Question 2: Suppose we have a simply supported uniform beam (i.e., with a pin support on one end and roller support on t

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Question 2 Suppose We Have A Simply Supported Uniform Beam I E With A Pin Support On One End And Roller Support On T 1 (184.74 KiB) Viewed 34 times

Question 2: Suppose we have a simply supported uniform beam (i.e., with a pin support on one end and roller support on the right) that is 10m long, and that has El/p = 16. Suppose that a load is put onto the beam so that the displacement is given by y(x) = sin(72/10). Further suppose that the load is suddenly removed at time t = 0, and that the beam vibrates as a result. . Remember that there is a difference in interpretation between positive deflection (i.e., positive y(x)) and positive vibration (i.e., positive u(x, t)). Assume for these calculations that the initial derivative w.r.t. time is zero. That is: u(x,0) = 0. (a) (0.5 Points) The PDE to solve is of the form + a¹. What is the value of a? (b) (0.5 Points) What are the initial conditions for the wave equation describing this rope configuration? (c) (1 Point) What are the boundary conditions for the PDE equation describing this vibrating beam? (d) (3 Points) Solve the partial differential equation for vibrating beam (i.e., find u(x, t)). Show all working! Note: . You should not need to calculate a Fourier series for the initial condition for this problem. . You do need to think about the values of Fn, like you did for Question 1 part (d). When you have finished solving part (d), fill in the following table and include it at the beginning of your submitted solution to part (d) (you still have to show all working underneath). Bn = Gn Hn =