Exact free vibration of multi-step Timoshenko beam system with several attachments

Farghaly, S.H.; El-Sayed, T.A.

doi:10.1016/j.ymssp.2015.11.025

Cited by 30 publications

(19 citation statements)

References 31 publications

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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%

“…Yesilce [19] investigated the free vibration of stepped beams using exact numerical assembly technique (NAT) and using approximate differential transformation method. Recently, Farghaly and El-Sayed [6] drive the exact solution for the lateral vibration of Timoshenko beam with generalized start, end, and intermediate conditions using numerical assembly technique (NAT).…”

Section: Shock and Vibrationmentioning

confidence: 99%

“…Several beam start and end conditions are investigated as listed in Table 4. The results are evaluated using the present NTM method and previously published numerical assembly technique NAT [6] method. The computational time required to obtain the first three frequency parameters * 1 , * 2 , and * 3 using both NAT and NTM methods is calculated and listed in Table 4.…”

Section: Verification Examplementioning

confidence: 99%

“…The time used for computing the first three natural frequencies is evaluated. The model results are also evaluated using NAT previously published in [6] at = 20 in order to compare the time saving when using the present method.…”

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

confidence: 99%

“…Numerical assembly technique (NAT) is one of the common methods used for the evaluation of the eigenvalue problem for beams with multiple discontinuity [6][7][8]. In this method, the size of the frequency equation determinant is 4 × 4 for beam with segments.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

confidence: 86%

Section: Shock and Vibrationmentioning

confidence: 99%

Section: Verification Examplementioning

confidence: 99%

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

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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 Numerical Assembly Technique for arbitrary planar beam structures based on an improved homogeneous solution

Krämer

Gfrerer

2023

Proc Appl Math and Mech

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The Numerical Assembly Technique (NAT) is extended to investigate arbitrary planar frame structures with a focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial discretization. To this end, we systematically introduce a frame structure as a set of nodes, beams, bearings, springs, and external loads and formulate the corresponding boundary and coupling conditions. As the underlying homogeneous solution of the governing equations, we use a novel approach recently presented in the literature. This greatly improves the numerical stability and allows the stable computation of very high natural frequencies accurately. We show this improvement by investigating the condition number of the system matrix and also by the use of variable precision arithmetic.

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A two-parameter multiple shooting method and its application to the natural vibrations of non-prismatic multi-segment beams

Hołubowski,

Jarczewska

2023

Appl. Math. Mech.-Engl. Ed.

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Exact free vibration of multi-step Timoshenko beam system with several attachments

Cited by 30 publications

References 31 publications

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

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

The Numerical Assembly Technique for arbitrary planar beam structures based on an improved homogeneous solution

A two-parameter multiple shooting method and its application to the natural vibrations of non-prismatic multi-segment beams

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