Today, we will talk about vibration of more general body. For example, vibration of cars, vibration or train, or vibration of rocket, for example. You'll remember that we studied the vibration of single degree of freedom system. Expanding the idea of single degree of freedom system, we go to two degree of freedom system, and we did understand what's the difference between two degree of freedom system and single degree of freedom system. Then we found that the mode shape certainly important to understand two degree of freedom system. Then what about vibration of car? Car is excited, for example, by the load profile. Obviously, as we experienced, the body will vibrate, or when he experienced the wind than wind the noise, we can experience. Wind noise is the result of vibration of for example this window. The vibration of window will excite the air of the inside of car that we can hear the wind noise. So we can see that to understand the vibration of this kind of general body, we need to have certain solid foundation to understand this kind of complicated system. What would be the simpler model that can represent this kind of general vibration? Well, one possible element would be the vibration of a shell. What it means by the shell, shell is a structure that has a curvature like this. What would the simpler model compare with the shell? That will be beam. For example, the length scale of this direction is larger than the length scale in cross-sectional dimension. The beam usually has a property of a rigidity often denoted by EI, E is Young's modulus, I is moment of inertia. Then what would be the next simple case? That could be very long beam compare with the cross-sectional dimension. Then it is interesting that approach to very simple structure element that is called a string. String is nothing but the elements that carry or sustain the tension. Beam bridges to the rigidity bending. Shell, of course, it does resist the bending, but the bending of this shell is stronger than the bending of this beam for unit for the same mass. So let's start with the string, and then go to the beam, and then go to the shell. That hopefully, open the gate to us to understand this general vibration. On our simple example that tells certainly all of this vibration would be musical instrument over here. You can see the curvature over here, you can see the plate, between bending and the shell, there should be a plate. Sorry, plate. Plate does have a bending rigidity curve of course, unless bending rigidity than the shell. So plate, sharp curvature, and we can see also sharp structure over here, there's a curvature. Then this part can be considered as a beam because cross sectional dimension of this part is smaller than the length scale. If you look at this side, you will see there is a string. You can hear different sounds because it does have different mass per unit length. If I increase the tension, the pitch of the string will be increased, or if I shorten the length of a string, the pitch will increase. So if you want to understand how this musical instrument radiate sound, you have to understand the string, plate, shell, and the beam. So let's start with the string.