Department of Civil Engineering

Permanent URI for this collectionhttp://localhost:4000/handle/123456789/1927

Browse

Subject: search.filters.subject.Nonlinear Vibration

Search Results

Now showing 1 - 5 of 5
  • No Thumbnail Available
    Item
    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.
  • No Thumbnail Available
    Item
    A semi-analytical approach for instability analysis of composite cylindrical shells subjected to harmonic axial loading
    (Elsevier, 2022-09) Kumar, Rajesh
    In this article, nonlinear vibration and dynamic stability analyses of simply supported laminated composite circular cylindrical shells subjected to periodic edge loading are carried out. A third-order shear deformation shell theory that considers all the nonlinear terms in all five kinematic parameters and rotary inertia is used to develop the present mathematical model so that the model is also valid for thick cylindrical shells. Hamilton’s principle, an energy-based approach, is used to obtain the governing partial differential equations (PDEs) of motion of the cylindrical shell. Further, these equations are reduced into ordinary differential equations by employing Galerkin’s method. The incremental harmonic balance (IHB) method in conjunction with the pseudo-arc-length method is used to obtain the frequency-amplitude response of the system. For obtaining the zone of instability regions, Bolotin’s method is adopted. For more practical significance, analysis of results is also extended by considering damping into account for the composite cylindrical shells. Time history response and phase portrait are plotted by adopting Newmark-beta method. The effects of the static load factor, dynamic load factor, modal damping coefficient, and stacking sequence on nonlinear vibration, instability regions and time history responses are also examined.
  • No Thumbnail Available
    Item
    Size-dependent nonlinear vibration and instability of a damped microplate subjected to in-plane parametric excitation
    (Elsevier, 2023-03) Kumar, Rajesh
    The semi-analytical framework for nonlinear vibration and dynamic instability of a damped microplate under periodic parametric excitation is presented. The microplate is modeled using the higher-order shear deformation theory (HSDT) in conjugation with the modified strain gradient theory (MSGT). The governing partial differential equations of motion are obtained using Hamilton’s principle and further solved using Galerkin’s method. The ordinary differential equations without the nonlinear terms are solved using Bolotin’s method to obtain the dynamic instability region. A combination of the incremental harmonic balance (IHB) and the arc-length continuation methods is used to obtain the nonlinear forced vibration response. The effect of initial displacements on the steady-state response of the microplate is discussed. The Newmark- method is used to obtain the time-history response plots. A comparison of results with those obtained from modified couple stress theory (MCST) and classical continuum theory (CCT) are examined. The effect of various parameters, such as the size of a plate, damping coefficient, static and dynamic loading factors, different boundary conditions, and different loading profiles, on the width of linear and nonlinear instability regions, are also studied.
  • No Thumbnail Available
    Item
    Geometrically nonlinear dynamic analysis of a damped porous microplate resting on elastic foundations under transverse patch loadings
    (Taylor & Francis, 2023-06) Kumar, Rajesh
    This is a unique study in which a damped porous microplate’s nonlinear vibration and response are analyzed semi-analytically using MSGT and HSDT under localized loading. The substrate is modeled using the Winkler-Pasternak elastic foundation. Partial differential equations are obtained using Hamilton’s principle and solved by Galerkin’s method. IHB and Newmark’s methods are used to trace the nonlinear vibration and response. The results show that uniform porosity leads to lower stiffness compared to symmetric porosity distribution. Pasternak foundation parameter has a larger impact on stiffness compared to Winkler parameter. The effect of geometric nonlinearity is weakened while using MSGT.
  • No Thumbnail Available
    Item
    Geometrically nonlinear dynamic analysis of a damped porous microplate resting on elastic foundations under in-plane nonuniform excitation
    (Taylor & Francis, 2023-07) Kumar, Rajesh; Patel, Shuvendu Narayan
    This article uses the semi-analytical approach to study the combined nonlinear vibration and nonlinear response of a damped porous microplate under nonuniform periodic parametric excitation to understand the complete nonlinear dynamic behavior of the plate. The plate is supported by a Winkler-Pasternak elastic foundation and modeled using modified strain gradient and third-order shear deformation theories to simulate the small-scale effects and shear deformation, respectively. Using Hamilton’s principle, the governing partial differential equations of motion are derived and solved using Galerkin’s method to convert them into ordinary differential equations (ODEs). These ODEs are solved using a combined incremental harmonic balance (IHB) and arc-length continuation approaches to get the nonlinear vibration (frequency–amplitude curves). The same ODEs are solved using the Newmark-β technique to obtain the nonlinear response (time–amplitude curves). The effect of elastic foundation parameters and aspect ratio on mode shape is presented. The effect of parameters such as the porosity coefficient, type of porosity, Winkler-Pasternak elastic foundation parameters, different size-dependent theories, plate thickness, size of plate, damping coefficient, different loading profiles, and loading concentrations on the nonlinear vibration and nonlinear response is examined. Also, the dependence of initial displacements on the frequency–amplitude curves with respect to the excitation frequency is demonstrated with the help of time-amplitude curves.