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Amit Kumar Rai

About


Ph.D. Indian Institute of Technology Kanpur 2020 (Mechanical Engineering)

M.Tech. MNNIT Allahabad 2010 (Applied Mechanics)

B.Tech KNIT Sultanpur 2007  (Mechanical Engineering)

RESEARCH INTEREST

Research area: Dynamics and Vibrations of Beams, Plates and Shells; Computational mechanics; Functionally Graded Materials.

 

 

Academic Qualifications


Ph.D. (July 2014 – March 2020) (Mechanical Engineering/Solid Mechanics and Design): IIT Kanpur
M. Tech. (2008 - 10) (Applied Mechanics): Motilal Nehru National Institute of Technology Allahabad
B.Tech.(2003–07) (Mechanical Engineering): Kamla Nehru Institute of Technology Sultanpur
 

Research Statement


My research interests lie in the field of linear and nonlinear dynamic analysis of structures
incorporation with large amplitude vibration. Specifically, my research focuses on the dynamics
response of structures under moving loads. An important class of structural dynamics problem,
which always attracted the researchers involves the dynamic response of an elastic system due
to moving loads. These classes of problems are interesting problems in engineering. The dynamic
response quantities, such as deflections, stresses are always higher than the static response, so its
dynamic behavior needs to be studied properly. The elastic system, such as strings, beam, plates,
and shells are subjected to moving point loads. Most of the structures in the transportation field, e.g.
roadways, runways, bridges, guide-ways, overhead cranes, cable-ways, rails, and in other fields
such as, weapon firing barrels are the practical examples. Also, moving load problems involving
circular plates are important in the manufacturing industry, for example cutting of thin annular
plates using point-cutting tools and wood/bar/pipe cutting saws. This makes the moving load
problem special in structural dynamics. The behavior of such structures under moving loads needs to
be understood for their proper design. Further, moving point loads has application in musical
instruments, like Tabla, Tibetan bowls, and Hawayein guitar.
In light of these real-life applications of moving load problems, my research program concentrates
on linear and nonlinear dynamic analysis of plate under moving point loads for different boundary
conditions. Specifically, my current research involves the nonlinear dynamic analysis of circular
plates subjected to moving concentrated loads. The plate under consideration is having two different
material properties namely, isotropic and polar orthotropic circular plate. In isotropic plate, we have
considered the material properties are independent of directions, while in orthotropic plate the
material properties vary in two orthogonal directions.
Isotropic plate:
The governing equations of motion and associated boundary conditions are obtained following
Kirchhoff's theory incorporating von-Karman nonlinearity and employing Hamilton's principle.
For plates made of linearly elastic and isotropic materials, the governing equations (PDEs) are
solved using Galerkin’s method. The resulting coupled and cubic nonlinear ordinary
differential equations are solved using the method of harmonic balance with the arc continuation
method for frequency response and the Runge-Kutta method for time response. The correctness of the
formulation is checked with the response obtained from Green's function approach for the linear
case. For linear case expression for the critical angular speed of the moving load is found as a
function of the natural frequencies of the plate. It is found that the resonance instability can be
avoided if the rotating load at a fixed radius is split into multiple loads rotating at the same radius.
The hardening frequency response of transverse displacement in the nonlinear case shows jumps
with an increasing steady-state angular velocity of circularly moving loads. The spectrums of time
histories of transverse and radial displacements show super- and sub-harmonics of the angular
speed of rotation of the load. The transverse and radial displacements have also been studied for
spirally and radially moving loads.
Orthotropic Plate
For plates made of orthotropic materials, nonlinear governing equations are derived by Hamilton's
principle. The plate material is assumed to be linearly elastic and polar orthotropic. von-Karman
strain displacement is used to capture the geometric nonlinearity. Towards finding the solution of
nonlinear equations eigenfrequencies and eigenfunctions are computed by solving the fourth order
differential equation with variable coefficients. Therefore, computing the response to moving point
loads, the eigenfrequencies and eigenfunctions are found using the Frobenius method. Galerkin’s
method is employed to solve nonlinear PDEs. The resulting coupled ordinary differential
equations are solved using the Runge-Kutta method. Method of harmonic balanced followed by arc
continuation method is used to find the effect of varying forced frequency on the amplitude of
circular orthotropic plate. Increasing radial direction modulus decreases the frequencies of
symmetric and anti-symmetric modes. Similar to the case of the isotropic plate a comprehensive
study of the linear response of orthotropic plate is carried out subjected to point load moving on
a circular path.

Latest Publications


  • 1 Rai, Amit K.; Shakti S. Gupta, Nonlinear vibrations of polar-orthotropic thin circular plate subjected to circularly moving point loads, 256, 112953, Composite Structures, 2020
  • 2 Rai, Amit K., and Shakti S. Gupta, Nonlinear vibrations of a thin isotropic circular plate subjected to moving point loads., 0954406220976156., Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2020
  • 3 Rai, Amit K.,; Shakti S. Gupta, Nonlinear vibration of circular plate under moving point loads., 1, 610, US National Congress on Computational Mechanics, Austin, Texas USA, 2019
  • 4 Amit K. rai ; Shakti S. Gupta, Vibration of orthotropic circular plate under moving point load, IWCEM, Jaipur-2017, 2017
  • 5 Arpit Sharma; Amit K. rai ; Shakti S. Gupta, Vibration of simply supported circular plate subjected to moving point loads, 3, 3019-3020, 24th International Congress of Theoretical and Applied Mechanics. Montreal, Canada., 2016
  • View More

    Research Areas


    • Computational Mechanics
    • Functionally Graded Material.
    • Dynamic analysis of beams and plates.
    • Nonlinear vibration

    Publications


  • 1 Rai, Amit K.,; Shakti S. Gupta, Nonlinear vibration of circular plate under moving point loads., 1, 610, US National Congress on Computational Mechanics, Austin, Texas USA, 2019
  • 2 Amit K. rai ; Shakti S. Gupta, Vibration of orthotropic circular plate under moving point load, IWCEM, Jaipur-2017, 2017
  • 3 Arpit Sharma; Amit K. rai ; Shakti S. Gupta, Vibration of simply supported circular plate subjected to moving point loads, 3, 3019-3020, 24th International Congress of Theoretical and Applied Mechanics. Montreal, Canada., 2016
  • Patents


    # Patents Year

    Created: 23 November 2019