymptotically approach the three-dimensional solutions of piezoelectricity as the number of sampling surfaces tends to infinity.

scholarly journals Anti-Optimisation Applied to the Analysis of Rotor/Stator Interaction

2013 ◽  
Author(s):  
Tore Butlin ◽  
Alain Batailly
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
High Amplitude ◽  
Three Dimensional Model ◽  
Constant Frequency ◽  
Worst Case ◽  
Peak Displacement ◽  
Contact Points ◽  
Novel Approach ◽  
Non Linear

There is a drive towards minimising operating clearances within turbomachines in order to limit reverse leakage flows and hence improve their efficiency. This increases the likelihood of contact occurring between the blade and the casing, which can give rise to high amplitude vibration. Modelling this interaction represents a significant computational challenge. The non-linear contact precludes the use of well-established linear methods, and is also subject to uncertainties: the contact law is imprecisely known and the exact geometry of imperfections that trigger contact may be unknown. In this paper a novel approach is presented that aims to account for the uncertainties associated with the non-linearity in a non-probabilistic way. The worst case is sought, by framing the system as a constrained anti-optimisation problem. The target to be maximised represents a metric of the output of interest. The degrees of freedom of the anti-optimisation are the non-linear input forces (considered as external loads), and the constraints are designed to capture what is thought to be known about the non-linear contact law and geometry. A realistic three-dimensional model of a turbine blade is used to explore the approach, with contact considered at the leading and trailing edge. The blade dynamics are described in terms of a linear transfer function matrix and the target metric of interest is chosen to be the peak displacement of the contact points. The non-linearity is taken to result from an offset shaft, giving a sinusoidal clearance variation. The blade is driven at constant frequency and the scope of the study is limited to finding bounds on periodic solutions. A variety of constraint conditions are explored that describe aspects of the non-linearity. For example, only compressive forces are permitted (no tension from the contact), and the displacement must not exceed the clearance. The method yields encouraging initial results: constraints can be identified that give efficient estimates of the upper bound response of the system as a function of drive frequency. The results are compared with a benchmark time-domain simulation and are found to correctly over-predict the response without being overly conservative. Broad trends are also in agreement with the benchmark solution. The proposed method appears to be a promising approach for efficiently accounting for uncertainties associated with the non-linearity and thus improving blade design.

scholarly journals Design, Fabrication, and Testing of a Novel 3D 3-Fingered Electrothermal Microgripper with Multiple Degrees of Freedom

Micromachines ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 444
Author(s):  
Guoning Si ◽  
Liangying Sun ◽  
Zhuo Zhang ◽  
Xuping Zhang
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Polyimide Film ◽  
Zebrafish Embryos ◽  
Multiple Degrees Of Freedom ◽  
Electrothermal Actuator ◽  
3D Space ◽  
Pick And Place

This paper presents the design, fabrication, and testing of a novel three-dimensional (3D) three-fingered electrothermal microgripper with multiple degrees of freedom (multi DOFs). Each finger of the microgripper is composed of a V-shaped electrothermal actuator providing one DOF, and a 3D U-shaped electrothermal actuator offering two DOFs in the plane perpendicular to the movement of the V-shaped actuator. As a result, each finger possesses 3D mobilities with three DOFs. Each beam of the actuators is heated externally with the polyimide film. The durability of the polyimide film is tested under different voltages. The static and dynamic properties of the finger are also tested. Experiments show that not only can the microgripper pick and place microobjects, such as micro balls and even highly deformable zebrafish embryos, but can also rotate them in 3D space.

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