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Volume 36, Issue 3
Periodic Solutions for a Damped Rayleigh Beam Model with Time Delay

Bochao Chen & Yong Li

DOI: 10.4208/cmr.2020-0015

Commun. Math. Res., 36 (2020), pp. 296-319.

Published online: 2020-07

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  • Abstract

Vibrations of a beam can be described as an Euler-Bernoulli beam, or as a Rayleigh beam or as a Timoshenko beam. In this paper, we establish the existence of periodic solutions in time for a damped Rayleigh beam model with time delay, which is treated as a bifurcation parameter. The main proof is based on a Lyapunov-Schmidt reduction together with the classical implicit function theorem. Moreover, we give a sufficient condition for a direction of bifurcation.

  • Keywords

Beam equations, damping, time delay, periodic solutions.

  • AMS Subject Headings

35L75, 37K50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-36-296, author = {Chen , Bochao and Li , Yong}, title = {Periodic Solutions for a Damped Rayleigh Beam Model with Time Delay}, journal = {Communications in Mathematical Research }, year = {2020}, volume = {36}, number = {3}, pages = {296--319}, abstract = {

Vibrations of a beam can be described as an Euler-Bernoulli beam, or as a Rayleigh beam or as a Timoshenko beam. In this paper, we establish the existence of periodic solutions in time for a damped Rayleigh beam model with time delay, which is treated as a bifurcation parameter. The main proof is based on a Lyapunov-Schmidt reduction together with the classical implicit function theorem. Moreover, we give a sufficient condition for a direction of bifurcation.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2020-0015}, url = {http://global-sci.org/intro/article_detail/cmr/17850.html} }
TY - JOUR T1 - Periodic Solutions for a Damped Rayleigh Beam Model with Time Delay AU - Chen , Bochao AU - Li , Yong JO - Communications in Mathematical Research VL - 3 SP - 296 EP - 319 PY - 2020 DA - 2020/07 SN - 36 DO - http://doi.org/10.4208/cmr.2020-0015 UR - https://global-sci.org/intro/article_detail/cmr/17850.html KW - Beam equations, damping, time delay, periodic solutions. AB -

Vibrations of a beam can be described as an Euler-Bernoulli beam, or as a Rayleigh beam or as a Timoshenko beam. In this paper, we establish the existence of periodic solutions in time for a damped Rayleigh beam model with time delay, which is treated as a bifurcation parameter. The main proof is based on a Lyapunov-Schmidt reduction together with the classical implicit function theorem. Moreover, we give a sufficient condition for a direction of bifurcation.

Chen , Bochao and Li , Yong. (2020). Periodic Solutions for a Damped Rayleigh Beam Model with Time Delay. Communications in Mathematical Research . 36 (3). 296-319. doi:10.4208/cmr.2020-0015
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