NATURAL VIBRATIONS OF COMPOSITE BEAMS REINFORCED WITH NANO CARBON TUBES ON ELASTIC FOUNDATIONS ACCORDING TO THE THEORY OF HIGH-ORDER SHEAR STRAIN

Abstract

This paper develops the Ritz method to analyze the natural vibrations of laminated composite beams reinforced with Nano Carbon tubes. Beams placed on elastic foundation with Winkler elastic foundation model and beam calculation theory according to high-order shear strain theory. The central system of equations of the problem is established by the energy method combined with the Largrang - II equation. The results calculated by the proposed method are compared with those calculated by the finite element method to check suitability and accuracy. The investigation results show that: The elastic foundation coefficient affects almost linearly to the natural vibration frequency of the beam. The beam's natural frequency increases as the volume ratio of the Nano Carbon fiber increases. At the same time, in all distribution forms of Nano Carbon fiber, the X-shaped distribution or the beam with the greatest stiffness and the double-ended connection type is the mount with the highest vibration frequency in the investigated connection cases. In addition, when the angle of inclination of the Nano Carbon fiber increases or the ratio of span length and section height increases, the vibration frequency of the beam decreases.