Dynamic Analysis and critical speed of rotating laminated conical shells with orthogonal stiffeners using generalized differential quadrature method

Abstract

This paper presents effects of boundary conditions and axial loading on frequency characteristics of rotating laminated conical shells with meridional and circumferential stiffeners, i.e., stringers and rings, using Generalized Differential Quadrature Method (GDQM). Hamilton's principle is applied when the stiffeners are treated as discrete elements. The conical shells are stiffened at uniform intervals and it is assumed that the stiffeners have similar material and geometric properties. Equations of motion as well as equations of the boundary condition are transformed into a set of algebraic equations by applying the GDQM. Obtained results discuss the effects of parameters such as rotating velocities, depth to width ratios of the stiffeners, number of stiffeners, cone angles, and boundary conditions on natural frequency of the shell. The results will then be compared with those of other published works particularly with a non-stiffened conical shell and a special case where angle of the stiffened conical shell approaches zero, i.e. a stiffened cylindrical shell. In addition, another comparison is made with present FE method for a non-rotating stiffened conical shell. These comparisons confirm reliability of the present work as a measure to approximate solutions to the problem of rotating stiffened conical shells.

A Mixed Layerwise-Differential Quadrature Method for 3-D Vibration and Buckling Analyses of Orthogonally Stiffened Composite Conical Shell

“…The present theory estimates more accurate results than the smearing method, since the former assumes the stiffeners as discrete elements while Crenwelge and Muster 26 consider the properties of the stiffeners averaged throughout the shell. Also, comparing the present results with those reported in Daneshjou et al 34 reveals a satisfactory agreement. The slight divergence in high modes (n > 6) is attributed to different theories among these two researches.…”

“…In Fig. 5, an additional comparison is made between the theoretically and experimentally produced natural frequencies of orthogonal stiffened conical shell by Crenwelge and Muster 26 and Daneshjou et al 34 and the theory proposed here. The present theory estimates more accurate results than the smearing method, since the former assumes the stiffeners as discrete elements while Crenwelge and Muster 26 consider the properties of the stiffeners averaged throughout the shell.…”

“…On the other hand, little research has been found on stiffened conical shell. [26][27][28][29][30][31][32][33][34] Besides, this research just focuses on conical shells and the stiffeners have been modelled using smearing methods except for the work directed by Talebitooti et al 34 They assessed natural frequency of rotating stiffened conical shell in which the stiffeners are modelled by discrete elements based on CLT. Also, the refinement of thin-shell theories has resulted in a number of the so-called first-and higher-order shear deformation theories to include the effects of transverse shear deformations.…”

A nonlocal strain gradient theory for rotating thermo-mechanical characteristics on magnetically actuated viscoelastic functionally graded nanoshell

“…By applying the above displacement field in the differential equations extracted by applying the Hamilton principle equations (29)–(34) and using the numerical solution of GDQM, it leads to an equation in the form of equation (40), that is an eigenvalue problem, which can be used to obtain the natural frequency of the system (Daneshjou et al, 2013)…”

Vibration analysis of a rotating variable thickness bladed disk for aircraft gas turbine engine using generalized differential quadrature method

“…Comparing to the other numerical methods, the DQM can lead to almost accurate results using a considerably smaller number of grid points and hence requiring relatively little computational effort. [13][14][15][16][17][18][19] The generalized differential quadrature method (GDQM) is an improvement of the DQM especially for solving higher order differential equations, which is more computationally efficient and accurate. 20 Unlike the DQM, the GDQM considers a general situation, where the derivatives of a function are approximated using a linear weighted sum of all the functional values and also some derivatives of the functional values.…”