On Initial Conditions for a Boundary Stabilized Hybrid Euler–Bernoulli Beam

Proceedings Mathematical Sciences

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 𝑦0(𝑥) and initial velocity 𝑦1(𝑥). 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 𝑡0 may be sufficiently large, provided that {𝑦0, 𝑦1} 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