Free vibration analysis of axially moving beams using the transfer matrix method

Lee, Jung Woo; Lee, Jung Youn; Lee, Dongmin

doi:10.1007/s12206-021-0303-z

Cited by 11 publications

(10 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By changing the state vector, the new transfer matrix function is obtained as follows and using equation (10), the transfer matrix can be determined as follows…”

Section: Rotational Euler-bernoulli Beammentioning

confidence: 99%

“…and F includes N/2 state variables that are known on the first point and E contains N/2 state variables that are unknown on the first point. Therefore, equation (10)…”

Section: Riccati Transformationmentioning

confidence: 99%

“…Consequently, it seems that TMM is an appropriate method for analyzing the vibration of the engineering structures. [10][11][12] The free vibration of Euler-Bernoulli and Timoshenko beams with a variable cross-section is discussed using TMM in Ref. 4.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, it seems that TMM is an appropriate method for analyzing the vibration of the engineering structures. 10–12…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An efficient technique in transfer matrix method for beam-like structures vibration analysis

Feyzollahzadeh

Bamdad

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

Rotating beam-like structures are widely used in various engineering fields, and the transfer matrix method is a classic analytical method for vibration analysis. Due to eliminating numerical difficulties, Riccati transfer matrix method has been applied. Since this method demands an inverse matrix procedure, a novel algorithm is presented to reduce the matrix order with less computation time. The proposed technique is performed for the vibration analysis of the rotary beam-like structures to characterize the frequencies without limitations from the rotational speed. Rather than numerical problems in the classical approach, this new technique exhibits an improved performance while the key factor for efficiency is the computation time. Comparing the results achieved through the finite element and Rayleigh–Ritz methods shows an acceptable agreement with high accuracy responses. In addition, the computation time for Riccati transformation adoption and the classical transfer matrix method is investigated. This evaluation demonstrates the priority of using this technique in terms of computation cost.

show abstract

“…By changing the state vector, the new transfer matrix function is obtained as follows and using equation (10), the transfer matrix can be determined as follows…”

Section: Rotational Euler-bernoulli Beammentioning

confidence: 99%

“…and F includes N/2 state variables that are known on the first point and E contains N/2 state variables that are unknown on the first point. Therefore, equation (10)…”

Section: Riccati Transformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Consequently, it seems that TMM is an appropriate method for analyzing the vibration of the engineering structures. 10–12…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An efficient technique in transfer matrix method for beam-like structures vibration analysis

Feyzollahzadeh

Bamdad

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

show abstract

“…Axially moving beams have numerous applications in various branches of engineering, such as manufacturing, civil, mechanical, chemical, and aerospace engineering [1][2][3][4]. Typical applications explored in previous studies include conveyor belts, medical nanorobots, power saw, band saw, and magnetic tape [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Transverse Response of an Axially Moving Beam with Intermediate Viscoelastic Support

Ali

Khan

Jamal

et al. 2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This study presented the transverse vibration of an axially moving beam with an intermediate nonlinear viscoelastic foundation. Hamilton’s principle was used to derive the nonlinear equations of motion. The finite difference and state-space methods transform the partial differential equations into a system of coupled first-order regular differential equations. The numerical modeling procedures are utilized for evaluating the effects of parameters, such as axial translation velocity, flexure rigidities of the beam, damping, and stiffness of the support on the transverse response amplitude and frequencies. It is observed that the dimensionless fundamental frequency and magnitude of axial speed had an inverse correlation. Furthermore, increasing the flexure rigidity of the beam reduced the transverse displacement, but at the same instant, fundamental frequency rises. Vibration amplitude is found to be significantly reduced with higher damping of support. It is also observed that an increase in the foundation damping leads to lower fundamental frequencies, whereas increasing the foundation stiffness results in higher frequencies.

show abstract

Nonlinear dynamic and stability of a small size moving beam under thermal conditions

Ali

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

Nonlinear transverse vibration of a micro‐size moving beam like structure under the influence of thermal conditions is studied. Hamilton principle is used to derive the nonlinear equation of motion. The derived equation of transverse motion is discretized using the Galerkin technique. The vibration attributes of the moving beam, such as frequencies of the transverse response, time response, and stability analysis, are investigated at different temperatures. For stability analysis, bifurcation diagrams are presented under the influence of temperature, length‐scale parameter, and excitation frequencies at various axial speeds of the beam.

show abstract

Free vibration analysis of axially moving beams using the transfer matrix method

Cited by 11 publications

References 42 publications

An efficient technique in transfer matrix method for beam-like structures vibration analysis

An efficient technique in transfer matrix method for beam-like structures vibration analysis

Transverse Response of an Axially Moving Beam with Intermediate Viscoelastic Support

Nonlinear dynamic and stability of a small size moving beam under thermal conditions

Contact Info

Product

Resources

About