Development of a Dynamic Stiffness Element for Free Vibration Analysis of a Moving Functionally Graded Beam

2015 ◽  
Author(s):  
J.R. Banerjee ◽  
W.D. Gunawardana
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Functionally Graded Beam

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

2020 ◽  
Vol 23 (16) ◽  
pp. 3415-3428
Author(s):  
Yusuf Cunedioglu ◽  
Shkelzen Shabani
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Crack Depth ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Single Edge ◽  
Functionally Graded Beam ◽  
Cross Sectional

Free vibration analysis of a single edge cracked multi-layered symmetric sandwich stepped Timoshenko beams, made of functionally graded materials, is studied using finite element method and linear elastic fracture mechanic theory. The cantilever functionally graded beam consists of 50 layers, assumed that the second stage of the beam (step part) is created by machining. Thus, providing the material continuity between the two beam stages. It is assumed that material properties vary continuously, along the thickness direction according to the exponential and power laws. A developed MATLAB code is used to find the natural frequencies of three types of the stepped beam, concluding a good agreement with the known data from the literature, supported also by ANSYS software in data verification. In the study, the effects of the crack location, crack depth, power law gradient index, different material distributions, different stepped length, different cross-sectional geometries on natural frequencies and mode shapes are analysed in detail.

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.

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