In this article, various non‐polynomial higher‐order shear deformation theories are applied for the first time to analyze the free vibration and transient responses of plates with functionally graded material (FGM) supported on an elastic foundation. The shear deformation theories account for the non‐linear variation of the transverse shear strains with various warping functions, namely trigonometric, inverse hyperbolic, and inverse trigonometric ones. These models also inherently satisfy the traction‐free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plates and do not require any shear correction factor. A two‐parameter model, namely Winkler‐Pasternak's elastic foundation model, is utilized to develop the interaction between the FGM plates and the elastic medium. The governing equations of motion are obtained using Hamilton's principle and solved analytically using Navier's solution scheme. Furthermore, the transient responses of the plates are obtained using Newmark's average acceleration method. The applicability of the present theories is established by solving several numerical problems and validating the results with the solutions available in the literature. The effects of various parameters like span‐thickness ratios, aspect ratios, gradation coefficients, mechanical loads, and foundation stiffness on the fundamental frequencies and the transient responses of the plates are thoroughly investigated. The comparison of the results reveals the efficiency of the non‐polynomial functions, and the capability of efficient prediction of the structural responses of the FGM plates at a similar computational cost compared to established models in the literature. Furthermore, the results show that the stiffness of the elastic foundation can tweak the stiffness characteristics of the FGM plate resulting in significant changes in the natural frequencies and more controlled displacement‐time responses.
The influence of the number and position of the carbon fiber lamina on the natural frequency and damping ratio of the carbon-glass hybrid composite Abstract: Discontinuous fiber reinforced composites are being used in many antivibration applications due to their time and temperature dependent specific mechanical properties. For utilization of this material to specific engineering applications there is a need to understand the damping behavior of composites under dynamic loading. For this work, unreinforced and 20 % long and short reinforced glass fiber polypropylene composite materials were tested for free transverse vibration damping characteristics under static as well as fatigue loading conditions. The damping characteristics are quantified by decay pattern and natural frequency. Presence of reinforced fibers increases the damping capacity. Among reinforcements, short fiber reinforced polypropylene shows increased damping capacity then long glass fiber reinforced polypropylene.
Increasing utilization of thermoplastic composites in the structural application necessitates understanding of damage tolerance characteristics. In this work, unreinforced, 20 % short, 20 % long glass fiber reinforced polypropylene were injection molded and considered. Test specimens with different notch sizes were tested under static as well as fatigue loading conditions. Under static load condition, short fiber reinforced and unreinforced test material exhibited notch strengthening effect; whereas long fiber reinforced material exhibited notch weakening effect. Failure morphology under fatigue condition exhibited the influence of notch size and length of reinforced fibers over performance. Significant difference between notched and unnotched specimens is observed at low cycle fatigue and very less difference in performance is observed at high cycle fatigue condition.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.