Vibration characteristics of stepped beams made of FGM using differential transformation method

Wattanasakulpong, Nuttawit; Charoensuk, Jarruwat

doi:10.1007/s11012-014-0054-3

Cited by 30 publications

(14 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The algorithm ensures that no natural frequency of the structure is missed, and it has featured in literally hundreds of papers. It is worth noting that earlier investigations on the free vibration of FGBs were focused on individual FGBs except for a few isolated cases where stepped FGBs with collinear axes were reported [40,41]. Accordingly, the literature on the free vibration of frameworks containing FGBs is virtually non-existent.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

Banerjee

Ananthapuvirajah

2018

Journal of Sound and Vibration

View full text Add to dashboard Cite

The free vibration analysis of functionally graded beams (FGBs) and frameworks containing FGBs is carried out by applying the dynamic stiffness method and deriving the elements of the dynamic stiffness matrix in explicit algebraic form. The usually adopted rule that the material properties of the FGB vary continuously through the thickness according to a power law forms the fundamental basis of the governing differential equations of motion in free vibration. The differential equations are solved in closed analytical form when the free vibratory motion is harmonic. The dynamic stiffness matrix is then formulated by relating the amplitudes of forces to those of the displacements at the two ends of the beam. Next, the explicit algebraic expressions for the dynamic stiffness elements are derived with the help of symbolic computation. Finally the Wittrick-Williams algorithm is applied as solution technique to solve the free vibration problems of FGBs with uniform cross-section, stepped FGBs and frameworks consisting of FGBs. Some numerical results are validated against published results, but in the absence of published results for frameworks containing FGBs, consistency checks on the reliability of results are performed. The paper closes with discussion of results and conclusions.

show abstract

Section: Introductionmentioning

confidence: 99%

Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

Banerjee

Ananthapuvirajah

2018

Journal of Sound and Vibration

View full text Add to dashboard Cite

show abstract

“…This is in contrast to the traditional approach, where a zero centre of approximation is usually used for restoring the original, e.g. [36][37][38][39][40][41][42].…”

Section: Dtm Applied To Free Vibrations Of Inhomogeneous and Non-unifmentioning

confidence: 98%

“…Thus, the computational cost of the DTM increases with increasing the number of the beam sections, because more recurrent equations have to be solved. In [38] the DTM has been exploited to the free vibration analysis of FGM two-section-beams with thickwise material gradients. Natural frequencies of similar stepped FGM two-section-beams with elastically constrained ends have been calculated with the DTM in [39].…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of functionally graded beams with non-uniform cross-section using the differential transform method

et al. 2017

View full text Add to dashboard Cite

show abstract

“…It was shown by the authors that there is disaggreement between theoretical and experimental results. Wattanasakulpong and Charoensuk [10] studied one-step beam made of functionally graded material.…”

Section: Introductionmentioning

confidence: 99%

The Transfer Matrix Method for Modal Analysis of Cracked Multistep Beam

Khiem¹,

Ninh²,

Hai³

2017

JST

View full text Add to dashboard Cite

The present study addresses the modal analysis of multistep beam with arbitrary number of cracks by using the transfer matrix method and modal testing technique. First, there is conducted general solution of free vibration problem for uniform beam element with arbitrary number of cracks that allows one to simplify the transfer matrix for cracked multistep beam. The transferring beam state needs to undertake only at the steps of beam but not through crack positions. Such simplified the transfer matrix method makes straightforward to investigate effect of cracks mutually with cross-section step in beam on natural frequencies. It is revealed that step-down and step-up in beam could modify notably sensitivity of natural frequencies to crack so that the analysis provides useful indication for crack detection in multistep beam. The proposed theory was validated by an experimental case study.

show abstract

Vibration characteristics of stepped beams made of FGM using differential transformation method

Cited by 30 publications

References 28 publications

Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

Free vibration analysis of functionally graded beams with non-uniform cross-section using the differential transform method

The Transfer Matrix Method for Modal Analysis of Cracked Multistep Beam

Contact Info

Product

Resources

About