Exact free vibration analysis for mechanical system composed of Timoshenko beams with intermediate eccentric rigid body on elastic supports: An experimental and analytical investigation

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

doi:10.1016/j.ymssp.2016.05.029

Cited by 20 publications

(12 citation statements)

References 17 publications

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“…There are quite a number of studies in related fields, which deal with Timoshenko double-beam systems, finite element method, difference schemes, and various algorithms for nonlinear partial differential equations. We refer to the recent works of Asadollahi et al [35], Farghaly and El-Sayed [36], Kaya and Yokus [37], Osman et al [38], Rashidi et al [39], Shirvan et al [40], Sohail et al [41], Sulaiman et al [42], Yokus et al [43,44], and Zhao et al [45], et al…”

Section: Formulation Of the Problemmentioning

confidence: 99%

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A numerical algorithm for the nonlinear Timoshenko beam system

Peradze

Kalichava

2020

Numerical Methods Partial

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Section: Formulation Of the Problemmentioning

confidence: 99%

“…Let us return to condition (36), which we divide into five parts. To each of the five rows of the block representation of B ′ B, we assign a subsystem of Equation (36). Denote by kl ij the element of the block B kl , the row number and the column number of which are, respectively, equal to i and j.…”

Section: Proofmentioning

confidence: 99%

A numerical algorithm for the nonlinear Timoshenko beam system

Peradze

Kalichava

2020

Numerical Methods Partial

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“…The exact free vibration of a mechanical system composed of two elastic Timoshenko segments carried on an intermediate eccentric rigid body or on elastic supports was introduced by Farghaly and El-Sayed [34]. Their analysis was based on both analytical and experimental methods.…”

Section: Shock and Vibrationmentioning

confidence: 99%

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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“…The free vibration analysis of a two-part elastic segment with intermediate rigid body has been studied according to Bernoulli–Euler beam theory (Ilanko, 2003; Naguleswaran, 2004; Lin, 2010). The free vibration of a mechanical system composed of two elastic Timoshenko segments carried on an intermediate eccentric rigid body has been investigated analytically and experimentally (Farghaly and El-Sayed, 2017). The experimental results for several test samples were in good agreement with those obtained analytically (Farghaly and El-Sayed, 2017).…”

Section: Introductionmentioning

confidence: 99%

“…The free vibration of a mechanical system composed of two elastic Timoshenko segments carried on an intermediate eccentric rigid body has been investigated analytically and experimentally (Farghaly and El-Sayed, 2017). The experimental results for several test samples were in good agreement with those obtained analytically (Farghaly and El-Sayed, 2017).…”

Section: Introductionmentioning

confidence: 99%

Frequency equation using new set of fundamental solutions with application on the free vibration of Timoshenko beams with intermediate rigid or elastic span

El-Sayed

Farghaly

2017

Journal of Vibration and Control

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Stepped beams are crucial power transmission components in many mechanical engineering systems. These beams may be dynamically analyzed using the stepped Timoshenko model or the rigid mass model. In this paper, a new set of fundamental solutions is derived in order to normalize the Timoshenko beam equation at the origin of the coordinates. This set of solutions is used to derive the frequency equation of both stepped and rigid mass models. The validity ranges of these models were investigated by comparing the modal frequency results of both models. In addition, selected cases were compared using mode shape analysis. Three different models with classical end conditions are considered through this work. These are free–free, pinned–pinned and clamped–free beam configurations. The numerical results of the current work show that increasing the intermediate diameter ratio and decreasing the length ratio of the rigid mass results in decreasing the percentage deviation between the rigid mass model results and the elastic model results.

show abstract

Exact free vibration analysis for mechanical system composed of Timoshenko beams with intermediate eccentric rigid body on elastic supports: An experimental and analytical investigation

Cited by 20 publications

References 17 publications

A numerical algorithm for the nonlinear Timoshenko beam system

A numerical algorithm for the nonlinear Timoshenko beam system

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

Frequency equation using new set of fundamental solutions with application on the free vibration of Timoshenko beams with intermediate rigid or elastic span

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