Vol. 6, No. 6, 2011

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Large-amplitude dynamic analysis of stiffened plates with free edges

Anirban Mitra, Prasanta Sahoo and Kashinath Saha

Vol. 6 (2011), No. 6, 883–914

Large-amplitude free-vibration analysis of stiffened plates subjected to uniformly distributed transverse loading with free flexural boundary conditions is presented. The free edge is taken with different combinations of clamped and simply supported end conditions for three types of stiffened plates classified according to number and orientation of stiffeners. The computational domain is divided into an adequate number of subdomains based on the number, orientation, and location of stiffeners to generate the appropriate grid of computation points. Nonlinear strain displacement relations are considered in the formulation but the effects of shear deformation have been neglected. The analysis involves two steps. First the static displacement field of the system is solved for. The second step takes up the free-vibration analysis on the basis of the known static displacement field. The mathematical formulation of the static problem is based on the principle of minimum potential energy, whereas Hamilton’s principle has been applied for the dynamic analysis. The results are validated with the published results of other researchers. The dynamic behavior is presented in the form of backbone curves in a dimensionless frequency-amplitude plane. Three-dimensional mode shape plots are also presented along with contour plots in a few specific cases.

stiffened plate, geometric nonlinearity, large-amplitude vibration, variational methods, backbone curves
Received: 23 August 2010
Revised: 12 January 2011
Accepted: 13 January 2011
Published: 11 December 2011
Anirban Mitra
Department of Mechanical Engineering
Jadavpur University
Kolkata 700 032
Prasanta Sahoo
Department of Mechanical Engineering
Jadavpur University
Kolkata 700 032
Kashinath Saha
Department of Mechanical Engineering
Jadavpur University
Kolkata 700 032