Steady-state transverse response of an axially moving beam with time-dependent axial speed

The transverse vibration characteristic of the viscoelastic sandwich beam with axial speed is studied under the coupled temperature field and displacement field. Based on the theory of Euler - Bernouli beam and the constitutive relation of Kelvin viscoelastic material model, the transverse vibration equation of the axially moving beam is established ; considering the interaction of the material deformation and the heat conduction, the coupled governing equation of the beam is obtained. and the coupled thermoelastic dynamics system are obtained by Galerkin method. The related thermal parameters on the vibration frequency are analyzed by using numerical method.

Download Full-text

Transverse Response of an Axially Moving Beam with Intermediate Viscoelastic Support

Mathematical Problems in Engineering ◽

10.1155/2021/2218832 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Sajid Ali ◽

Sikandar Khan ◽

Arshad Jamal ◽

Mamon M. Horoub ◽

Mudassir Iqbal ◽

...

Keyword(s):

Differential Equations ◽

Fundamental Frequency ◽

Equations Of Motion ◽

Inverse Correlation ◽

Axially Moving Beam ◽

Transverse Displacement ◽

Axial Translation ◽

Moving Beam ◽

Axially Moving ◽

Transverse Response

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.

Download Full-text

Vibration of an axially moving beam with a tip mass

Mechanics Research Communications ◽

10.1016/0093-6413(93)90028-m ◽

1993 ◽

Vol 20 (5) ◽

pp. 391-397 ◽

Cited By ~ 2

Author(s):

Heow-Pueh Lee

Keyword(s):

Axially Moving Beam ◽

Moving Beam ◽

Axially Moving ◽

Tip Mass

Download Full-text

Parametric and Internal Resonances of an Axially Moving Beam with Time-Dependent Velocity

Modelling and Simulation in Engineering ◽

10.1155/2013/919517 ◽

2013 ◽

Vol 2013 ◽

pp. 1-18 ◽

Cited By ~ 5

Author(s):

Bamadev Sahoo ◽

L. N. Panda ◽

G. Pohit

Keyword(s):

Internal Resonance ◽

Multiple Scales ◽

Time History ◽

Mean Value ◽

Phase Portraits ◽

Axially Moving Beam ◽

Internal Resonances ◽

Moving Beam ◽

Axially Moving ◽

The Stability

The nonlinear vibration of a travelling beam subjected to principal parametric resonance in presence of internal resonance is investigated. The beam velocity is assumed to be comprised of a constant mean value along with a harmonically varying component. The stretching of neutral axis introduces geometric cubic nonlinearity in the equation of motion of the beam. The natural frequency of second mode is approximately three times that of first mode; a three-to-one internal resonance is possible. The method of multiple scales (MMS) is directly applied to the governing nonlinear equations and the associated boundary conditions. The nonlinear steady state response along with the stability and bifurcation of the beam is investigated. The system exhibits pitchfork, Hopf, and saddle node bifurcations under different control parameters. The dynamic solutions in the periodic, quasiperiodic, and chaotic forms are captured with the help of time history, phase portraits, and Poincare maps showing the influence of internal resonance.

Download Full-text