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Erschienen in:
2018 | OriginalPaper | Buchkapitel
3. Methods of Solution of the Equation of Motion
verfasst von : Gian Paolo Cimellaro, Sebastiano Marasco
Erschienen in: Introduction to Dynamics of Structures and Earthquake Engineering
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Abstract
The chapter analyzes different methods of solution of the equation of motion. The equation of motion for a forced SDOF system can be solved in closed form if the external excitation can be expressed as a harmonic function (analytical solution). Moreover, the dynamic response of a system subjected to a generic excitation can be evaluated using other approaches based on the decomposition of the irregular external force (Fourier series or Duhamel integral application). In these cases, the solution is achieved by the superposition property, so that they can be applied for a linear system. Clearly, this represents a limit to of the dynamic response of a real system in which the applied excitation causes irreversible deformation. In order to bypass the intrinsic limit of the previously proposed solution approaches, numerical methods are used. All the following examples and considerations are related to a damped SDOF system subjected to an external excitation.