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Dynamics of structures with MATLAB® applications by Ashok K. Jain

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Chapter 7

Direct Integration of Equation of Motion

7.1 INTRODUCTION

In the previous chapters, the second-order differential equation of motion has been solved using the basic principles of calculus. The forcing function had a simple nature and it was convenient to solve the differential equation. In case a single-degree-of-freedom (SDOF) system or a multi-degree-of-freedom (MDOF) system is subjected to a random acceleration-time history or if the system is nonlinear, it will be very difficult to solve its differential equation using the methods discussed so far. Direct integration methods or step-by-step integration methods are used for the solution of such problems as illustrated in Figure 7.1. A very small time step Δt is chosen and the ...

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