Free Oscillations of the Orthotropic Cylindrical Shell

Abstract

The paper considers the problem of free oscillations of the orthotropic cylindrical shell of a finite length. This problem was intensively studied in USSR in the second half of the 20th century, but it did not lose its relevance now, for example, works of Dr. Sc. (Eng.) L.G. Gulgazaryan and others should be mentioned. The Corresponding Member of the Academy of Sciences of the USSR Babenko K.I. presented briefly fundamentals of the theory of non-saturable numerical methods in his books. Research in computational mathematics in this area was not sufficiently promoted, and the results remain still practically unknown abroad. At present, actual rediscovery of the those computational methods was started in the West under the "spectral methods" name, as well as in the form of the modern (h--p)-specializations of the finite element method, where the grid was being refined (i.e., for h → 0) simultaneously increasing the degree of polynomials used in approximation of functions within one finite element. Modern algorithm without saturation is presented, and specific calculations are considered showing its high efficiency