Free Vibration of Thin-Walled Composite Shell Structures Reinforced with Uniform and Linear Carbon Nanotubes: Effect of the Elastic Foundation and Nonlinearity

In this work, we discuss the free vibration behavior of thin-walled composite shell structures reinforced with carbon nanotubes (CNTs) in a nonlinear setting and resting on a Winkler–Pasternak Foundation (WPF). The theoretical model and the differential equations associated with the problem account...

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Bibliographic Details
Published inNanomaterials (Basel, Switzerland) Vol. 11; no. 8; p. 2090
Main Authors Mahmure, Avey, Tornabene, Francesco, Dimitri, Rossana, Kuruoglu, Nuri
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 17.08.2021
MDPI
Subjects
Carbon nanotubes
CNT
Composite structures
Computer applications
Differential equations
Elastic foundations
Free vibration
Galerkin method
Investigations
Mathematical models
Mechanical properties
Nanotechnology
Nanotubes
nonlinear free vibration
nonlinear frequency
Nonlinear systems
Nonlinearity
Nuclear power plants
Numerical analysis
Parameter sensitivity
shallow shell structures
Shells (structural forms)
Soil mechanics
Soil properties
Vibration
Vibration response
Vibrations
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Summary:In this work, we discuss the free vibration behavior of thin-walled composite shell structures reinforced with carbon nanotubes (CNTs) in a nonlinear setting and resting on a Winkler–Pasternak Foundation (WPF). The theoretical model and the differential equations associated with the problem account for different distributions of CNTs (with uniform or nonuniform linear patterns), together with the presence of an elastic foundation, and von-Karman type nonlinearities. The basic equations of the problem are solved by using the Galerkin and Grigolyuk methods, in order to determine the frequencies associated with linear and nonlinear free vibrations. The reliability of the proposed methodology is verified against further predictions from the literature. Then, we examine the model for the sensitivity of the vibration response to different input parameters, such as the mechanical properties of the soil, or the nonlinearities and distributions of the reinforcing CNT phase, as useful for design purposes and benchmark solutions for more complicated computational studies on the topic.
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ISSN:2079-4991
2079-4991
DOI:10.3390/nano11082090