Continuous Systems

  • Jan Awrejcewicz
  • Igor V. Andrianov
  • Leonid I. Manevitch
Part of the Springer Series in Synergetics book series (SSSYN, volume 69)


Let us consider the system in which the masses, interconnected by a weightless beam, interact with nonlinearly elastic supports distributed equidistantly along the length (Fig. 3.1). The corresponding equation of the free motion in the absence of friction is written in the form
$$ m{\rm{ }}\sum\limits_{j = -\infty }^\infty {{{{\partial ^2}w} \over {\partial {t^2}}}\delta \left( {x -jl} \right)} + EJ{{{\partial ^4}w} \over {\partial {x^4}}} -S{{{\partial ^2}w} \over {\partial {x^2}}} + \sum\limits_{j = -\infty }^\infty {q\left( w \right)} \delta \left( {x -jl} \right) = 0; $$
here m is the magnitude of each concentrated mass, w[x, t) is the transversal displacement, l is the spacing between supports (masses), δ is the Dirac delta function, q(w) = aw + bw3, and S is the stretching force.


Cylindrical Shell Rectangular Plate Continuous System Shallow Shell Outer Solution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jan Awrejcewicz
    • 1
  • Igor V. Andrianov
    • 2
  • Leonid I. Manevitch
    • 3
  1. 1.Division of Control and Biomechanics (I-10)Technical University of LódzLódzPoland
  2. 2.Pridneprovye State Academy of Civil Engineering and ArchitectureDnepropetrovskUkraine
  3. 3.Institute of Chemical PhysicsRussian Academy of SciencesMoscowRussia

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