Skyscrapers and Safety: the Tuned Mass Damper

As humanity continues to expand outwards, there is an ever expanding need for space. Although some may argue that this necessitates human expansion into dangerous environments (i.e. the vacuum of space, the harsh Martian surface, and the pressure of water), expansion will likely take place through the development of dense urban habitats. This growth does not go outwards like a suburban neighborhood, but upwards, making ever high skyscrapers. In fact, it is projected by 2050 that the urban shares of people will be greater than rural shares in almost every single country in the world. (1) In this almost certain event of urbanization, skyscrapers become a necessity, conserving urban space and making cities more centralized and sustainable. (2)

However, as we build up and "scrape the sky," new challenges emerge. Natural phenomenon that seem inconsequential on ground level, become much more vigorous at higher altitudes. Even regular winds can sway buildings several inches in each direction, winds that occur more often and more vigorously as we reach higher in the atmosphere. (2) What we really need to worry about is the dynamics between the building and the environment. Building design can amplify the effects of winds creating vortices (powerful winds that form around corners of buildings) which can violently shake buildings. In addition, earthquakes, which occur almost everywhere and are especially dangerous for tall buildings crumpling them, which is a grim prospect for residents.

However, new technologies can help counter such oscillation effects. This Instructable is meant to explore one of the best ways to make skyscrapers more resilient against natural occurrences, the tuned mass damper. We will explore these ideas with a sophisticated model to better understand how it works and why exactly "Tuning" is important for the resilience of the structure.

1. UN Urbanization Country Profiles
2. Skyscrapers and Cities Article
3. Hong Kong Observatory - Wind and Pressure

Any 3D Printer + Filament

Fusion 360 for modelling

DC Motor + L298N Driver

Wheels

Arduino + Breadboard

Power Supply

LCD Screen

We need to be able to repeatedly create horizontal motion from the cyclical motion of the motor providing energy. There is several ways to do this, like a rack and pinion system, but using an eccentric CAM seemed like the most efficient way to transfer motion. The hitch on the shaker table is attached to an eccentric CAM which is attached to the motor. The eccentric CAM is slightly offset from the center of rotation of the motor, meaning as the motor spins the eccentric CAM is getting further or closer to the hitch.

Attached above is a wiring guide on how to wire the electronic parts of the shaker table together. However, beware the fact that using long jumper cables will create a rat's nest of cables. Also, make sure to match the pins from the electronics to the Arduino to prevent issues with programming later.

Note: The adjustable power supply was used for power of the motor, but any 12V power supply should theoretically work and is what I used for this project. 

The assembly for this is actually pretty easy. There are screw holes for you to attach a power switch, motor, and space in the back to attach an L298N driver and Arduino. You will be able to see the holes for this more clearly in the CAD. However, beware of the spacing between the motor and the L298N as they may intersect if the motor is too long or wide. Please feel free to edit the design to fit the components you have or let me know and I can help you with out with it.

Once the electronics are mounted to the base, we can attach the eccentric CAM to the motor and tighten it with the screw attached in the back. I used heat set inserts, a screw, and a washer, to make sure that the bearing does not fall out of the socket in its motion. I repeated the same step for the hitch.

The wheel design was highly customized to some wheels I had laying around. They use an axle and spacers to hold the wheel in place. Once in place, the axle is dead and the wheels spins freely about it. This is probably not the best design for efficiency, but again, I used what I had laying around. The best design would probably feature heavier wheels to act as a heavier base and bearing to reduce the amount of friction in the system. Again, please let me know if this is how you want to implement it and I can help you in the design process.

The building was constructed using custom snapping blocks made specifically for this project. They are fairly intuitive to use feature long structural pieces, and 3 axis connectors. They are toleranced to snap together. Match your structural pieces and connectors to the picture shown above. Once done, the long pieces get easily pushed into the square holes shown on the base of the shaker table.

