An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories | Zendy

RamazanAli JafariTalookolaei | Zendy; M. H. Kargarnovin | Zendy; Mohammad Taghi Ahmadian | Zendy; Maryam Abedi | Zendy

Open Access

An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories

Author(s) -

RamazanAli JafariTalookolaei,

M. H. Kargarnovin,

Mohammad Taghi Ahmadian,

Maryam Abedi

Publication year - 2011

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2011/842805

Subject(s) - vibration , nonlinear system , deflection (physics) , boundary value problem , homotopy analysis method , rotary inertia , structural engineering , buckling , bernoulli's principle , transverse vibration , timoshenko beam theory , euler's formula , mathematics , transverse plane , mathematical analysis , physics , classical mechanics , engineering , acoustics , quantum mechanics , thermodynamics

The objective of this study is to present a brief survey on the geometrically nonlinear free vibrations of the Bernoulli-Euler, the Rayleigh, shear, and the Timoshenko beams with simple end conditions using the Homotopy Analysis Method (HAM). Expressions for the natural frequencies, the transverse deflection, postbuckling load-deflection relation to, and critical buckling load are presented. The results of nonlinear analysis are validated with the published results, and excellent agreement is observed. The effects of some parameters, such as slender ratio, the rotary inertia, and the shear deformation, are examined as other parameters are fixed

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research