Nonlinear bending and vibration analyses of quadrilateral composite plates

Kumar, Amit; Singha, M.K.; Tiwari, Vikrant

doi:10.1016/j.tws.2017.01.011

Cited by 25 publications

(5 citation statements)

References 45 publications

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“…The non-dimensional critical aerodynamic pressure (λcr=λa3/D for isotropic and λcr=λa3/E2h3 for composite) for isotropic and composite square plates ( a / h = 100) are found to compare well with published results (Fernandes and Tamijani, 2017; Prakash et al, 2012; Singha and Ganapathi, 2005) in Table 2. The non-dimensional frequencies (ϖi=ωb2ρh/D/π2) of thin isotropic symmetric trapezoidal plates ( c = 0.2 a and a / h = 1000; b = a ) also match well with the published results, obtained from Galerkin’s method (Chopra and Durvasula, 1971) and the smoothed finite element method (Kumar et al, 2017), in Table 3.…”

Section: Resultssupporting

confidence: 84%

Aeroelastic analysis of pre-stressed variable stiffness composite panels

Rasool

Singha

2019

Journal of Vibration and Control

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The effect of in-plane stresses on the stability behaviors of constant stiffness and variable stiffness composite panels, exposed to aerodynamic pressure, is studied using the finite element method. The dynamic pressure from the high velocity airflow is evaluated from the first-order piston theory, and the eigenvalue analysis is performed to investigate the flutter or divergence type of instabilities in such composite panels under combined mechanical and aerodynamic loads. Attempt is made to understand the effect of the lamination parameter on the stability characteristics of edge-supported and cantilever composite trapezoidal panels. Finally, the limit cycle oscillation of variable stiffness plates subjected to aerodynamic pressure is investigated.

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Section: Resultssupporting

confidence: 84%

Aeroelastic analysis of pre-stressed variable stiffness composite panels

Rasool

Singha

2019

Journal of Vibration and Control

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“…Watts et al 45 studied geometrically nonlinear bending behavior of shear deformable isotropic and laminated composite straight-sided quadrilateral plates by using element free Galerkin method with moving kriging shape functions. Kumar et al 46 used smoothed finite element technique for linear and nonlinear analyses of shear deformable thin and thick arbitrary straight-sided quadrilateral plates. Their research showed the convergence of the present edge-based smoothed finite element method (ES-FEM) is comparatively slower for irregular quadrilateral plate compared to the rectangular plate.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration of a nanocomposite laminated piezoelectric trapezoidal actuator in subsonic airflow under combined electrical and forcing excitations

Noroozi

Bakhtiari-Nejad

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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The nonlinear dynamic and vibration behaviors of a cantilevered carbon nanotube-reinforced composite trapezoidal plate with two surface-bonded piezoelectric layers as an actuator in micro air vehicles are considered in this article. The plate is reinforced by single-walled carbon nanotubes and is exposed to subsonic airflow under combined parametric and external excitations. The large deflection von Karman plate assumptions and the classical laminated plate theory are applied to derive the governing equations of the motion of the piezoelectric nanocomposite laminated trapezoidal plate by using Hamilton's principle. The geometry of the trapezoidal plate is mapped into a rectangular computational domain. The Galerkin's approach is used for transforming the nonlinear partial differential equations of motion into nonlinear two-degrees-of-freedom ordinary differential equations of cubic nonlinearities. The case of 1:3 internal resonance and primary resonance is considered, and the multiple scales method is employed. The aerodynamic pressure distribution formula is modeled by linear potential flow theory. The frequency and time history responses and phase portrait in free forced vibrations are obtained to analyze the nonlinear dynamic behavior of the plate. The effects of different parameters such as the plate geometry, volume fraction of carbon nanotubes, and different excitations on the nonlinear vibration of the thin laminated plate are also discussed. A complex softening nonlinearity with two peaks in the higher mode is observed in frequency response curves. The influence of electrical excitation with several amplitudes and frequencies on dynamic stability is investigated using time response curves.

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“…37 Kumar et al. 38 studied vibrations of thin and thick arbitrary straight-sided quadrilateral plates. Torabi and Afshari 39 presented an optimization for flutter characteristics of cantilevered functionally graded sandwich trapezoidal plates by employing differential quadrature method and transformation of coordinates.…”

Section: Introductionmentioning

confidence: 99%

Two-frequency parametric excitation and combination resonance of a nanocomposite laminated piezoelectric trapezoidal plate in subsonic airflow

Noroozi

Bakhtiari-Nejad

Dardel

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this study, an analytical approach is presented to analyze the bifurcations and nonlinear dynamics of a cantilevered piezoelectric nanocomposite trapezoidal actuator subjected to two-frequency parametric excitations in the presence of subsonic airflow. The assumption of uniformly distributed single-walled carbon nanotubes along the thickness is taken into the consideration. The governing equations are built by the von-Karman nonlinear strain-displacement relations to consider the geometrical nonlinearity and the linear potential flow theory. The present study focuses on a specific resonance case deals with the occurrence of simultaneous resonances in the principal parametric resonance of the first mode and combination of the parametric resonance of the difference type involving two modes. The multiple scales method is employed to obtain the four nonlinear averaged equations which are solved by using the Runge-Kutta method. Moreover, the frequency-response curves, bifurcation diagrams, time history responses, and phase portrait are obtained to find the nonlinear dynamic responses of the plate. The effects of the amplitude of piezoelectric excitation, piezoelectric detuning parameter, and aerodynamic pressure are also studied. The results indicate that, the chaotic, quasi-periodic and periodic motions of the plate exist under certain conditions and the variation of controlling parameters can change the form of motions of the nanocomposite piezoelectric trapezoidal thin plate.

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Nonlinear bending and vibration analyses of quadrilateral composite plates

Cited by 25 publications

References 45 publications

Aeroelastic analysis of pre-stressed variable stiffness composite panels

Aeroelastic analysis of pre-stressed variable stiffness composite panels

Nonlinear vibration of a nanocomposite laminated piezoelectric trapezoidal actuator in subsonic airflow under combined electrical and forcing excitations

Two-frequency parametric excitation and combination resonance of a nanocomposite laminated piezoelectric trapezoidal plate in subsonic airflow

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