Dynamic stiffness method in the vibration analysis of circular cylindrical shell

Abstract

In this paper the dynamic stiffness method is used for free vibration analysis of a circular cylindrical shell. The dynamic stiffness matrix is formulated on the base of the exact solution for free vibration of a circular cylindrical shell according to the Flügge thin shell theory. The matrix is frequency dependent and, besides the stiffness, includes inertia and damping effects. The derived dynamic stiffness matrix is implemented in the code developed in a Matlab program for computing natural frequencies and mode shapes of a circular cylindrical shell. Several numerical examples are carried out. The obtained results are validated against the results obtained by using the commercial finite element program Abaqus as well as the available analytical solutions from the literature.

U ovom radu korišćena je metoda dinamičke krutosti za analizu slobodnih vibracija kružne cilindrične ljuske. Dinamička matrica krutosti formulisana je na osnovu tačnog rešenja sistema diferencijalnih jednačina problema slobodnih vibracija po Flügge-ovoj teoriji ljuski. To je frekventno zavisna matrica koja u sebi, pored krutosti, sadrži uticaj inercije i prigušenja. Izvedena dinamička matica krutosti implementirana je u za tu svrhu napisani Matlab program za određivanje sopstvenih frekvencija i oblika oscilovanja kružne cilindrične ljuske. Urađen je niz primera. Rezultati dobijeni primenom dinamičke matrice krutosti upoređeni su s rezultatima dobijenim pomoću komercijalnog programa zasnovanog na metodi konačnih elemenata Abaqus, kao i sa dostupnim analitičkim rezultatima iz literature.