An Analytical Solution Procedure for Dynamic Analysis of Soil-Structure Systems Subjected to Periodic Loading
Associate Professor, Department of Civil Engineering, Addis Ababa University, Ethiopia
Currently Operations Manager for Geotechnical Engineering
The dynamic analysis of multi-degree-of-freedom systems interacting with the foundation soil and acted by a system of periodic loads is considered. Such systems belong to the category of non-classically damped systems. The method of modal superposition is employed for coordinate transformation. The resulting coupled algebraic equations are easily solved analytically without resorting to iterations, which would otherwise be necessary in time-domain analyses for irregular excitations like earthquake ground motions. A practical method of compiling the non-proportional damping matrix is adapted for the intended purpose. The proposed method of solution is convenient to use on spreadsheets, with MATLAB or to integrate it with existing software for routine structural analyses. The application is illustrated in detail on a simplified model of a symmetrically-loaded frame founded on a rigid mat. The method is equally applicable to systems the superstructure of which is discretized using finite-element method and the foundation system consisting of a set of isolated rigid footings or piles under isolated rigid pile caps.
Keywords: Non-proportional damping, geometric damping, modal superposition, periodic loading, soil-structure interaction.
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