Free vibration analysis of two dimensional functionally graded materials Timoshenko beam

Subject Areas : Information Technology in Engineering Design (ITED) Journal

Mohammad Rahim Torshizian ¹ (Mechanical Engineering Department, Mashhad Branch, Islamic Azad University, Mashhad, Iran.)
Abdalhosein Okhovatpour ² (MS.c., Mechanical Engineering Department, Mashhad Branch, Islamic Azad University, Mashhad, Iran)

Received: 2017-03-13 Accepted : 2017-03-13 Published : 2015-08-23

Keywords:

Abstract :

In this research is investigated the free vibration analysis of two dimensional functionally graded material beams with considering Timoshenko's theory. Material properties of the beam are assumed to vary continuously in the length and thickness direction and follow from exponentially function. The governing equations of motions are derived by using Hamilton's principle. Both axial and rotary inertia of the beam are considered in present analysis. The governing differential equations of motions are converted to a set of first order differential equations using the state space technique and natural frequencies are determined. The effects of length to thickness ratio, gradient indices and boundary conditions on natural frequencies are investigated.

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