Free Vibration Analysis of Shells of Revolution Using GDQ Method

SOMMARIO. In questo lavoro, il Metodo Generalizzato di Quadratura Differenziale (GDQ) viene applicato allo studio del comportamento dinamico di gusci di rivoluzione a doppia curvatura. Per l'analisi dinamica di tali elementi strutturali si fa riferimento alla teoria del primo ordine (FSDT). I risultati ottenuti con la tecnica in parola vengono confrontati con quelli ottenuti attraverso programmi FEM come Abaqus, Ansys, Femap/Nastran, Straus, Pro/Mechanica. ABSTRACT. In this paper, the Generalized Differential Quadrature (GDQ) Method is applied to study the dynamic behaviour of double curved shells of revolution. The First-order Shear Deformation Theory (FSDT) is used to analyze the above moderately thick structural elements. GDQ results are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Femap/Nastran, Straus, Pro/Mechanica. In this work, the analysis will be performed by following two different investigations. In the first one, the solution is obtained by using the numerical technique termed Generalized Differential Quadrature (GDQ) method, which leads to a generalized eigenvalue problem. The mathematical fundamentals and recent developments of the GDQ method as well as its major applications in engineering are discussed in detail in the book by Shu (1). The solution is given in terms of generalized displacement components of the points lying on the middle surface of the thick shell (2-4). Then, in order to verify the accuracy of the present method, numerical results will also be computed by using commercial programs. The convergence and the stability of some natural frequencies for the considered structure are reported. The approximate solutions show good convergence characteristics and appear to be accurate when tested by comparison to finite element analyses. In a nutshell, the aim of the present paper is to demonstrate an efficient and accurate application of the differential quadrature approach, by solving the equations of motion governing the free vibrations of thick shells of revolution, taking two co-ordinates into account. 2. SHELL GEOMETRY AND FUNDAMENTAL SYSTEM The co-ordinates along the meridional and circumferential directions are ϕ α and ϑ α ,