A Rod Carrying Concentrated Masses in the Air or Liquid Flow: Statics, Vibrations, Natural Frequencies and Modes
Authors: Naumov A.M. | Published: 19.09.2013 |
Published in issue: #5(638)/2013 | |
Category: Calculation and Design of Machinery | |
Keywords: 3-D curved rod (spatially curved rod), statics, aerodynamic forces, liquid flow, flow rate, dynamics, small oscillations, natural frequencies, eigenvectors, associated basis, Cartesian basis, transformation matrix, concentrated masses, preloaded rod |
Elastic rod-shaped construction elements interacting with air or liquid flow are widespread in engineering. However, scientific literature describes very few solved problems on static and dynamic behavior of rods carrying concentrated masses in the air or liquid flow. The paper presents the equations of static equilibrium of a rod carrying concentrated masses in the air or liquid flow; the equations of small oscillations of said rod in the deformed state; as well as the numerical algorithm for finding natural frequencies and eigenvectors for such rods. As an example, the problem of deep nonlinear deformation of a hard hose carrying two concentrated masses in water flow and the definition of the static stress-strain state is solved; and for said hose the modes which correspond to the first two natural frequencies are defined. The proposed algorithm can solve a wide class of static and dynamic problems of rods interaction in an external flow.
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