Vibration control (seismic) is effective for shaking near the natural frequency of the structure
The natural frequency is the rate of vibration at which a structure is most prone to shaking, and is expressed in units of hertz (Hz). ［The lower the number, the slower the shaking, and the higher the number, the faster and finer the shaking.
Let's take an example: suppose the typical sway of Building A is as shown in the figure below, and its natural frequency is 1 Hz. This value is specific to Building A, which is determined by the height of the building, the thickness of the columns, and other factors. During an earthquake, seismic waves are input from the ground, and the building will sway mainly with this 1 Hz component (a shaking that travels back and forth once per second).
Next is an example of pedestrian bridge B. The typical sway of a pedestrian bridge should be that the bridge portion deforms in the vertical direction as shown in the figure below. If the natural frequency of this pedestrian bridge is 3 Hz, the slightly uncomfortable fluffy swaying that is felt when large vehicles pass by or when other people are walking on the bridge is caused by the vibration of the natural vibration component.
Figure 1 Example of natural frequencies
Thus, if the actual vibration (shaking) problem is such that the vibration component actually occurring matches the natural frequency of the structure, the installation of a vibration control device will have a favorable effect and will likely lead to a solution to the problem.
As mentioned above, in many cases, the main component of the vibration problem = natural frequency component of the shaking in question, but in some cases this is not the case. In such cases, vibration control is not expected to be effective and other vibration countermeasures should be considered.
The figure below shows the installation of a mass damper (TMD) on the roof of Building A as shown in the previous figure, in order to reduce the lateral shaking of the entire building during an earthquake. If the building is in a state of vibration control by mass damper, will it be effective in any case against vibration (swaying) from the same ground as an earthquake? For example, do you think it would be effective in suppressing the “rattle rattle rattle...” vibration that occurs when an electric drill is being used to drill the ground in front of the building (which can be transmitted into the building and cause a noise problem called “individual propagation noise”)?
⇒The answer is no. When vibrations with various frequency components are input from the ground, such as seismic waves, the natural frequency of the building is also stimulated, resulting in a large response. On the other hand, if only fast and fine vibration components are input from the ground, such as an electric drill, the natural frequency of the building is not stimulated and only the fine frequency components respond (transmitted and shaken). Therefore, in the latter case, no natural frequency component is generated on the building side and no vibration control effect is obtained.
Figure 2: Image of vibration control (seismic) measures
Let me add a few technical details at the end. A graphical representation of what I have just described is shown in the figure below. Such a graph is called the frequency response characteristic of vibration, and it shows the tendency of a structure to sway on the frequency axis. The horizontal axis is the vibration frequency frequency [Hz]. （The left side of the graph represents slow shaking (like the shaking of a building during an earthquake), and the right side represents fast and fine shaking (like the buzzing of an electric toothbrush). The vertical axis represents the degree of swaying. In other words, this kind of graph shows how fast a structure tends to shake. The graph below is an example of Building A mentioned earlier. The gray line is the case without vibration control. Building A is most likely to sway at 1 Hz (= natural frequency of Building A) at the peak of the graph. When a vibration control device is installed in this building, the peak becomes smoother as shown in green, indicating that the building is less prone to swaying (i.e., swaying is reduced) around the 1 Hz peak where it was originally prone to swaying. Conversely, at a distance from this peak, the gray and green areas overlap, meaning that there is no change in sway susceptibility with or without vibration control (i.e., no effect from vibration control).
Figure 3 Frequency response characteristics graph of vibration