Free Flexural Vibration Analysis of Arbitrary Plates With Arbitrary Stiffeners

Abstract

Isoparametric element tends to lock in shear for very thin plates. Though numerical techniques such as reduced-integration or selective reduced-integration are used to avoid this effect, they do not necessarily guarantee the solution to the problem, even if they increase notably the possibility of convergence with the exact solution. In the present formulation, a new four-noded stiffened-plate bending element, having the elegance of the isoparametric element to model the arbitrary shape of the plate but without any numerical disturbing feature like shear-locking problem, is presented. Another unique feature is the arbitrary placement of the stiffener inside the plate element without any restriction of its orientation. Stiffened plates having various shapes, boundary conditions, and disposition of stiffeners are analyzed and compared with available results in the literature wherever possible.

Prediction of the sound transmission loss of a stiffened window

“…A square plate clamped in all edges having a centrally placed concentric stiffener has been analyzed by Nair and Rao 29 and several other investigators. 18,30 The plate was 0.6 m long, 0.6 m wide, and 1 mm thick, with a central stiffener (3.11 mm  20.25 mm) lying in the width direction. The plate and the stiffener were made of the same material, with Young's modulus 68.7 GPa, density 2780 kg/m 3 , and Poisson's ratio 0.34.…”

“…The four-node rectangular stiffened plate element 18 was used in the FEM model. The mesh size of the element should be determined by considering both solution accuracy and computational cost.…”

“…The stiffened plate element provided by Barik and Mukhopadhyay 18 was used here. The advantages of this element are that (1) the in-plane displacements are taken into account and (2) the stiffeners can be of arbitrary shape and their positions inside the element are without restriction.…”

“…where N w f g is the shape function for the lateral displacement field. 18 Once the mass matrix fM ps g e and the stiffness matrices fK ps g e and K b…”

“…Allowing an arbitrary stiffener shape and position made the design more flexible. To meet these aims, a coupled finite element and boundary element method (FEM/BEM) was developed, in which the elegant stiffened-plate element proposed by Barik and Mukhopadhyay 18 was adopted. Section Theoretical model provides a summary of this numerical method, while section Numerical results and discussion reports the numerical results for the natural frequencies of various stiffened plates and compares them with earlier published results.…”