Geometrically nonlinear free vibration analysis of laminated composite plates: A finite element assessment of a higher order non-polynomial shear deformation theory

Adhikari, Balakrishna; Dash, P. R.

doi:10.1080/15376494.2018.1553259

Cited by 15 publications

(9 citation statements)

References 36 publications

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“…Next, the validation of the nonlinear frequency ratio of an eight layer simply supported cross-ply laminate true[true( 0∘/ 90∘true)2true]s is presented in Table 2 together with the results of Ganapathi et al. 45 and Adhikari and Dash 16 and both the solutions are well matching with each other. The frequency ratio of the laminate is increasing with an increase in the amplitude of vibration i.e.…”

Section: Resultsmentioning

confidence: 87%

“…By applying equations (6) to (8), equation (11) can be rewritten as Now, by substituting the equations (5) and (7) and following the procedure explained in Adhikari and Dash, 16 equation (12) can further be modified as…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The detailed procedure of the direct iteration technique is well formulated in Adhikari and Dash. 16 Further, the nonlinear static behavior of the laminated FG-CNTRC plate is evaluated by employing the Newton-Raphson method. Furthermore, the nonlinear transient response of the FG-CNTRC plate is obtained by using the nonlinear Newmark’s time integration technique.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…10 investigated the large amplitude free vibration of a laminated composite plate using Green Lagrange strain field based on a higher order quasi 3-D theory. Further, Adhikari and Dash 16 formulated a finite element procedure for the large amplitude free vibration of the laminated composite plates based on an inverse trigonometric shear deformation theory (ITSDT). They outlined the mode switching phenomenon of laminated composite plate for a higher amplitude of vibration ( i.e.…”

Section: Introductionmentioning

confidence: 99%

“…The nonlinear simultaneous governing equations of the FG-CNTRC plate are obtained by applying the Lagrange equation of motion. For the free vibration analysis of the FG-CNTRC plate, the nonlinear equations have been solved based on the direct iteration technique 16 and the forced vibration response of the plate is obtained by using nonlinear Newmark’s time integration technique as explained in a later section. The large amplitude free vibration and forced vibration response are determined in von-Karman sense of nonlinearity, which means the formulation is limited to only for large deflection and small strains i.e.…”

Section: Introductionmentioning

confidence: 99%

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Geometrically nonlinear static and dynamic analysis of CNT reinforced laminated composite plates: A finite element study

Adhikari

Singh

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this paper, a finite element study is conducted using the Green Lagrange strain field based on vonKarman assumptions for the geometric nonlinear static and dynamic response of the laminated functionally graded CNT reinforced (FG-CNTRC) composite plate. The governing equations for determining the nonlinear static and dynamic behavior of the FG-CNTRC plate are derived using the Lagrange equation of motion based on Reddy's higher order theory. Using the direct iteration technique, the nonlinear eigenvalues for analyzing the free vibration response are obtained and the nonlinear dynamic responses of the FG-CNTRC plate are encapsulated based on the nonlinear Newmark integration scheme. The impact of the amplitude of vibration on mode switching phenomena and the consequence of the duration of the pulse on the free vibration regime of the plate are outlined. Also, the effect of time dependent loads is studied on the normal stresses of the plate. Furthermore, the impact on the nonlinear static and dynamic response of the laminated FG-CNTRC plate of various parameters such as span-thickness ratio (b/h ratio), aspect ratio (a/b ratio), different edge constraints, CNT fiber gradation, etc. are also studied.

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