Department of Civil Engineering

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Author: search.filters.author.Patel, Shuvendu NarayanSubject: search.filters.subject.Dynamic instability

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    Nonlinear dynamic instability and dynamic response of stiffened laminated composite plates subjected to in-plane pulsating patch loading
    (Taylor & Francis, 2023-11) Patel, Shuvendu Narayan
    In this article, the nonlinear dynamic instability of stiffened laminated composite plates is studied in the finite element (FE) framework subjected to uniform in-plane harmonic patch loading. The harmonic load is applied to the two opposite sides of the stiffened plate. The linear and nonlinear time-history response analysis is also studied. The skin and the stiffener are modeled using an eight-node isoparametric degenerated shell element and a three-node curved beam element, respectively. A system of matrices is developed by considering the Green–Langrange strain–displacement relationship. In the linear case, the Bolotin method is used to analyze the dynamic instability region (DIR). The nonlinear instability behavior of the laminated composite stiffened plate is studied by applying the Incremental Harmonic Balance Method (IHB). The Newmark-β method is used to solve the linear and nonlinear time-history response equations to understand the instability behavior of the stiffened plates. The effect of the parameters such as the length of the in-plane loading patch, varying number of stiffeners in x-direction and the position of the patch on the nonlinear vibrations and nonlinear dynamic response is examined.
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    Nonlinear vibration and instability of a randomly distributed CNT-reinforced composite plate subjected to localized in-plane parametric excitation
    (Elsevier, 2022-01) Kumar, Rajesh; Patel, Shuvendu Narayan; Watts, Gaurav
    This study presents a semi-analytical formulation for the nonlinear vibration and dynamic instability of a randomly distributed carbon nanotube-reinforced composite (RD-CNTRC) plate. Three cases of localized in-plane periodic loadings are studied. The analytical stress fields within the RD-CNTRC plate for all the in-plane stress components (σij, (i, j = x, y)) are developed by solving the in-plane elastic problem using Airy's stress approach. The effective mechanical properties of the RD-CNTRC plate are evaluated by the Eshelby-Mori-Tanaka technique. The plate is modeled based on higher-order shear deformation theory (HSDT) in conjunction with the von-Kármán nonlinearity. Using Hamilton's principle, the governing partial differential equations (PDEs) are derived, whose approximate solution is sought, referring to the Galerkin method. The resulting nonlinear ODEs are solved using the Incremental Harmonic Balance (IHB) Method to compute the nonlinear vibration response of the RD-CNTRC plate. Further dropping the nonlinear terms, these ODEs are solved by Bolotin's method to trace the instability region. The proposed semi-analytical method is an effective strategy for studying the influence of different parameters such as agglomeration models, CNT mass fraction, pre-loading, and boundary conditions on the nonlinear vibration and dynamic instability characteristics of the RD-CNTRC plates. The reduced computational effort allows the design phase to be supported in selecting parameters when designing RD-CNTRC plates with stability and vibration requirements.
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    Instability and Vibration Analyses of Functionally Graded Carbon Nanotube–Reinforced Laminated Composite Plate Subjected to Localized In-Plane Periodic Loading
    (ASCE, 2021-11) Kumar, Rajesh; Patel, Shuvendu Narayan
    Carbon nanotubes (CNTs) have attracted many researchers during the last three decades due to their versatile nature and excep-tional mechanical properties. In this study, a functionally graded CNT-reinforced laminated composite (FG-CNTRLC) plate subjected todifferent types of localized in-plane loadings was analyzed semianalytically to determine its dynamic instability and nonlinear vibrationcharacteristics. The effective mechanical properties of the FG-CNTRLC plate were estimated using the extended rule-of-mixture technique.The FG-CNTRLC plate was modeled based on higher-order shear deformation theory (HSDT) in conjunction with von Kármán nonlinearity.The distribution of prebuckling stresses within the plate due to localized in-plane loading was estimated by solving the in-plane elasticityproblem using Airy’s stress approach. The nonlinear governing partial differential equations (PDEs) of the FG-CNTRLC plate were derivedusing Hamilton’s principle. The Galerkin method was used to convert these nonlinear PDEs to the nonlinear ordinary differential equations(ODEs). The nonlinear ODEs were solved using the incremental harmonic balance (IHB) method to obtain the nonlinear vibration responseof the FG-CNTRLC plate. After dropping the nonlinear terms, the linear ODEs were solved by the Bolotin method to trace the dynamicinstability regions. The effect of different parameters such as volume fraction of CNTs, different types of localized in-plane loadings, typesof CNTs distribution, the static and dynamic load factor on the dynamic instability regions, and the nonlinear vibration characteristics of theFG-CNTRLC plate, were examined