A water tank having a natural frequency of 0.5 Hz is subjected to an earthquake with a sinusoidal variation of acceleration with respect to time. The earthquake has displacement amplitude of 9″and exciting frequency of 1 Hz. Determine the amplitude of displacement and acceleration at the top end of water tank. Take ζ=5%.

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FEA for Dynamic Problems

Finite element analysis or FEA is a computational tool that evaluates the approximate solution for a particular engineering problem. The tools provided by FEA help to evaluate the solutions of partial differential equations (PDEs) computationally following a numerical approach. Solutions of the PDEs can also be performed by following traditional algebraic approaches, but when the problem gets towards the complex side, it becomes very tedious and almost impossible to arrive at the solutions. In such cases, the FEA fulfills the purpose by evaluating the equations following multiple time steps and iterations. The more the time steps and iterations, the more accurate the solution. The solution plotted by FEA analysis and mathematical approaches varies asymptotically.