It is time to let the motor run and plot the acceleration of the building. This is actually quite easy due to the way the L298N is setup. These lines of code alone will allow us to control the direction and speed of the motor. Pins 7 and 8 are digital and will tell the direction for the motor to go, clockwise and counterclockwise respectively. However, Pin 9 is a digital PWM pin, meaning we are able to send out a number from 0 to 255 in the second parameter of analogWrite(). The higher the number the faster it will go.

void setup() {
  pinMode(9, OUTPUT);
  pinMode(8, OUTPUT);
  pinMode(7, OUTPUT);
}

void loop() {
  analogWrite(9, 225); <---
  digitalWrite(8, HIGH);
  digitalWrite(7, LOW);
}

We will also want to see the acceleration of the building in the axis it is moving back and forth in. We cam use the built in MPU6050 library in Arduino to achieve this. Below is code that concatenates both the control and tracking for the shaker table. This code takes in values from the accelerometer and outputs it to serial, which can we see via the built in serial plotter. One interesting addition is printing -6 and 6 to serial. This is done because the Arduino Serial Plotter automatically scales the y-axis to match the values of the data for 100 time units. However, we want to see more information so by outputting a constant unit we scale the axis for ourselves. 

#include <Adafruit_MPU6050.h>
#include <Adafruit_Sensor.h>
#include <Wire.h>
Adafruit_MPU6050 mpu;

void setup(void) {
  Serial.begin(115200);

  mpu.setAccelerometerRange(MPU6050_RANGE_16_G);
  mpu.setGyroRange(MPU6050_RANGE_250_DEG);
  mpu.setFilterBandwidth(MPU6050_BAND_21_HZ);
  Serial.println("");
  delay(100);
  pinMode(9, OUTPUT);
  pinMode(8, OUTPUT);
  pinMode(7, OUTPUT);
}

void loop() {
  sensors_event_t a, g, temp;
  mpu.getEvent(&a, &g, &temp);

  /* Print out the values */
  Serial.print("AccelY:");
  Serial.print(a.acceleration.y);
  Serial.print(",");
  Serial.print("LowerBound:");<----
  Serial.print(-6);
  Serial.print(",");
  Serial.print("UpperBound:");<----
  Serial.print(6);
  Serial.println("");
  delay(10);

  analogWrite(9, 255);
  digitalWrite(8, HIGH);
  digitalWrite(7, LOW);
}

If we simply do one rotation of the motor and allow the building to sway freely after that we will notice an acceleration graph like the one shown above. The accelerations decay over time due to natural dampening from the frictional forces inside of the building. From regular wind, this could allow the building to sway several feet in each direction, which would be especially unpleasant for top story occupants. However, during extreme weather events, the absence of any safety mechanisms can allow the acceleration to reach levels that could permanently damage the buildings. Thus, we introduce the mass damper.

Theoretically, with a mass damper, energy from swaying in the building will be converted to kinetic energy and friction in the massive mass. However, when it is untuned we can see that it not only does not help, but introduces erratic accelerations. Erratic accelerations that would speed up the rate at which the building gets damaged. In order to envision this, I have attached a fun video that demonstrates this concept.

In order to tune this mass damper, we need to know the period at which the building oscillates when we shake it. We actually already know this value. We can associate the time value on the x-axis with real time in seconds and find that it oscillates at around 3 Hz. Meaning the period is 1/3. This allows us to solve for the only unknown in this equation, L, the length of the pendulum. Using some algebra, we find that the pendulum needs to be 2.76 cm or 1.09 inches.

As we can see on the graph, when compared to the graph in Step 6, the acceleration of the building decreases much more rapidly. By tuning the damper, it was more effectively able to convert the energy in the shaker system into heat, rather redirecting the mechanical energy back into the system, which creates violent oscillations.

What if extreme environment habitats embraced their unique surroundings to enhance human well-being?

In this case, the kinetic energy from the tuned mass damper in extreme wind and earth activity can be used to move a turbine and generate electricity for all residents. In addition, during normal wind activity, we can take advantage of the height of the skyscraper to attach a wind turbine to the top of the building and generate electricity at a constant rate. 

What did you learn through this process that you could apply to addressing a problem of the built environment in your own community? 

As my NY community continues to grow in height, we can adopt these novel technologies to help improve the safety of the buildings. However, it is more important to take this creative engineering mindset to other problems in our community and help improve safety and efficiency of our neighborhoods. For example, in extreme flooding scenarios, we can think of creative, yet realistic, methods of protecting the homes and businesses in the area. 

Conclusion:

Skyscrapers are the most important habitat to consider as we expand as a human species. The resilience of these structures will protect the thousands of people that rely upon it for shelter. These skyscrapers can increase integration with nature by using a resilient safety system among natural oscillations in the environment, a resilient electrical production system, and bringing nature to the skyscrapers, "terraforming" a concrete building into a enclosed natural environment, where people will not have to worry about external natural factors, but internal factors they can control.