FLEXURAL MOTIONS UNDER ACCELERATING LOADS OF STRUCTURALLY PRESTRESSED BEAMS WITH GENERAL BOUNDARY CONDITIONS

Authors

  • BABATOPE OMOLOFE DEPARTMENT OF MATHEMATICAL SCIENCES, SCHOOL OF SCIENCES, THE FEDERAL UNIVERSITY OF TECHNOLOGY, PMB 704, AKURE, ONDO STATE, NIGERIA
  • SUNDAY TUNBOSUN ONI DEPARTMENT OF MATHEMATICAL SCIENCES, SCHOOL OF SCIENCES, THE FEDERAL UNIVERSITY OF TECHNOLOGY, PMB 704, AKURE, ONDO STATE, NIGERIA

Keywords:

RAYLEIGH BEAM, RESONANCE PHENOMENON, ASYMPTOTIC METHOD, CONCENTRATED MASSES, TRANSVERSE VIBRATION, SLENDERNESS RATIO

Abstract

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THE TRANSVERSE VIBRATION OF A PRISMATIC RAYLEIGH BEAM RESTING ON ELASTIC FOUNDATION AND CONTINUOUSLY ACTED UPON BY CONCENTRATED MASSES MOVING WITH ARBITRARILY PRESCRIBED VELOCITY IS STUDIED. A PROCEDURE INVOLVING GENERALIZED FINITE INTEGRAL TRANSFORM, THE USE OF THE EXPRESSION OF THE DIRAC DELTA FUNCTION IN SERIES FORM, A MODIFICATION OF THE STRUBLE’S ASYMPTOTIC METHOD AND THE USE OF THE FRESNEL SINE AND COSINE FUNCTIONS IS DEVELOPED TO TREAT THIS DYNAMICAL BEAM PROBLEM AND ANALYTICAL SOLUTIONS FOR BOTH THE MOVING FORCE AND MOVING MASS MODEL WHICH IS VALID FOR ALL VARIANT OF CLASSICAL BOUNDARY CONDITIONS ARE OBTAINED. THE PROPOSED ANALYTICAL PROCEDURE IS ILLUSTRATED BY EXAMPLES OF SOME PRACTICAL ENGINEERING INTEREST IN WHICH THE EFFECTS OF SOME IMPORTANT PARAMETERS SUCH AS BOUNDARY CONDITIONS, PRESTRESSED FUNCTION, SLENDERNESS RATIO, MASS RATIO AND ELASTIC FOUNDATION ARE INVESTIGATED IN DEPTH.  RESONANCE PHENOMENON OF THE VIBRATING SYSTEM IS CAREFULLY INVESTIGATED AND THE CONDITION UNDER WHICH THIS MAY OCCUR IS CLEARLY SCRUTINIZED. THE RESULTS PRESENTED IN THIS PAPER WILL FORM BASIS FOR A FURTHER RESEARCH WORK IN THIS FIELD.

Author Biographies

BABATOPE OMOLOFE, DEPARTMENT OF MATHEMATICAL SCIENCES, SCHOOL OF SCIENCES, THE FEDERAL UNIVERSITY OF TECHNOLOGY, PMB 704, AKURE, ONDO STATE, NIGERIA

FACULTY MEMBER, DEPARTMENT OF MATHEMATICAL SCIENCES, SCHOOL OF SCIENCES, THE FEDERAL UNIVERSITY OF TECHNOLOGY, PMB 704, AKURE, ONDO STATE, NIGERIA

 

SUNDAY TUNBOSUN ONI, DEPARTMENT OF MATHEMATICAL SCIENCES, SCHOOL OF SCIENCES, THE FEDERAL UNIVERSITY OF TECHNOLOGY, PMB 704, AKURE, ONDO STATE, NIGERIA

FACULTY MEMBER, DEPARTMENT OF MATHEMATICAL SCIENCES, SCHOOL OF SCIENCES, THE FEDERAL UNIVERSITY OF TECHNOLOGY, PMB 704, AKURE, ONDO STATE, NIGERIA

 

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Published

2010-09-02

Issue

Vol. 7 No. 3 (2010)

Section

Articles

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