Application of dynamic stiffness method in numerical free vibration analysis of stiffened plates

Abstract

The free vibration analysis of stiffened plate assemblies has been performed in this paper by using the dynamic stiffness method. Rectangular Mindlin plate dynamic stiffness element has been formulated. Using the rotation matrices, dynamic stiffness matrices of single plates have been derived in global coordinate system. The global dynamic stiffness matrix of plate assembly has been derived by using similar assembly procedure as in the finite element method. The natural frequencies of stiffened plate assemblies with different boundary conditions have been computed and validated against the results obtained by using the commercial software package Abaqus. High accuracy of the results has been demonstrated.

U okviru ovog rada, analizirane su slobodne vibracije ploča sa ukrućenjima, primenom metode dinamičke krutosti. Formulisan je pravougaoni element Mindlin-ove ploče, zasnovan na metodi dinamičke krutosti. Primenom matrica rotacije, formirane su dinamičke matrice krutosti pojedinačnih ploča u globalnom koordinatnom sistemu. Korišćenjem sličnog postupka kao u metodi konačnih elemenata, izvedena je globalna dinamička matrica krutosti sistema ploča. Određene su sopstvene frekvencije ploča sa ukrućenjima za različite konturne uslove i upoređene sa vrednostima dobijenim u komercijalnom programskom paketu Abaqus. Dobijeni su rezultati visoke tačnosti.