title_body: How does frame stiffness affect a quadcopter? When choosing a frame for a drone, something I hear mentioned occasionally is how flexible the carbon fiber is. It seems that the general opinion is: more flex in a frame is worse. How would having a frame with flex in it be bad for a high-powered quadcopter? Would it impact the efficiency and performance of the quadcopter?
upvoted_answer: Background
  
  Stiffness, oscillation, and vibration damping are separate concepts but all somewhat relevant to the question. Each affects flight dynamics, and each is (somewhat) a function of material choice. 
  
  For example, titanium is very stiff, and it rings like a bell. CF is very stiff, but it rings like mud. Aluminum is in between.
  
  Stiffness
  
  Stiffness is a good thing when you don't want your structure to be compliant[*]. Stiffness means that the frame isn't deflecting, which is important for the presumed laws of motion. Put another way, a quadcopter's autopilot assumes that all the motors are pointed in a fixed direction[**]. If those directions change, i.e. because of flexing, then the most fundamental assumptions of its flight dynamics are false. It's no surprise flight flight performance degrades!
  
  Of course, any structure will bend/deflect/twist under load, no matter how stiff. What's important is whether it does any of these sufficiently enough to compromise your flight goal. If you're trying to do telescopic videography then a little bit of error is immediately visible in the results. If you're learning to fly, then so long as the autopilot keeps things sunny-side up you're fine.
  
  Oscillation
  
  Oscillation, such as control-surface flutter, occur when the  entire structure starts deforming like a spring. This can dramatically build up and quickly rip the airframe to shreds. (It really is that fast, that violent, and that scary.)
  
  If a quad's arms are insufficiently damped, oscillations can occur. Most frequently, it will occur as a twist about the arm axis, but I've also seen it happen in the flapping direction. Because of differences in dynamics between a multirotor and a fixed-wing, it's unlikely that your quad will suffer inflight failure but it's also very hard to keep control, both for you and the autopilot. 
  
  The closer you get to instability, the more energy you have to expend to keep things stable. In the case of a multi, at the very least this translates into decreased flight time.
  
  The more powerful your input (e.g. a powerful quadcopter), the easier it is to drive a system past a critical damping threshold. The Tacoma Narrows Bridge was famous for this when the wind  was blowing and the bridge was slightly wet. More recently, these out of control harmonic oscillations have famously been seen on the Millennium Bridge in London (surprisingly due to human footfall) and the Humen Perl River Bridge in China (heavy winds).
  
  A full discussion of how to control oscillation is outside the scope of this answer. However, it is relevant to note that some materials are springier than others, and these materials are the ones more likely to have pathological  oscillation.
  
  Vibration
  
  Vibration is a form of oscillation, but I'm breaking it out so I can specifically address how it affects sensor data. Vibration is an issue when it causes signal integrity issues with the IMU (i.e. accelerometer + gyrometer)[***]. This can confuse the autopilot, leading it to make incorrect estimations of the aircraft's roll-pitch-yaw, and as a result respond inappropriately. This can and does cause crashes.
  
  Again, a full discussion of how to control vibration is outside the scope of this answer. And once again, the springier the material is, the more it is likely to have pathological vibration.
  
  Composites vs. metals
  
  Composites (e.g. carbon fiber, fiberglass, kevlar, ...) have what are called anisotropic properties. This means that they don't have the same properties in all directions. Consider a square sheet of aluminum. No matter which axis you pull it on, it has the same strength, stiffness, heat transfer, etc... This is isotropic.
  
  Now consider the same sheet made out of unidirectional carbon fiber. Along the carbon fiber axis it's incredibly strong. But turned 90 degrees, where the only thing holding it together is the glue, you'll find that it has no strength whatsoever.
  
  You would be correct in assuming that this difference in properties extends to oscillation and vibration. The upshot is that composites can be tricky to chose because two seemingly similar structures (e.g. a tube) can have very different properties. 
  
  
  
  [*] Able to move and bend, like the Goshawk.
  
  [**] See math in https://drones.stackexchange.com/a/323/46.
  
  [***] For example, aliasing and clipping.