Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam


Avcar M.

STRUCTURAL ENGINEERING AND MECHANICS, vol.55, no.4, pp.871-884, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 4
  • Publication Date: 2015
  • Doi Number: 10.12989/sem.2015.55.4.871
  • Title of Journal : STRUCTURAL ENGINEERING AND MECHANICS
  • Page Numbers: pp.871-884
  • Keywords: rotary inertia, shear deformation, material non-homogeneity, natural frequency, beam, FREE-VIBRATION ANALYSIS, DIFFERENTIAL TRANSFORM METHOD, LINEARLY VARYING THICKNESS, CLOSED-FORM SOLUTIONS, HIGHER-ORDER SHEAR, NATURAL FREQUENCIES, RECTANGULAR-PLATES, ROTATORY INERTIA, TIMOSHENKO BEAMS, EFFICIENT

Abstract

In the present study, separate and combined effects of rotary inertia, shear deformation and material non-homogeneity (MNH) on the values of natural frequencies of the simply supported beam are examined. MNH is characterized considering the parabolic variations of the Young's modulus and density along the thickness direction of the beam, while the value of Poisson's ratio is assumed to remain constant. At first, the equation of the motion including the effects of the rotary inertia, shear deformation and MNH is provided. Then the solutions including frequencies of the first three modes for various combinations of the parameters of the MNH, depth to length ratios, and shear corrections factors are reported. To show the accuracy of the present results, two comparisons are carried out and good agreements are found.