Proceedings Mathematical Sciences | |
On Initial Conditions for a Boundary Stabilized Hybrid Euler–Bernoulli Beam | |
Sujit K Bose1  | |
[1] BE-, Salt Lake City, Kolkata 00 0, India$$ | |
关键词: Euler–Bernoulli beam equation; hybrid system; initial conditions; small deflection; exponential energy decay.; | |
DOI : | |
学科分类:数学(综合) | |
来源: Indian Academy of Sciences | |
【 摘 要 】
We consider here small flexural vibrations of an Euler–Bernoulli beam with a lumped mass at one end subject to viscous damping force while the other end is free and the system is set to motion with initial displacement ð‘¦0(ð‘¥) and initial velocity ð‘¦1(ð‘¥). By investigating the evolution of the motion by Laplace transform, it is proved (in dimensionless units of length and time) that$$int_0^1 y_{xt}^2 dx ≤ int_0^1 y_{xx}^2 dx, quad t>t_0,$$where ð‘¡0 may be sufficiently large, provided that {ð‘¦0, ð‘¦1} satisfy very general restrictions stated in the concluding theorem. This supplies the restrictions for uniform exponential energy decay for stabilization of the beam considered in a recent paper.
【 授权许可】
Unknown
【 预 览 】
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RO201912040506536ZK.pdf | 34KB | download |