### Modal(Seismic) Analysis [Part 1]

If you say seismic design, you may think of it as a matter only for building or civil structure. However, seismic design is also required for machine tools such as various process equipment, energy storage devices and racks of server computers.

Shall we find out more about seismic design?

Is this mean, we feel comfortable under any magnitude of earthquake? Before looking at the theory of analysis for seismic design, let's look at the purpose of seismic design. What is a seismic design? Does it mean that there will be no damage at all under the earthquake?
Seismic design means, according to the magnitude of the earthquake divided by a certain standard, the damage level is determined as following: For small earthquakes, they do not suffer any damage.

For medium-sized earthquakes, they are destroyed to the extent that they can be used after maintenance reinforcement. For strong earthquakes, even if structural members are destroyed, collapses that cause personal injury or destruction of facilities do not occur suddenly. Of course, in the case of mechanical products, the damage level can be determined depending on the purpose of the product.
What is the reason why the damage level is differently determined depending on the size of the earthquake? Isn’t it okay just to be a sturdy design that would not be destroyed by any size of earthquake? Of course, if we have infinite time and resources, we can. However, a good design should not be unconditionally robust but a cost and resource friendly design. So, in the event of a strong earthquake, it is designed to allow a certain degree of destruction but to prevent damage to people.

Essential Elements for Seismic Design, Seismic Analysis:

Since seismic design is oriented to the structure design that can withstand earthquakes, analysis due to earthquake loads must be performed first. In this case, there are two methods commonly used for the analysis: equivalent static analysis and dynamic analysis.
The equivalent static analysis method is a method of converting the influence of an earthquake into a static load for a general structure. More specifically, when most of the masses participate in the 1st mode among the various mode shapes, it is a method of calculating and applying the load value of the 1st mode as a formula. This method can reduce time and cost in the analysis since it expresses the behavior of the structure more easily than other analysis methods. It should be noted that this method is valid if the behavior of the seismic waves and structures is typical (ie, dominated by the 1st mode). If not, we should use dynamic analysis.
There are many dynamic analysis methods, such as Transient-response Analysis and Response Spectrum Analysis.

The transient response method is a method of applying seismic waves directly to a structure. It is a method of applying virtual seismic waves suitable for seismic design using existing seismic information to the structure. However, it is not possible to predict the vibration of the ground in an area where an earthquake has not occurred. Therefore, in many cases, each country applies the design standard and the vibration of the ground is artificially edited using the past records.
The transient response method can examine the overall behavior of the structure with time, and the response spectra method shows the peak response value of the maximum displacement and maximum stress that can occur in the structure. For earthquakes, the response spectrum method is often used because safety can usually be assessed by using the maximum response value. In the mechanical field, the response spectrum method is used for seismic analysis, impact simulation for explosion of torpedoes, etc.

Response Spectrum, Seismic Analysis focused on the maximum response of structures:

Response spectrum refers to the graphical representation of the maximum response of a structure when a seismic load is applied, depending on the type and shape of the various structures.
When we input the characteristics of the earthquake and the structure, we can obtain the maximum seismic response according to the natural period of the structure through the graph. Even though there is a disadvantage in that the load input is not intuitive and the displacement of the structure over time is not obtained because the spectral data is used without directly input of the seismic waves, this method is widely used because it is very easy to obtain the maximum response and the analysis time is short. The response spectrum will vary depending on what the response physical value is, such as the displacement response spectrum, the pseudo- velocity response spectrum, and the pseudo- acceleration response spectrum.

In addition, since the response spectrum for a specific earthquake is abruptly changed according to the vibration period, a standard design response spectrum is used which is simplified in the form of a straight line.