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lecture_1 - ME 163 Vibrations Lecture 1 Why study...

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ME 163 Vibrations Lecture 1 Why study vibrations? In engineering, most commonly we want to suppress them. Although, as the video shown in class indicates, we can use our knowledge to produce some unusual effects with cars. You wouldn’t want to buy a car that at 45 mph produces a howling sound as mine currently does (and I am not selling cause I just need some rubber inserts and the problem is fixed). Car suspension Figure 1: Car suspension diagram In order to fix the problems more complicated than that, we need to use some serious modeling, where we take just the essentials of the vehicle description, and turn them into a set of equations, by utiliz- ing Newtonian mechanics. In the car suspension figure 1 the basic elements of the system are indicated, and we reduce analysis to just four coordinates: y 1 , y 2 , y c and θ , describing the position of the front 1
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wheel, rear wheel, center of mass, and the angular orientation of the car with respect to the ground ( θ is usually small, but not in that video...). Then we solve these equations. Some of them we can solve analytically. Having an analytical solution provides us with a lot of good intuition about the problem at hand. Unfortunately, analytical solutions are not always available. This is why we will make heavy use of software like MATLAB in this class, to solve equations and evaluate the solutions from vibrations engineering perspective. Wave energy harvesting In the video you saw in class, it becomes clear how complicated the vibration problems can become when you are designing a device that captures wave energy for electricity production. Sophisticated software tools and vibration concepts are deployed. By the end of this class you should be able to understand and perform much of the analysis that goes into building a vibration-energy capturing device. Of course, step one is to be able to write the model of the ensuing motion. Recall from dynamics: we do this using Newton’s laws (later in this class, we will learn another approach , termed Lagrangian mechanics, that simplifies this task somewhat at the expense of learning some advanced theory). Newton’s law of motion Newton told us that change in time of linear momentum of a body equals the force applied to it. If mass is constant, this statement sim- plifies to ”mass times acceleration equals force”: m a = F ( x , t ) (assuming mass m does not change in time t , and its position vector x whose acceleration is a = ¨ x moves in 3-D space under influence of force F ). Being able to derive this equation in various coordinate systems (Cartesian, polar in particular) using the free-body diagram approach is the key background for this class. Remember that the force F needs to be modeled. The law of gravity tells you the expression for that force in the case of two massive bodies at distance r from each other.
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