Power Steering Problems
If your car shudders or vibrates only when you're turning, it's a little easier to narrow down the source of your problem, since it is probably from the power steering system. Take a look at the power steering system's hoses to see if there are any visible leaks, and check the reservoir to see if the power steering fluid needs to be topped off.
You can also try to replicate the sound while the car is not moving. According to YourMechanic, if the problem is somewhere in the power steering system, you should feel the same vibrations from turning the steering wheel even while the car is in park.