Gyroscopically Stabilized Building
By William Chen and Daniel Li, THINK 2014 Winners
Earthquakes are frequent phenomena that wreak tremendous havoc on infrastructures globally, especially in regions that lie on Earth's seismic fault lines like California, Japan, and other Pacific countries. Because these natural occurrences are impossible to scientifically predict, we built a self-stabilizing building to reduce property damage and ultimately save human lives. The goal of our project is to engineer a 3-story building (0.3 by 0.3 by 1.0 meters) that incorporates a novel design based on Arduino gyroscopic sensors and servo motors to counteract an earthquake's lateral movements. Doing so also plays off of the building's natural tendency to stay at rest, leaving the topmost level nearly unmoved. The plan may be implemented into infrastructures in regions that lie on the edge of the Pacific Plate, Eurasian Plate, and Indo-Australian Plate. Residential, corporate, and government buildings may implement the infrastructure design to prevent property damage, reduce human casualties, and benefit urban society.
Earthquakes occur when there is a sudden slip of a fault between two plates, which causes the ground to shake due to seismic waves. However, since they occur in all types of weather, climate zones, and seasons and at any time, earthquakes are also unpredictable. According to United States Geological Survey from 2000 to 2001, there has been an average of 63,000 deaths per year, most of these attributed to building destruction. From this, the problem we have identified is the amplified damage to taller buildings, which causes a great number of deaths. From here, there are two factors: the natural frequency (buildings that are taller have much higher natural frequencies), which is typically known as the vibrations the building produces, and the ground frequency, or ground motion. Resonance frequency occurs when the motion of the ground is centered on the building's natural frequency, which amplifies the building's response. This is the dynamic amplification effect; when the ground motion is at a frequency that is equal to the building's natural frequency, the infrastructure suffers the greatest possible damage. This tends to happen to taller buildings as ground motion usually matches natural frequency when the building is 9 stories or higher. For example, on September 19, 1985, the Mexico City earthquake ground frequency coincided with majority of the 20-story tall buildings, which resulted in their collapse. However, according to the Multidisciplinary Center for Earthquake Engineering Research, other building with different heights and frequency, located next to the 20-story tall buildings, were undamaged.
As a building responds to ground motions produced by an earthquake, the bottom of the structure moves immediately, but the upper portions do not because of their mass and inertia. The horizontal force, or base shear, created by ground motion resulting from an earthquake that must be resisted by the building. The more the ground moves, or the greater the weight of the building, the more force that must be resisted by the building. Seen in the diagram below, the taller building must resist much more inertial force. The problem is with tall buildings: their tendency for natural frequency and ground motion to align and their greater inertia than that of a small building causes them to topple over.
To solve this problem, we came up with an idea of a dynamic building, one that could adjust and stabilize itself during the event of an earthquake. Currently, methods used to construct taller buildings to withstand earthquakes include damping and drift (as well as the composition of building's material, involving factors such as ductility and strength). The former is when an engineer or architect aims to disrupt the harmonic relationship between the ground and natural frequencies by dampening the vibration; this is done by connecting nonstructural elements such as partitions, ceilings, and exterior walls. Modern office buildings with open flooring and few partitions tend to be deficient in damping and therefore suffer more damage in an earthquake. It is best for a building to have a high level of damping characteristics – basically serving as a shock absorber. With damping design, a building is less likely to resonate in tune with the ground. Second is maximizing the potential of drift, which is the extent to where a building can sway. Engineers and architects find the sweet spot so a building is not too flexible but also not too rigid so that it cannot withstand an earthquake. The solution we propose envelops both of these concepts. We decided on gyroscopically calibrated joints which could be implemented as a connection point for a building; this would allow for minimal motion at the highest level (reiterating the damping method) and allow for flexibility without compromising the building's integrity. This distorts the relation of the ground motion and natural frequencies' harmonic tendencies; the new ground motion is essentially the previous floor's motion and the new natural frequency is the remaining height of the structure.
