A Direct Solution for the Transverse Vibration of Euler-Bernoulli Wedge and Cone Beams

Naguleswaran, S.

doi:10.1006/jsvi.1994.1176

Cited by 76 publications

(44 citation statements)

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“…The parameter Ω calculated by the authors is slightly higher than the values given by Naguleswaran (1994). The relative error δ does not exceed 1.7% for the truncated cone and 0.5% for the truncated wedge and the difference does not exceed 0.3% in average.…”

Section: Computational Examples Validation Of Resultscontrasting

confidence: 49%

“…The results obtained in this study from the calculations for beams characterized by the convergence of lateral faces from 1 to 10 are compared to the results of a benchmark solution for free vibrations of Euler--Bernoulli beam, given by Naguleswaran (1994). The comparison is contained in Table 2 (truncated cone beam) and Table 3 (truncated wedge beam); a dimensionless frequency parameter Ω, presented in these tables, is described by:…”

Section: Computational Examples Validation Of Resultsmentioning

confidence: 99%

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2018

ACTA SCIENTIARUM POLONORUM - Architectura Budownictwo

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Section: Computational Examples Validation Of Resultscontrasting

confidence: 49%

Section: Computational Examples Validation Of Resultsmentioning

confidence: 99%

Untitled

2018

ACTA SCIENTIARUM POLONORUM - Architectura Budownictwo

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“…On the other hand, the results show that increasing the number of spans results in increasing the computational time. The comparison between the computational time using the present NTM and previously published NAT shows that the Shock and Vibration Table 10: The first three eigenvalues for C-F conical beam using NTM in comparison with those of the exact solution presented in [30] and NAT results using the program of [6].…”

Section: Percentage Modal Deviation Between Fe(3d) and Ntmmentioning

confidence: 86%

“…The results of Table 10 show that increasing the number of spans results in increasing the accuracy of the evaluated beam eigenvalues in comparison with the exact solution in [30]. On the other hand, the results show that increasing the number of spans results in increasing the computational time.…”

Section: Percentage Modal Deviation Between Fe(3d) and Ntmmentioning

confidence: 94%

A Normalized Transfer Matrix Method for the Free Vibration of Stepped Beams: Comparison with Experimental and FE(3D) Methods

El-Sayed

Farghaly

2017

Shock and Vibration

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The exact solution for multistepped Timoshenko beam is derived using a set of fundamental solutions. This set of solutions is derived to normalize the solution at the origin of the coordinates. The start, end, and intermediate boundary conditions involve concentrated masses and linear and rotational elastic supports. The beam start, end, and intermediate equations are assembled using the present normalized transfer matrix (NTM). The advantage of this method is that it is quicker than the standard method because the size of the complete system coefficient matrix is 4 × 4. In addition, during the assembly of this matrix, there are no inverse matrix steps required. The validity of this method is tested by comparing the results of the current method with the literature. Then the validity of the exact stepped analysis is checked using experimental and FE(3D) methods. The experimental results for stepped beams with single step and two steps, for sixteen different test samples, are in excellent agreement with those of the threedimensional finite element FE(3D). The comparison between the NTM method and the finite element method results shows that the modal percentage deviation is increased when a beam step location coincides with a peak point in the mode shape. Meanwhile, the deviation decreases when a beam step location coincides with a straight portion in the mode shape.

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“…(Naguleswaran [7], 1994) found a solution for transverse vibration of Euler Bernoulli beams and conical beams. In (Abrate [1], 1995), were obtained natural frequencies Euler Bernoulli beams (EB) when solution of the equation of EB was expressed by elementary functions.…”

Section: Introductionmentioning

confidence: 99%