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Asked: 2023-12-13T21:00:47+05:30 In:

What are the limitations of the response spectra method in seismic analysis?

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What are the drawbacks of the response spectra method in seismic analysis?

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    1. The response spectra method applies only to linear elastic systems. Here is why.

      To perform response spectrum analysis, the equation of motion of the N degrees freedom system has to be decoupled into N number of single-degree freedom (SDOF) systems. To carry out this, the system should have N number of independent modes to decouple the coupled equation using the modal orthogonality principle.

      In the case of non-linear systems, the modes are interdependent. This is because the natural frequency of a non-linear system is a function of the amplitude of vibration. Hence the natural frequency is not a constant value as in linear systems. The equation of the natural frequency of non-linear systems is written as

      \omega =\sqrt{\frac{k}{m} +3\epsilon \beta x^{2}}

      Where x is the displacement of the system,

      \beta \, is the cubic stiffness coefficient.

      Hence due to the lack of constant modal properties in non-linear systems, the modes are interdependent.

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