Analytical modeling of laminated composite plates integrated with piezoelectric layer using Trigonometric Zigzag theory

2020 ◽  
Vol 54 (29) ◽  
pp. 4691-4708
Author(s):  
Aniket Chanda ◽  
Rosalin Sahoo
Keyword(s):  
Transverse Shear ◽  
Piezoelectric Layer ◽  
Composite Plate ◽  
Laminated Composite ◽  
Composite Plates ◽  
Solution Technique ◽  
Shear Stresses ◽  
Smart Composite ◽  
Laminated Composite Plate ◽  
Zigzag Theory

The analytical solution for static analysis of laminated composite plate integrated with piezoelectric fiber reinforced composite actuator is obtained using a recently developed Trigonometric Zigzag theory. The kinematic field consists of five independent field variables accommodating non-linear variation of transverse shear strains through the thickness of the laminated composite plate. The principle of minimum potential energy is adopted to derive the governing equations of equilibrium. Navier’s solution technique is employed to convert the system of coupled partial differential equations into a system of algebraic equations. The electric potential is assumed to vary linearly through the thickness of the piezoelectric layer. The analytical formulation also does not include voltage as an additional primary variable. The response in the form of deflection and stresses are obtained for smart composite plates subjected to electro-mechanical loads and compared with the elasticity solutions and available results reported by other researchers in the existing literature. The transverse shear stresses are accurately determined by an efficient post-processing technique of integrating the equilibrium equations of elasticity. Parametric studies on actuation in the response of the smart composite plate are also presented graphically in order to have a clear understanding of the static behavior.

Stress analysis of smart composite plate structures

2020 ◽  
pp. 095440622097544
Author(s):  
Aniket Chanda ◽  
Utkarsh Chandel ◽  
Rosalin Sahoo ◽  
Neeraj Grover
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Laminated Composite ◽  
Composite Plates ◽  
Higher Order ◽  
Hyperbolic Function ◽  
Solution Technique ◽  
Shear Stresses ◽  
Laminated Composite Plates ◽  
Equilibrium Equations

In the present study, the electro-mechanical responses of smart laminated composite plates with piezoelectric materials are derived using a two-dimensional (2 D) displacement-based non-polynomial higher-order shear deformation theory. The kinematics of the mathematical model incorporates the deformation of laminates which account for the effects of transverse shear deformation and a non-linear variation of the in-plane displacements using inverse sine hyperbolic function of the thickness coordinate. The equilibrium equations are obtained using the minimization of energy principle known as the principle of minimum potential energy (PMPE) which is also based on a variational approach and the solutions are obtained using Navier’s solution technique for diaphragm supported smart laminated composite plates. The responses obtained in the form of deflection and stresses are compared with three dimensional (3 D) solutions and also with different polynomial and non-polynomial based higher-order theories in the literature. The transverse shear stresses are obtained using 3 D equilibrium equations of elasticity to enhance the accuracy of the present results. Various examples are numerically solved to establish the efficiency of the present model.

Forced Vibration Responses of Smart Composite Plates using Trigonometric Zigzag Theory

2021 ◽  
pp. 2150067
Author(s):  
Aniket Chanda ◽  
Rosalin Sahoo
Keyword(s):  
Forced Vibration ◽  
Piezoelectric Materials ◽  
Composite Plates ◽  
Solution Technique ◽  
Integration Scheme ◽  
Shear Stresses ◽  
Smart Composite ◽  
Plate Structure ◽  
Vibration Responses ◽  
Zigzag Theory

The Trigonometric Zigzag theory is utilized in this research for analytically evaluating the forced vibration responses of smart multilayered laminated composite plates with piezoelectric actuators and sensors. This theory, as the name suggests, incorporates a trigonometric function, namely the secant function for describing the nonlinear behavior of transverse shear stresses through the thickness of the smart composite plates. The kinematics for the in-plane displacement components are obtained by superposing a globally varying nonlinear field through the thickness of the plate structure on a piecewise linearly varying zigzag field with slope discontinuities at the layer interfaces. The model also satisfies the inter-laminar continuity conditions of tractions at the interfaces of the multilayered plate. The equations of motion are derived using Hamilton’s principle, and the separation of the variables technique is extended to assume the solutions for the primary variables in space and time and solved analytically using Navier’s solution technique along with Newmark’s time integration scheme. A detailed analytical investigation of the dynamic behavior of the smart laminated plate coupled with piezoelectric materials like PVDF and piezoelectric fiber-reinforced composite (PFRC) is carried out by considering several forms of the time-dependent electromechanical excitations and also covering different geometrical and material features of the smart plate structure. The responses are found to be in close agreement with the elasticity solutions and some new results are also presented to show the dynamic controlling capacity of the piezoelectric layers.

