Recursive eigenvalue search algorithm for transfer matrix method of linear flexible multibody systems

Bestle, Dieter; Abbas, Laith K.; Rui, Xiaoting

doi:10.1007/s11044-013-9399-y

Cited by 72 publications

(57 citation statements)

References 5 publications

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“…This procedure can be cumbersome for several reasons. Therefore, reliable and efficient algorithms called recursive scanning approach are applied (see [17] for more details of the proposed algorithm) by switching from zero search for Δ to minimization of the absolute value |Δ| of the determinant, which is equally well applicable to both the real and the complex cases. The algorithm general idea is as follows.…”

Section: Reliability Of the Suggested Scenariomentioning

confidence: 99%

“…The algorithm proceeds until the required precision of roots is achieved. MS-TMM natural frequency results are obtained using fMin1D algorithm [17] …”

Section: Reliability Of the Suggested Scenariomentioning

confidence: 99%

“…The given values of damping are 1,1 = 2,1 = 1,2 = 2,2 = = 5 √ / 2 . Next, it is the turn to implement fMin2D algorithm [17] for complex eigenproblem solution. For undamped given system as it is computed above, values do not exceed more than 10, which is equivalent to ( = ≤ 1500 rad/sec).…”

Section: Free Vibration Of Damped Elastically Coupled Triplementioning

confidence: 99%

“…Motivated by the interesting study by Kukla [2] which was published on the problem of the natural longitudinal vibrations of two rods coupled by many translational springs and by the two novel algorithms based on the new recursive scanning approach presented by Bestle et al [17], this paper presents a unique yet simple scenario of obtaining the exact free vibration characteristics of undamped/damped multilevel beam coupled elastically. The scenario developed in this paper is based on MS-TMM and Euler-Bernoulli beam theory.…”

Section: Introductionmentioning

confidence: 99%

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Free Vibration Characteristic of Multilevel Beam Based on Transfer Matrix Method of Linear Multibody Systems

Abbas

Rui

2014

Advances in Mechanical Engineering

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In this paper, an approach based on transfer matrix method of linear multibody systems (MS-TMM) is developed to analyze the free vibration of a multilevel beam, coupled by spring/dashpot systems attached to them in-span. The Euler-Bernoulli model is used for the transverse vibration of the beams, and the spring/dashpot system represents a simplified model of a viscoelastic material. MS-TMM reduces the dynamic problem to an overall transfer equation which only involves boundary state vectors. The state vectors at the boundaries are composed of displacements, rotation angles, bending moments, and shear forces, which are partly known and partly unknown, and end up with reduced overall transfer matrix. Nontrivial solution requires the coefficient matrix to be singular to yield the required natural frequencies. This paper implements two novel algorithms based on the methodology by reducing the zero search of the reduced overall transfer matrix's determinate to a minimization problem and demonstrates a simple and robust algorithm being much more efficient than direct enumeration. The proposal method is easy to formulate, systematic to apply, and simple to code and can be extended to complex structures with any boundary conditions. Numerical results are presented to show the validity of the proposal method against the published literature.

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Section: Reliability Of the Suggested Scenariomentioning

confidence: 99%

“…The algorithm proceeds until the required precision of roots is achieved. MS-TMM natural frequency results are obtained using fMin1D algorithm [17] …”

Section: Reliability Of the Suggested Scenariomentioning

confidence: 99%

Section: Free Vibration Of Damped Elastically Coupled Triplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Free Vibration Characteristic of Multilevel Beam Based on Transfer Matrix Method of Linear Multibody Systems

Abbas

Rui

2014

Advances in Mechanical Engineering

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“…The transfer matrix method of multibody system (MS-TMM) [10] was developed by Xiaoting Rui in 1993 and was mainly divided into the transfer matrix method of linear multibody system [11] and discrete time transfer matrix method [12]. The former method mainly determined the vibration characteristics of a linear multibody system [13], while the latter mainly solved the time-varying, nonlinear, large motion, controlled, or another general multibody system dynamic problem [14].…”

Section: Introductionmentioning

confidence: 99%

Study on the Seismic Response of a Portal Frame Structure Based on the Transfer Matrix Method of Multibody System

Ding

Zhuang

Wang

2014

Advances in Mechanical Engineering

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Portal frame structures are widely used in industrial building design but unfortunately are often damaged during an earthquake. As a result, a study on the seismic response of this type of structure is important to both human safety and future building designs. Traditionally, finite element methods such as the ANSYS and MIDAS have been used as the primary methods of computing the response of such a structure during an earthquake; however, these methods yield low calculation efficiencies. In this paper, the mechanical model of a single-story portal frame structure with two spans is constructed based on the transfer matrix method of multibody system (MS-TMM); both the transfer matrix of the components in the model and the total transfer matrix equation of the structure are derived, and the corresponding MATLAB program is compiled to determine the natural period and seismic response of the structure. The results show that the results based on the MS-TMM are similar to those obtained by ANSYS, but the calculation time of the MS-TMM method is only 1/20 of that of the ANSYS method. Additionally, it is shown that the MS-TMM method greatly increases the calculation efficiency while maintaining accuracy.

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2017

Transfer Matrix Method for Multibody Systems

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Recursive eigenvalue search algorithm for transfer matrix method of linear flexible multibody systems

Cited by 72 publications

References 5 publications

Free Vibration Characteristic of Multilevel Beam Based on Transfer Matrix Method of Linear Multibody Systems

Free Vibration Characteristic of Multilevel Beam Based on Transfer Matrix Method of Linear Multibody Systems

Study on the Seismic Response of a Portal Frame Structure Based on the Transfer Matrix Method of Multibody System

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