Galerkin methods for natural frequencies of high-speed axially moving beams

Ding, Hu

doi:10.1016/j.jsv.2010.03.005

Cited by 136 publications

(57 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…   ″ ′    ″ (9) 계산상의 편의 및 일반화된 결론을 얻기 위하여 이 연구에서는 다음과 같은 무차원 파라미터 및 좌 표를 정의한다. 참 고 문 헌…”

Section: 운동방정식unclassified

“…Lee 등 (8) . 최근 Galerkin 방법을 이용하여 고 속으로 움직이는 보의 고유진동수 해석 및 주변에 유체로 둘러싸인 축방향으로 이송되는 보의 안정성 해석에 대한 연구결과도 발표되어지고 있다 (9,10) . 유 체유동에 의한 파이프의 동적 불안정 문제에 관한 연구는 부가질량, 크랙 및 끝단질량과 유속의 연성 관계에 의하여 전체 시스템의 안정성에 미치는 영 향에 대한 연구결과들이 발표되어지고 있다 (11,12) .…”

unclassified

See 1 more Smart Citation

Stability Analysis of Axially Moving Simply Supported Pipe Conveying Fluid

Son

Hur²,

Lee³

et al. 2012

Transactions of the Korean Society for Noise and Vibration Engi

View full text Add to dashboard Cite

show abstract

Section: 운동방정식unclassified

unclassified

Stability Analysis of Axially Moving Simply Supported Pipe Conveying Fluid

Son

Hur²,

Lee³

et al. 2012

Transactions of the Korean Society for Noise and Vibration Engi

View full text Add to dashboard Cite

show abstract

“…Many systems in mechanical and industrial applications, such as band saw blades, power transmission chains and belts, robotic manipulators, conveyor belts, and cable tramways, can be modeled as axially moving continua [1][2][3][4][5][6]. One of the interesting features of such systems is the presence of the axial speed, which renders the system gyroscopic; as a result, traveling waves arise along the beam and the flexural stiffness of the beam is weakened.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamical Behavior of Axially Accelerating Beams: Three-Dimensional Analysis

Ghayesh

Farokhi

2016

Journal of Computational and Nonlinear Dynamics

View full text Add to dashboard Cite

The three-dimensional (3D) nonlinear dynamics of an axially accelerating beam is examined numerically taking into account all of the longitudinal, transverse, and lateral displacements and inertia. Hamilton's principle is employed in order to derive the nonlinear partial differential equations governing the longitudinal, transverse, and lateral motions. These equations are transformed into a set of nonlinear ordinary differential equations by means of the Galerkin discretization technique. The nonlinear global dynamics of the system is then examined by time-integrating the discretized equations of motion. The results are presented in the form of bifurcation diagrams of Poincare maps, time histories, phase-plane portraits, Poincare sections, and fast Fourier transforms (FFTs). The three-dimensional (3D) nonlinear dynamics of an axially accelerating beam is examined numerically taking into account all of the longitudinal, transverse, and lateral displacements and inertia. Hamilton's principle is employed in order to derive the nonlinear partial differential equations governing the longitudinal, transverse, and lateral motions. These equations are transformed into a set of nonlinear ordinary differential equations by means of the Galerkin discretization technique. The nonlinear global dynamics of the system is then examined by time-integrating the discretized equations of motion. The results are presented in the form of bifurcation diagrams of Poincar e maps, time histories, phase-plane portraits, Poincar e sections, and fast Fourier transforms (FFTs).

show abstract

“…Chakraborty and Mallik [16] examined the stability of an axially moving beam analytically by means of the method of multiple scales. Chen and coworkers [17][18][19][20][21][22] contributed to the field by examining the natural frequencies, steady-state responses, stability, and nonlinear dynamics of axially moving beams and strings with either constant or time-dependent axial speeds via employing both elastic and viscoelastic constitutive relations. Ravindra and Zhu [23] utilized a single-mode Galerkin approximation so as to examine the nonlinear dynamics of an axially moving continuum both analytically and numerically.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams

Farokhi

Ghayesh

Hussain

2015

Journal of Vibration and Acoustics

View full text Add to dashboard Cite

The three-dimensional nonlinear global dynamics of an axially moving viscoelastic beam is investigated numerically, retaining longitudinal, transverse, and lateral displacements and inertia. The nonlinear continuous model governing the motion of the system is obtained by means of Hamilton's principle. The Galerkin scheme along with suitable eigenfunctions is employed for model reduction. Direct time-integration is conducted upon the reduced-order model yielding the time-varying generalized coordinates. From the time histories of the generalized coordinates, the bifurcation diagrams of Poincaré sections are constructed by varying either the forcing amplitude or the axial speed as the bifurcation parameter. The results for the threedimensional viscoelastic model are compared to those of a three-dimensional elastic model in order to better understand the effect of the internal energy dissipation mechanism on the dynamical behavior of the system. The results are also presented by means of time histories, phase-plane diagrams, and fast Fourier transforms (FFT). Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic BeamsThe three-dimensional nonlinear global dynamics of an axially moving viscoelastic beam is investigated numerically, retaining longitudinal, transverse, and lateral displacements and inertia. The nonlinear continuous model governing the motion of the system is obtained by means of Hamilton's principle. The Galerkin scheme along with suitable eigenfunctions is employed for model reduction. Direct time-integration is conducted upon the reduced-order model yielding the time-varying generalized coordinates. From the time histories of the generalized coordinates, the bifurcation diagrams of Poincar e sections are constructed by varying either the forcing amplitude or the axial speed as the bifurcation parameter. The results for the three-dimensional viscoelastic model are compared to those of a three-dimensional elastic model in order to better understand the effect of the internal energy dissipation mechanism on the dynamical behavior of the system. The results are also presented by means of time histories, phase-plane diagrams, and fast Fourier transforms (FFT).

show abstract

Galerkin methods for natural frequencies of high-speed axially moving beams

Cited by 136 publications

References 27 publications

Stability Analysis of Axially Moving Simply Supported Pipe Conveying Fluid

Stability Analysis of Axially Moving Simply Supported Pipe Conveying Fluid

Nonlinear Dynamical Behavior of Axially Accelerating Beams: Three-Dimensional Analysis

Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams

Contact Info

Product

Resources

About