Free Vibration of a Functionally Graded Timoshenko Beam using the Dynamic Stiffness Method

2012 ◽  
Author(s):  
H. Su ◽  
J.R. Banerjee
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Dynamic Stiffness ◽  
Functionally Graded ◽  
Stiffness Method ◽  
Dynamic Stiffness Method

scholarly journals Mode shape analysis of multiple cracked functionally graded beam-like structures by using dynamic stiffness method

2017 ◽  
Vol 39 (3) ◽  
pp. 215-228 ◽  
Author(s):  
Tran Van Lien ◽  
Ngo Trong Duc ◽  
Nguyen Tien Khiem
Keyword(s):  
Timoshenko Beam ◽  
Dynamic Stiffness ◽  
Beam Theory ◽  
Functionally Graded ◽  
Theoretical Development ◽  
Mode Shapes ◽  
Functionally Graded Beam ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Fgm Beam

Mode shapes of multiple cracked beam-like structures made of Functionally Graded Material (FGM) are analyzed by using the dynamic stiffness method. Governing equations in vibration theory of multiple cracked FGM beam are derived on the base of Timoshenko beam theory; power law variation of material; coupled spring model of crack and taking into account the actual position of neutral axis. A general solution of vibration in frequency domain is obtained and used for constructing dynamic stiffness matrix of the multiple cracked FGM Timoshenko beam element that provides an efficient method for modal analysis of multiple cracked FGM frame structures. The theoretical development is illustrated by numerical analysis of crack-induced change in mode shapes of multi-span continuous FGM beam.

scholarly journals Review of the dynamic stiffness method for free-vibration analysis of beams

2019 ◽  
Vol 1 (2) ◽  
pp. 106-116 ◽  
Author(s):  
J R Banerjee
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Solution Technique ◽  
Wide Range ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Vibration Problems

Abstract The application of the dynamic stiffness method (DSM) for free-vibration analysis of beams is surveyed in this paper. The historical development of the DSM, which has taken place in several stages, is discussed in detail with reference to the free-vibration problems of beams. In particular, the suitability of the DSM in solving the free-vibration problems of beams through the application of the well-known Wittrick–Williams algorithm as a solution technique is highlighted. The literature concerning homogeneous isotropic metallic beams, for which the DSM is well established, is reviewed first, after which, with the rapid and ongoing emergence of advanced composite materials, the development of the DSM in solving the free-vibration problems of anisotropic beams is discussed. The free-vibration analysis of functionally graded beams using the DSM is also highlighted. The survey covers the DSM application for free-vibration analysis of a wide range of beams, including sandwich beams, rotating beams, twisted beams, moving beams and bending-torsion coupled beams, amongst others. Some aspects of the contributions made by the author and his research team are also highlighted. Finally, the future potential of the DSM in solving complex engineering problems is projected.

Sign in / Sign up

Export Citation Format

Share Document