In a larger sense, the goal is to have as many gyroscopically calibrated joints as possible in a building: the more there are, the less the distance between each of them. Our solution (seen in the diagram below) makes use of the building's own inertia. In turn, this would minimize the shear force immensely as the weight of the building does not act as horizontal as it had before, reducing the shear force's vector. So essentially what we are having here is a continued segmented building where everything would be a joint, akin to a centipede's connected joints. The goal is to minimize the distance between the joints so that the shock wave from the earthquake would be transferred, absorbed, and dissipated by such joints as many times as possible.
However, implementing this solution presents new problems. The first issue is the joints' ability to support the weight of the building. The second question is the structural integrity of the building's internals. A solution to the first issue is to find the maximum capacity of weight the joint could sustain and start implementing the joints from the remainder of the building (translating to the weight the joint could support). Solving the second issue requires a modification on all internal infrastructure (stairs, elevators, etc.) and requires intensive modifications. For our initial prototype, we are focusing on testing the frame of the apparatus, so we do not have any internal parts aside from the housing the Arduino microprocessor, sensors, and motors.
Ultimately, this solution offers insight to solving the problem with taller buildings. As we progress into the 21st century, newer buildings will only become taller, and all the while earthquakes will still occur. Gyroscopically calibrated joints present a solution to keep these buildings stable.
Materials and Methods
Using a power drill, we bolted four wooden columns to each floor. Each vertical pillar was connected to another pillar by two pan-and-tilt kits with two servomotors, which control the degree of tilt. Arduino components including the microcontroller, breadboard, and IMU gyroscope-accelerometer were mounted in the center of each floor. Jumper cables were used for wiring instead of soldering wires. After building the three-floor structure, we tested the building's response to a shifting base. However, there was an inherent design flaw in the first design. Once the floors were nailed into all four columns, the floors were unable to shift in the event of a simulated earthquake. This is because once they were fastened to a situated point, they remained static and could no longer adjust dynamically as a unit or in unison. This would not work because it would not allow for the pillars to move. Imagine all the pillars on an equal plane and all of them were tilted 45 degrees so that the tip each pillar was still on the same plane as the next. This would not allow for any movement as the board that this is mounted on is attached to entire surface area of the pillar top. In terms of the mechanics of such movement, each individual joint requires two pivotal joints to level the final plane to a flat position.
Floors are not parallel to the ground. When the motors readjust, the floor's 90-degree angle becomes acute.
One column is not long enough to achieve a parallel floor. Since the column is firmly attached to the floor, this scenario is not possible.
Spaces between the floor and column cannot form.
This orientation is required for the motors to move properly, but it is not possible.
To diagnose the problem, we disassembled the device until we were left with the base floor and its four pillars without the top of the base. The first movement of a joint (regardless of x or y direction) shifts the shaft of the column at an angle, which (without the floor affixed to the top) adjusted fine. So this is where the problem arose: since all of the pillars are flat at the top, they are not flat with the contact of the consecutive floor, giving a static overall position. For the second design, we placed the two motors in the same x direction, facing each other vertically, so the building would be able to move. The diagrams below illustrate the second design in action.
Images show before vs. after. The motors allow for only one direction of shift in the x direction.
Image shows the prototype of second design.
When we connected the two pan-and-tilt kits together, two-directional shifts would not be feasible; rather, an x and y shift would require a grand total of 4 motors: two in x and two in y. This can be imagined from the aforementioned figure with an added third and fourth motors in the plane coming out of the page. As a result, the pan-and-tilt kits were connected parallel to each other to accommodate for a stronger bond with duct tape. There was not enough space to bind the pan-and-tilt kits with screws because the servomotors occupied most of the space. So the second design accommodates movement in one direction, because two motors can only facilitate direction in one plane.
