Semi-analytical solution for static and free vibration of multilayered functionally graded elastic plates with imperfect interfaces

Abstract

In this paper, the three-dimensional static behavior and the free vibration of simply supported multilayered functionally graded elastic plates with bonding imperfections is derived. The imperfect interfaces between the adjacent layers are modeled by the spring-type layer model. In each layer, a well-adapted semi-analytical solution coupling the state-space approach with the fourth-order Runge-Kutta numerical procedure is elaborated. In consequence, the intricate three-dimensional problem has been reduced to a one-dimensional recursive problemwith which arbitrary functionally graded material’s model and number of layers can be easily handled. The predicted solution in each layer has been propagated from the bottom to the top layers of the plate using the propagator matrix method and taking into account the transfer matrix at the imperfect interfaces. The transfer relationship linking the top and the bottom surfaces of the multilayered functionally graded plate is therefore obtained. The accuracy and reliability of the proposed methodological approach have been clearly demonstrated by several numerical tests. The predicted numerical results have been well compared with the available ones obtained by the pseudo-Stroh formalism, discrete layer approach, finite elements method, Layerwise method, variable kinematic model, sinusoidal and hyperbolic shears deformations theories, respectively. These results showed that the imperfect interfaces have a strong effect on the static behavior and the natural frequencies of multilayered functionally graded plates. In addition, the obtained results showed that when the dimensionless interface parameter increase the natural frequencies decrease quickly.

Keywords:

• Functionally graded materials
• multilayered plate
• imperfect interfaces
• state-space approach
• semi-analytical method
• Runge-Kutta method

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partly funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia as well as by the Moroccan Ministry of Higher Education and Scientific Research and the CNRST‐Morocco via the research project PPR2/06/2016. The authors, therefore, acknowledge with thanks the DSR‐KAU and the CNRST financial supports.