Phân tích dao động tự do của dầm FGM Timoshenko bằng phương pháp độ cứng động lực

In this paper, free vibration of a functionally graded material (FGM) beam is investigated based on the Timoshenko beam theory and dynamic stiffness method. Material properties vary continuously throughout the thickness direction according to the volume fraction constituent defined by power law function. First, a consistent theory of vibration is established for FGM Timoshenko beam taking into account the actual position of neutral axis that is a useful tool for analysis of coupled vibration in the beam. Then, frequency equation obtained provides an efficient method for free vibration analysis of FGM Timoshenko beam. The theoretical development has been illustrated and validated by numerical examples. Keywords: FGM; timoshenko beam; natural frequency; dynamic stiffness method; Received: July 21th, 2016, revised: August 4th, 2016, accepted: October 13th, 2016