Geometrically Non-Linear Frequency Response of Axially Functionally Graded Beams Resting on Elastic Foundation Under Harmonic Excitation

Hareram Lohar, Anirban Mitra and Sarmila Sahoo
Additional contact information
Hareram Lohar: Department of Mechanical Engineering, Jadavpur University, Kolkata, India
Anirban Mitra: Department of Mechanical Engineering, Jadavpur University, Kolkata, India
Sarmila Sahoo: Department of Civil Engineering, Heritage Institute of Technology, Kolkata, India

International Journal of Manufacturing, Materials, and Mechanical Engineering (IJMMME), 2018, vol. 8, issue 3, 23-43

Abstract: This article presents geometrically nonlinear forced vibration analysis of an axially functionally graded (AFG) non-uniform beam resting on an elastic foundation. The mathematical formulation is displacement based and derivation of governing equations is accomplished following Hamilton's principle. The foundation has been mathematically incorporated into the analysis as a set of linear springs. According to the basic assumption of the present method force equilibrium condition is satisfied at a maximum excitation amplitude value. Thus, the dynamic problem is equivalently represented as a static one, which is solved by following a numerical implementation of the Broyden method. It is a method that utilizes the Jacobian matrix and subsequent correction of the initial Jacobian to solve a system of nonlinear equations. The large amplitude dynamic behaviour of the system in terms of non-dimensional frequency response curves is validated against established results and new results are furnished for a parabolic tapered AFG beam on a linear elastic foundation.

Date: 2018
References: Add references at CitEc
Citations:

Downloads: (external link)
http://services.igi-global.com/resolvedoi/resolve. ... 18/IJMMME.2018070103 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:igg:jmmme0:v:8:y:2018:i:3:p:23-43

Access Statistics for this article

International Journal of Manufacturing, Materials, and Mechanical Engineering (IJMMME) is currently edited by J. Paulo Davim

More articles in International Journal of Manufacturing, Materials, and Mechanical Engineering (IJMMME) from IGI Global
Bibliographic data for series maintained by Journal Editor ().