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(1)

It can be shown that when we have no external force and system is subjected to ground excitation , then the equation of motion turns to this form:

(2)

Let’s say we have n SDoF systems with mass of , damping coefficient of and stiffness of for i’th system. Equation of motion for each system when subjected to ground excitation is:

(3)

This differential equation can numerically solve by methods like Newmark-Beta or central difference or … then will be obtained. Same approach can be use to obtain the (ground speed) and (ground displacement) from . After solving the eq. 3 for all systems, we will have , and and also which is period of i’th system. Defining these parameters

(4)

(5)

(6)

The spectrum for i’th system is obtained by

Then we will have , , and for every system and now can draw them into three charts of against , against and against ,. Here is the example charts for this record:

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The top most chart is which vertical axis is denoted by , second one is and third one is .

Last edited Aug 29, 2014 at 5:52 PM by epsi1on, version 4