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 UNCOUPLED VIBRATIONS IN FUNCTIONALLY GRADED TIMOSHENKO BEAM

2016 ◽  
Vol 54 (6) ◽  
pp. 785 ◽  
Author(s):  
Nguyen Tien Khiem ◽  
Nguyen Ngoc Huyen
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Flexural Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Power Law Distribution ◽  
Material Parameters ◽  
Flexural Vibrations ◽  
Fgm Beam

Free vibration of FGM Timoshenko beam is investigated on the base of the power law distribution of FGM. Taking into account the actual position of neutral plane enables to obtain general condition for uncoupling of axial and flexural vibrations in FGM beam. This condition defines a class of functionally graded beams for which axial and flexural vibrations are completely uncoupled likely to the homogeneous beams. Natural frequencies and mode shapes of uncoupled flexural vibration of beams from the class are examined in dependence on material parameters and slendernes

EXACT VIBRATION FREQUENCIES AND MODES OF BEAMS WITH INTERNAL RELEASES

2002 ◽  
Vol 02 (01) ◽  
pp. 63-75 ◽  
Author(s):  
M. EISENBERGER
Keyword(s):  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Beam Element ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Dynamic Stiffness Matrix ◽  
Continuous Beams ◽  
Stiffness Method ◽  
Dynamic Stiffness Method

The exact vibration frequencies of continuous beams with internal releases are found using the dynamic stiffness method. Two types of releases are considered: hinge and sliding discontinuities. First, the exact dynamic stiffness matrix for a beam element with a release is derived and then used in the assembly of the structure dynamic stiffness matrix. The natural frequencies are found as the values of frequency that make this matrix singular. Then the mode shapes are found exactly. Examples are given for continuous beams with different releases.

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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