Implementing Basic Displacement Function to Analyze Free Vibration Rotation of Non-Prismatic Euler-Bernoulli Beams

Subject Areas : Structural Engineering

Pouria  Hajikarimi ¹ (Instructor, Department of Civil Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran)
Reza  Attarnejad ² (Professor, School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran)

Received: 2016-10-02 Accepted : 2016-12-18 Published : 2017-03-30

Keywords: Free vibration, Euler-Bernoulli beam, Non-prismatic, Basic Displacement Functions, Energy methods,

Abstract :

Rotating beams have been considerably appealing to engineers and designers of complex structures i.e. aircraft’s propeller and windmill turbines. In this paper, a new flexibility-based method is proposed for the dynamic analysis of rotating non-prismatic Euler-Bernoulli beams. The flexibility basis of the method ensures the true satisfaction of equilibrium equations at any interior point of the elements. Following structural/mechanical principles, exact shape functions and consequently exact structural matrices i.e. consistent mass, geometric stiffness and flexural stiffness matrices are derived in terms of special so-called “Basic Displacement Functions”. The method is considered as the logical extension of conventional finite element method. Being straightforward formulated, the method can be incorporated into any standard finite element programs. The method poses no restrictions on either type of cross-section or variation of cross-sectional dimensions. The effects of rotational speed parameter and taper ratio on the variation of natural frequencies are studied and the results compare well with the other existing methods in the technical literature.