Problem 13.10 The curvature of a slender column subject to an axial load P (Fig. P13.10) can bemodeled byd’ydx 2where+ply=0p=EIwhere E = the modulus of elasticity, and / = the moment of...

solve a b c, need estimate price.


Problem 13.10 The curvature of a slender column subject to an axial load P (Fig. P13.10) can be modeled by d’y dx 2 where +ply=0 p= EI where E = the modulus of elasticity, and / = the moment of inertia of the cross section about its neutral axis. This model can be converted into an eigenvalue problem by substituting a centered finite- difference approximation for the second derivative to give where 7 = a node located at a position along the rod’s interior, and Ax = the spacing between nodes. This equation can be expressed as Vor —Q=-AC py, +, =0 Writing this equation for a series of interior nodes along the axis of the column yields a homogeneous system of equations. For example, if the column is divided into five segments (i.e., four interior nodes), the result is Q2-A*p?) = 0 0 » =1 2-Ax*p?) -1 0 "| _o 0 =1 Q2-A*p?) =) Ys 0 0 -1 C-A pH)». An axially loaded wooden column has the following characteristics: E£ = 10x10? Pa, I=1.25%10- m*, and L=3 m. For the five-segment, four-node representation: (a) Implement the polynomial method with MATLAB to determine the eigenvalues for this system. (b) Use the MATLAB eig function to determine the eigenvalues and eigenvectors. (¢) Use the power method to determine the largest eigenvalue and its corresponding eigenvector.