Dynamic stability of weak equations of continuous systems

Abstract

The stability analysis method is developed for distributed dynamic problems with relaxed assumptions imposed on solutions. The problem is motivated by structural vibrations with external time-dependent parametric excitations which are controlled using surface-mounted or -embedded actuators and sensors. The strong form of equations involves irregularities which lead to computational difficulties for estimation and control problems. In order to avoid irregular terms resulting from differentiation of the force and moment terms the dynamics equations are written in a weak form. The weak form of dynamics equations of linear mechanical structures is obtained using variational calculus. The study of stability of stochastic weak system is based on examining properties of Liapunov functional along a weak solution.

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Correspondence to Andrzej Tylikowski.

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Tylikowski, A. Dynamic stability of weak equations of continuous systems. Arch Appl Mech 79, 659–665 (2009). https://doi.org/10.1007/s00419-008-0283-9

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Keywords

  • Weak formulation
  • Dynamic stability
  • Different boundary conditions
  • Liapunov method