Transient analysis of smart composite laminate

2020 ◽  
pp. 030932472095781
Author(s):  
Rosalin Sahoo ◽  
Aniket Chanda
Keyword(s):  
Transverse Shear ◽  
Composite Plate ◽  
Transient Analysis ◽  
Accurate Estimation ◽  
Solution Technique ◽  
Integration Scheme ◽  
Shear Stresses ◽  
Smart Composite ◽  
Transverse Shear Stresses ◽  
Elasticity Solutions

In the present study, the transient analysis of smart laminated composite plates is presented analytically using inverse hyperbolic zigzag theory. This theory is displacement based with five unknown primary mid-plane variables in conjunction with the zigzag parameters resembling the membrane and the bending components. The inter-laminar continuity conditions of transverse shear stresses at the interfaces of the smart composite plate are artificially enforced. The dynamic version of principle of virtual work is used to derive the basic equations and solved subsequently with the Navier’s solution technique. Newmark’s time integration scheme is adopted to obtain the solutions of the coupled ordinary differential equations in the time frame. The equilibrium equations of elasticity are employed in order to obtain accurate estimation of transverse shear stresses. Numerical problems on diaphragm supported smart composite plate are solved by evaluating the static responses and comparing them with elasticity solutions in the existing literature. Then the transient responses are derived for a number of time-dependent electro-mechanical loads such as triangular, sine, ramp, and staircase variation. Results show excellent accuracy with the elasticity solutions available in the literature. Further, the dynamic controlling capacity of the piezoelectric layer is studied by evaluating the electrical loads that diminish the mechanical vibrations from the system.

Thermoelastic bending analysis of laminated composite plates according to various shear deformation theories

2014 ◽  
Vol 5 (1) ◽  
Author(s):  
Atteshamuddin Shamshuddin Sayyad ◽  
Bharati Machhindra Shinde ◽  
Yuwaraj Marotrao Ghugal
Keyword(s):  
Shear Stress ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Virtual Work ◽  
Plate Theory ◽  
Thermal Response ◽  
Laminated Composite ◽  
Composite Plates ◽  
Shear Stresses ◽  
Laminated Composite Plates

AbstractThis study presents the thermoelastic analysis of laminated composite plates subjected to sinusoidal thermal load linearly varying across the thickness. Analytical solutions for thermal displacements and stresses are investigated by using a unified plate theory which includes different functions in terms of thickness coordinate to represent the effect of shear deformation. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Governing equations of equilibrium and associated boundary conditions of the theory are obtained using the principle of virtual work. The Navier solution for simply supported laminated composite plates has been developed. Numerical results are presented to demonstrate the thermal response of the laminated composite plates.

Large Deflection of a Laminated Composite Plate With Different Extensional and Flexural Material Properties

2010 ◽  
Author(s):  
Rifat Arıko¨k ◽  
Zahit Mecitog˘lu
Keyword(s):  
Material Properties ◽  
Composite Plate ◽  
Large Deflection ◽  
Virtual Work ◽  
Flexural Modulus ◽  
Laminated Composite ◽  
Composite Plates ◽  
Equation System ◽  
Laminated Composite Plate ◽  
Element Analysis

This paper presents the large deflection elastic analysis of the hand lay-up composite plates with different extensional and flexural modulus including geometric nonlinearity effects that are taken into account with the von Ka´rma´n large deflection theory of thin plates. Governing equations of the motion are derived by means of the virtual work principle. Then the Galerkin method is applied to reduce the nonlinear coupled differential equations into a nonlinear algebraic equation system. The MATLAB and MATHEMATICA software are used to solve the equation system. Because of the common nonuniformities in hand lay-up fabric laminates such as resin surface layers and unequal layer thickness, the flexural and extensional modulus of such laminated composites are different. By the way, since the bending and in-plane effects are together affect to the nonlinear behavior of a composite laminate, it should give more reliable results when using different flexural and extensional modulus in the analysis. In this study, the results of approximate analysis, ANSYS finite element analysis and experimental study are obtained and compared for a fully-clamped laminated composite plate subjected to a uniform pressure load. The material properties used in the analysis are determined tension and three-point bending tests.

scholarly journals SOUND TRANSMISSION LOSS ACROSS A FINITE CLAMPED DOUBLE-LAMINATED COMPOSITE PLATE WITH POROELASTIC MATERIAL

2020 ◽  
Vol 57 (6A) ◽  
pp. 150
Author(s):  
Thanh Ngoc Pham
Keyword(s):  
Composite Plate ◽  
Transmission Loss ◽  
Sound Transmission ◽  
Laminated Composite ◽  
Double Series ◽  
Composite Plates ◽  
Thin Plates ◽  
Sound Transmission Loss ◽  
Laminated Composite Plate ◽  
Poroelastic Material

A theoretical study of sound transmission loss across a clamped double-laminated composite plate filled with poroelastic material is formulated. Biot’s theory is employed to describe wave propagation in elastic porous media. The two face composite plates are modeled as classical thin plates. By using the modal superposition theory, a double series solution for the sound transmission loss of the structure is obtained with the help of the Galerkin method. The analytical model is validated against previous experimental results of a single sound wave under normal incidence. The numerical results suggest that the density of poroelastic material, the type of composite materials and the composite plies arrangement have significant effects on the sound transmission loss of considered structure.

