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please show how to solve using matlab. please Consider the cantilever beam shown below The beam is supported on one end such that both its
please show how to solve using matlab. please
Consider the cantilever beam shown below The beam is supported on one end such that both its position y and its slope dy/dz are fixed at zero. One end might be embedded in concrete or firmly secured. Suppose the beam is of length L and is thin and uniform. The vertical deflection y of the beam due to its own weight can then be modeled using the following relation: JE d^2y/dz^2 = rho g(1 + dy/dz)^3/2 [z(z - L/2) + L^2/2] where J is the moment of inertia of the beam cross section about its principal axis and E is Young's modulus, which depends on the material from which the beam is made. The constant rho is the linear mass density of the beam, and g is the acceleration due to gravity. The equation represents an initial value problem because the boundary conditions are that y and dy/dz are both zero at z = 0 This second-order nonlinear beam deflection equation can be converted to a system of two first order equations by introducing the state variables x = [y dy/dz]^T Thus, the first-order system of ODEs become dx_1/dz = x_2 dx_2/dz = rho/JE (1 + x^2_2)^3/2 [z(z - L/2) + L^2/2] Show the derivation of these two equations. Let L = 2 m, rho = 10 kg/m, and the moment of inertia times Young's modulus is JE = 2400 kg-m^3/s^2. Begin with an end condition of x(0) = 0 and calculate the maximum deflection at the end of the beam (L). Use a 4th order Runge-Kutta method to solve the equationsStep by Step Solution
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