Development of dynamic stiffness method for free vibration of functionally graded Timoshenko beams. (15th January 2015)

• Record Type: Journal Article
• Authors: Su, H.; Banerjee, J.R.
• Is Part Of: Computers & structures. Volume 147(2015)
• Page Start: 107
• Page End: 116
• Publication Date: 2015-01-15
• Subjects: Free vibration -- Functionally graded beams -- Dynamic stiffness method -- Wittrick–Williams algorithm -- Timoshenko beam theory; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2014.10.001
• Languages: English
• ISSNs: 0045-7949

Abstract

Abstract: The free vibration of functionally graded Timoshenko beams is investigated by developing the dynamic stiffness method. Material properties of the beam are assumed to vary continuously in the thickness direction. The governing differential equations of motion are solved and expressions for axial force, shear force and bending moment are derived. The dynamic stiffness matrix is then formulated by relating the amplitudes of forces and displacements at the ends of the beam. The Wittrick–Williams algorithm is used as solution technique to yield the natural frequencies and mode shapes of some illustrative examples. The results are discussed and some conclusions are drawn.