Vibrations of Systems with Geometric Symmetry. Quasi-symmetrical Systems

  • Liudmila Ya. BanakhEmail author
  • Mark L. Kempner
Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)


Systems with symmetries of various types have long attracted the attention of scientists in all fields: chemistry, physics, and biology. Systems with geometric symmetry find wide application in many areas of engineering. They form various kinds of machine platforms, cyclically repeated forms of stators, rotors with blades mounted on them, etc. Symmetric systems are widely applied also in the civil engineering where their use is convenient due to technological process, type-design, and architectural requirements. There exists a large body of literature devoted to the study of the statics and dynamics of symmetrical structures. As a matter of fact, it is possible to identify a number of characteristic features in the dynamic behavior of symmetric systems that make their use particularly convenient. Thus, in particular, the following basic properties are typical for such systems:


Stiffness Matrix Projective Operator Forced Vibration Symmetric System Multiple Root 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Mechanical Engineering Research InstituteMoscowRussia
  2. 2.RehovotIsrael

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