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.

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.

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.

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.

scholarly journals Experimental and Theoretical Investigations of the Impact Localization of a Passive Smart Composite Plate Fabricated Using Piezoelectric Materials

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
M. M. S. Dezfouli ◽  
Mohd Roshdi Hassan ◽  
Mohd Hafidz Ruslan ◽  
Sohif Mat ◽  
B. Bakhtyar
Keyword(s):  
Composite Plate ◽  
Piezoelectric Materials ◽  
Low Cost ◽  
Composite Plates ◽  
Smart Composite ◽  
Impact Location ◽  
Theoretical Investigations ◽  
Cartesian Coordinate ◽  
The Impact ◽  
Impact Localization

Two passive smart composite plates are fabricated using one and two PZT patches that are cheaper than the PZT wafer. The composite plate is fabricated in low temperature through the hand lay-up method to avoid PZT patch decoupling and wire spoiling. The locus of the impact point is identified using the output voltage to identify the impact location using one sensor. The output voltages of the sensors are analyzed to identify the impact location using two sensors. The locations of the impacts are determined based on the crossing points of two circles and the origin of an intended Cartesian coordinate system that is concentric with one of the sensors. This study proposes the impact location identification of the passive smart composite using the low-cost PZT patch PIC155 instead of common embedded materials (wafer and element piezoelectric).

An analytical solution for bending, buckling and vibration responses of FGM sandwich plates

2017 ◽  
Vol 21 (2) ◽  
pp. 727-757 ◽  
Author(s):  
Rafik Meksi ◽  
Samir Benyoucef ◽  
Abdelkader Mahmoudi ◽  
Abdelouahed Tounsi ◽  
El Abbas Adda Bedia ◽  
...  
Keyword(s):  
Free Vibration ◽  
Transverse Shear ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Numerical Study ◽  
Functionally Graded ◽  
Solution Technique ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Vibration Responses

In this study, a new shear deformation plate theory is introduced to illustrate the bending, buckling and free vibration responses of functionally graded material sandwich plates. A new displacement field containing integrals is proposed which involves only four variables. Based on the suggested theory, the equations of motion are derived from Hamilton’s principle. This theory involves only four unknown functions and accounts for quasi-parabolic distribution of transverse shear stress. In addition, the transverse shear stresses are vanished at the top and bottom surfaces of the sandwich plate. The Navier solution technique is adopted to derive analytical solutions for simply supported rectangular sandwich plates. The accuracy and effectiveness of proposed model are verified by comparison with previous research. A detailed numerical study is carried out to examine the influence of the critical buckling loads, deflections, stresses, natural frequencies and sandwich plate type on the bending, buckling and free vibration responses of functionally graded sandwich plates.

Finite Element Large-Amplitude Free and Forced Vibrations of Rectangular Thin Composite Plates

1991 ◽  
Vol 113 (3) ◽  
pp. 309-315 ◽  
Author(s):  
C. K. Chiang ◽  
C. Mei ◽  
C. E. Gray
Keyword(s):  
Finite Element ◽  
Forced Vibration ◽  
Large Amplitude ◽  
Laminated Composite ◽  
Composite Plates ◽  
Thin Plates ◽  
Element Formulation ◽  
Aspect Ratios ◽  
Mode Method ◽  
Vibration Responses

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration responses of arbitrarily laminated anisotropic composite rectangular thin plates. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite rectangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The finite element results are compared with available approximate continuum solutions. The amplitude-frequency relations for convergence with gridwork refinement, different boundary conditions, aspect ratios, lamination angles, number of plies, and uniform versus concentrated loads are presented.

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