HIGH PRECISE ANALYSIS OF LATERAL VIBRATION OF QUINTIC NONLINEAR BEAM

Authors

  • HAMID M. SEDIGHI DEPARTMENT OF MECHANICAL ENGINEERING, SHAHID CHAMRAN UNIVERSITY, AHVAZ, IRAN
  • ARASH REZA DEPARTMENT OF MECHANICAL ENGINEERING, SHAHID CHAMRAN UNIVERSITY, AHVAZ, IRAN

Keywords:

QUINTIC NONLINEARITY, PARAMETER EXPANSION METHOD, NONLINEAR VIBRATION OF BEAM, EXACT FORMULATION OF BEAM CURVATURE

Abstract

THIS ARTICLE INTENDS TO ACHIEVE A NEW FORMULATION OF BEAM VIBRATION WITH QUINTIC NONLINEARITY, INCLUDING EXACT EXPRESSIONS FOR THE BEAM CURVATURE. TO ATTAIN A PROPER DESIGN OF THE BEAM STRUCTURES, IT IS ESSENTIAL TO REALIZE HOW THE BEAM VIBRATES IN ITS TRANSVERSE MODE WHICH IN TURN YIELDS THE NATURAL FREQUENCY OF THE SYSTEM. IN THIS DIRECTION, NEW POWERFUL ANALYTICAL METHOD CALLED PARAMETER EXPANSION METHOD (PEM) IS EMPLOYED TO OBTAIN THE EXACT SOLUTION OF FREQUENCY-AMPLITUDE RELATIONSHIP. AFTERWARDS, IT IS CLEARLY SHOWN THAT THE FIRST TERM IN SERIES EXPANSIONS IS SUFFICIENT TO PRODUCE A HIGHLY ACCURATE APPROXIMATION OF MENTIONED SYSTEM. FINALLY, PRECISENESS OF THE PRESENT ANALYTIC PROCEDURES IS EVALUATED IN CONTRAST WITH NUMERICAL CALCULATIONS METHODS, GIVING EXCELLENT RESULTS.

Downloads

Published

2013-01-28

Issue

Vol. 10 No. 2 (2013)

Section

Articles

License

Authors who publish with this journal agree to the following terms:

 

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY] that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).