Vibroacoustic analysis of a thin laminated composite plate with surface-boned piezoelectric patches and subjected to general boundary conditions

2021 ◽  
Vol 263 (4) ◽  
pp. 2501-2509
Author(s):  
Zhengmin Hu ◽  
Kai Zhou ◽  
Yong Chen
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Composite Plate ◽  
Laminated Composite ◽  
Composite Plates ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Acoustic Response ◽  
Laminated Composite Plates ◽  
Laminated Composite Plate

In this paper, a semi-analytical model is proposed to deal with the vibroacoustic problems of laminated composite plates with surfaced-boned piezoelectric patches and subjected to general boundary condition using the modified Fourier series method. Based on Kirchhoff plate theory, the dynamic equation of the laminated composite plate is derived using Hamilton's principle. In order to satisfy general boundary conditions, the displacement solution of the plate is expressed in the form of two-dimensional Fourier series and serval auxiliary functions. The acoustic response of the laminated composite plate due to a harmonic concentrated force is obtained with the Rayleigh integral. Besides, the mass and stiffness contribution of the piezoelectric patch are taken into consideration in the present study. Through enough convergent studies and comparative studies, the convergence, accuracy and universality of the proposed method are validated. The developed semi-analytical model can be used for efficient and accurate analysis and design of laminated composite plates equipped with shunted piezoelectric patches. Finally, the effects of the resistor and inductor shunt damping circuits on the vibration and acoustic response is discussed.

scholarly journals Bending Response of Cross-Ply Laminated Composite Plates with Diagonally Perturbed Localized Interfacial Degeneration

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Chee Zhou Kam ◽  
Ahmad Beng Hong Kueh
Keyword(s):  
Composite Plate ◽  
Laminated Composite ◽  
Composite Plates ◽  
Interface Element ◽  
Laminated Composite Plates ◽  
Laminated Composite Plate ◽  
Bending Performance ◽  
Element Approach ◽  
Bending Behavior ◽  
Bending Response

A laminated composite plate element with an interface description is developed using the finite element approach to investigate the bending performance of two-layer cross-ply laminated composite plates in presence of a diagonally perturbed localized interfacial degeneration between laminae. The stiffness of the laminate is expressed through the assembly of the stiffnesses of lamina sub-elements and interface element, the latter of which is formulated adopting the well-defined virtually zero-thickness concept. To account for the extent of both shear and axial weak bonding, a degeneration ratio is introduced in the interface formulation. The model has the advantage of simulating a localized weak bonding at arbitrary locations, with various degeneration areas and intensities, under the influence of numerous boundary conditions since the interfacial description is expressed discretely. Numerical results show that the bending behavior of laminate is significantly affected by the aforementioned parameters, the greatest effect of which is experienced by those with a localized total interface degeneration, representing the case of local delamination.

Hygro-thermally induced stress intensity factor of an edge crack piezo laminated composite plate

2019 ◽  
Vol 15 (6) ◽  
pp. 1053-1074
Author(s):  
Achchhe Lal ◽  
Khushbu Jain
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Piezoelectric Layer ◽  
Edge Crack ◽  
Composite Plate ◽  
Volume Fraction ◽  
Laminated Composite ◽  
Laminated Composite Plate ◽  
Content Type

Purpose The purpose of this paper is to evaluate hygro-thermo-mechanically induced normalized stress intensity factor (NSIF) of an edge crack symmetric angle-ply piezo laminated composite plate (PLCP) using displacement correlation method. Design/methodology/approach In the present work, the governing equations are solved through conventional finite element method combined with higher order shear deformation plate theory utilizing the micromechanical approach. Findings The effects of crack length, the thickness of the plate and piezoelectric layer, stacking sequences, fiber volume fraction, position of piezoelectric layer, change in moisture and temperature, and voltage on the NSIF are examined. The numerical results are presented in the form of a table for the better understanding and accuracy. The present outlined approach is validated with results available in the literature. These results can become a benchmark for future studies. Research limitations/implications The mathematical models theoretically have been developed by considering different parameters. The results are generated using MATLAB 2015 software developed by the authors’ side. Originality/value The fracture analysis of a single edge crack PLCP with the effect of a piezoelectric layer at the different location of cracked structures, plate thickness, and actuator voltage and hygro-thermo loading is the novelty of research for health monitoring and high-performance analysis.

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