Seismic response of asymmetric systems with linear and non-linear viscous dampers

Abstract

The free vibration characteristics, such as fundamental frequency and mode shape of stiffened plates employing standard finite element analysis, are investigated in this paper. The parametric study is presented for free vibration characteristics of stiffened plates with various parameters, such as type, orientation and number of stiffeners, boundary conditions and aspect ratio of plates and stiffener depth to plate thickness ratio. Typical mode shapes are also presented for clamped square eccentrically stiffened plates. Finally, design charts with non-dimensional parameters are proposed to determine the fundamental frequency of commonly adopted clamped stiffened plates in construction. These charts will be very much useful for designers for obtaining the fundamental frequencies of the stiffened plates of different dimensions without doing much complicated analysis or using standard computer codes. Keywords Stiffened plates • Frequency • Mode shape • Finite element analysis • Design charts List of Symbols a, b Length (span) and width of plate, respectively, in plan b st , d st Width and depth of stiffener, respectively {d} Eigen vector (mode shape) of stiffened plate E Young's modulus of isotropic plate and stiffener h Thickness of the plate [K e ], [K] Element and overall stiffness matrices of stiffened plates, respectively [K pe ], [K xe ], [K ye ] Element stiffness matrices of plate, x-directional stiffeners and y-directional stiffeners, respectively [M e ], [M] Element and overall mass matrices of stiffened plates, respectively [M pe ], [M xe ], [M ye ] Element mass matrices of plate, x-directional stiffeners and y-directional stiffeners, respectively

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