Dynamic Analysis of Rotating Beams with Nonuniform Cross Sections Using the Dynamic Stiffness Method

Huang, Kuo Chan; Liu, T. S.

doi:10.1115/1.1400118

Cited by 17 publications

(9 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The literature on the free vibration behaviour of rotating beams using only bending theory is surprisingly voluminous and has continued to grow to this day. The authors have compiled a selective sample of recent papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] which provide background information and useful cross-references on the subject.…”

Section: Introductionmentioning

confidence: 99%

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

Banerjee

Kennedy

2014

Journal of Sound and Vibration

View full text Add to dashboard Cite

a b s t r a c tThe paper addresses the in-plane free vibration analysis of rotating beams using an exact dynamic stiffness method. The analysis includes the Coriolis effects in the free vibratory motion as well as the effects of an arbitrary hub radius and an outboard force. The investigation focuses on the formulation of the frequency dependent dynamic stiffness matrix to perform exact modal analysis of rotating beams or beam assemblies. The governing differential equations of motion, derived from Hamilton's principle, are solved using the Frobenius method. Natural boundary conditions resulting from the Hamiltonian formulation enable expressions for nodal forces to be obtained in terms of arbitrary constants. The dynamic stiffness matrix is developed by relating the amplitudes of the nodal forces to those of the corresponding responses, thereby eliminating the arbitrary constants. Then the natural frequencies and mode shapes follow from the application of the Wittrick-Williams algorithm. Numerical results for an individual rotating beam for cantilever boundary condition are given and some results are validated. The influences of Coriolis effects, rotational speed and hub radius on the natural frequencies and mode shapes are illustrated.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

Banerjee

Kennedy

2014

Journal of Sound and Vibration

View full text Add to dashboard Cite

show abstract

“…Substituting equations (22) and (23) into equation (20), the equation of motion for gear pairs is written as…”

Section: Excitation and Responsesmentioning

confidence: 99%

Dynamic analysis of gear pairs with a gross motion effect using the dynamic stiffness matrix method

Huang¹

2009

Proceedings of the Institution of Mechanical Engineers, Part K:

View full text Add to dashboard Cite

A continuum approach using the dynamic stiffness matrix (DSM) method (DSMM) is presented for the dynamic analyses of spur gear pairs incorporating the gross motion effect. A continuum dynamic model of spur gears was formulated based on the dynamic stiffness using the non-uniform Timoshenko beam theory. A systematic DSM for a gear pair was assembled including the elemental DSMs of two mating gears and non-linear Hertzian contact stiffness. The DSMs were updated at each computing step to reflect the time-varying property due to the moving mesh points. A bisection procedure was used to calculate the natural frequencies as the systematic DSM of the gear pair became singular. The mass and stiffness matrices were calculated by taking a numerical derivative of the systematic DSM. Finally, the gear dynamic responses caused by the external torque and gross motion excitation resulted. The effect of gross motion is also discussed.

show abstract

“…Gómez-Mancilla et al [48] have investigated the influence of transverse crack in a rotating shaft and noted that as the crack depth increase, an increase of the orbit completed is observed in the rotor. Huang and Liu [49] have presented a dynamic analysis of rotating beams with nonuniform cross sections using the dynamic stiffness method. They, however, used Hamilton's principle for the numerical analysis and prepared dynamic stiffness matrix for numerical analysis.…”

Section: Analysis Of Crack Rotor Through Several Other Techniquesmentioning

confidence: 99%

A Brief Review on Dynamics of a Cracked Rotor

Kumar

Rastogi

2009

International Journal of Rotating Machinery

View full text Add to dashboard Cite

Fatigue crack is an important rotor fault, which can lead to catastrophic failure if undetected properly and in time. Study and Investigation of dynamics of cracked shafts are continuing since last four decades. Some review papers were also published during this period. The aim of this paper is to present a review on recent studies and investigations done on cracked rotor. It is not the intention of the authors to provide all literatures related with the cracked rotor. However, the main emphasis is to provide all the methodologies adopted by various researchers to investigate a cracked rotor. The paper incorporates a candid commentary on various methodologies. The paper further deals an extended Lagrangian formulation to investigate dynamics of cracked rotor.

show abstract

Dynamic Analysis of Rotating Beams with Nonuniform Cross Sections Using the Dynamic Stiffness Method

Cited by 17 publications

References 9 publications

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

Dynamic analysis of gear pairs with a gross motion effect using the dynamic stiffness matrix method

A Brief Review on Dynamics of a Cracked Rotor

Contact Info

Product

Resources

About