Our last issue arose when we tried coding the Arduino to self-stabilize itself, but were unable to successfully implement a program using Kalman filter and other self-balancing algorithms. The Arduino forum and online resources such as from the Indian Institute of Technology (IIT) pointed towards a Direction Cosine Matrix (DCM) algorithm for precise control of servomotors. We learned that the conventional motor control for keeping sensor within a certain threshold is the Proportional Integral Derivative (PID) control loop. According to IIT Team Vidyut's "Platform: Balanced and Controlled", the formula for the PID algorithm is expressed as:
We got it to work for 2 motors, but it was more complicated for the 3 floors of our building. We leave the full implementation as future work.
|Arduino Mega 2560 Microcontroller Rev3||3||$46.98||Microcontroller board for gyroscope, accelerometer, servo motors|
|HS-422 Servomotor||24||$9.99||Adjust dynamically to keep floor level with respect to ground|
|Lynxmotion Aluminum Pan-and-tilt Kit||24||$9.95||Mounting bracket for each floor level|
|Ardumoto Shield||12||$24.95||Control 2 DC motors|
|RadioShack 4 AA Battery Holder||3||$2.49||Provide power for motors and microcontroller|
|48 Kirkland Signature AA Alkaline Batteries||1||$15.28||Power source|
|Triple Axis Accelerometer and Gyro Breakout MPU-6050||3||$39.95||To detect shifts|
|Jumper cables||4||$5.39||Wiring purposes|
|iSeismometer||1||free||Provides quantitative values|
|Screws and nuts||50||self||Connection joints|
|Wood columns||8||Building columns|
|Wood sheet||4||Building floors|
Although we were unable to fully implement the DCM algorithm, we settled on testing the building solely on its adjustable motors to test its ability to dampen the vibrational movement of a simulated earthquake. For a controlled experiment, we tested the building in which the movable joints were fixed in place with four supporting columns. For our next experiment, we tested the joints' ability to resist the ground movement. Based on the seismographs, we concluded that the movable joints were able to reduce the shaking at ground level.
The graphs below shows a dramatic difference in the x and y waves between the controlled and gyroscopically stabilized conditions. Note that the z waves are both small extremely small because the testing procedure only tested the building in two directions, x and y. The x, y, z spectrum shows the frequency of each direction. This diagram can be interpreted to show how the shaking affected the building's resistance to movement.
Based on the graphs, the x and z frequencies increase 1–2 times and the y frequency decreases 1–2 times. Ideally the jointed structure should have dampened the x-coordinate shifts, but this result may be due to inconsistent testing. However, the amplitude of the jointed building was greatly reduced compared to the controlled experiment, which shows how the implementation of joints mitigated the shaking effect. By reducing the amplitude, the observed magnitude of the earthquake decreases. Thus, a jointed structure may be implemented into buildings to become more resilient to an earthquake's devastating effects.
The seismograph above depicts the x, y, and z wave output for the controlled experiment. The x and y waves have extremely large amplitudes and small periods. The z waves are extremely small. The spectrum shows the x frequency as 4.00 Hz, y frequency as 4.00 Hz, and the z frequency as 13.30 Hz.
The seismograph above depicts the x, y, and z wave output for the movable joint experiment. The x and y waves have medium-sized amplitudes and spaced-out periods. The z waves are extremely small. The spectrum shows the x frequency as 7.40 Hz, y frequency as 2.70 Hz, and the z frequency as 21.40 Hz.
For future studies, we plan to implement a code that enables the building to stabilize itself. By developing a program in which the wavelength and frequency could be controlled with self-adjusting joints, our ultimate goal is to prevent natural frequency of the building from aligning with ground motion and effectively prevent structural damage. In addition, we plan to construct a consistent testing shaking table apparatus instead of moving the bottom board ourselves. In addition, we plan to include both x and y directional joints to accommodate for all lateral movements. In order to accomplish this, more pan-and-tilt kits and motors are required, in particular, four of each per floor to handle multi-directional shifts.
We thank the THINK team for planning our trip to MIT and providing an opportunity to meet MIT faculty member Dr. Prieto, who provided invaluable insight to our project. In addition, we thank Somak Das and Youyang Gu for their inputs and guidance along the way. Finally, we thank our sponsors Chevron, Schlumberger, and Thomson Reuters.