• On initial conditions for a boundary stabilized hybrid Euler-Bernoulli beam

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      https://www.ias.ac.in/article/fulltext/pmsc/111/03/0365-0370

    • Keywords

       

      Euler-Bernoulli beam equation; hybrid system; initial conditions; small deflection; exponential energy decay

    • Abstract

       

      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 displacementy0(x) and initial velocityy1 (x). By investigating the evolution of the motion by Laplace transform, it is proved (in dimensionless units of length and time) that$$\smallint _0^1 y_{xt}^2 dx \leqslant \smallint _0^1 y_{xx}^2 dx,t > t_0 $$, wheret0 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.

    • Author Affiliations

       

      Sujit K Bose1

      1. BE-188, Salt Lake City, Kolkata - 700 064, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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