Non-linear vibration of frames by the incremental dynamic stiffness method

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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  • A. Y T Leung
  • T. C. Fung


Original languageEnglish
Pages (from-to)337-356
Journal / PublicationInternational Journal for Numerical Methods in Engineering
Issue number2
Publication statusPublished - Feb 1990
Externally publishedYes


The dynamic stiffness method is extended to large amplitude free and forced vibrations of frames. When the steady state vibration is concerned, the time variable is replaced by the frequency parameter in the Fourier series sense and the governing partial differential equations are replaced by a set of ordinary differential equations in the spatial variables alone. The frequency-dependent shape functions are generated approximately for the spatial discretization. These shape functions are the exact solutions of a beam element subjected to mono-frequency excitation and constant axial force to minimize the spatial discretization errors. The system of ordinary differential equations is replaced by a system of non-linear algebraic equations with the Fourier coefficients of the nodal displacements as unknowns.