MATLAB

MATLAR 2015 PLOTS APS EDITOR PUBLISM VEW Init - 3 Section Compare - Go To - Comment 95 Breakpoints Rou nd Aance Run and O Program Files MATLAB MATLAR Product Server 2015 Problem 1 (50%) 10 For a multi-degree of freedom system that contains 2 masses and 2 springs, whose values are respectively m, - 10 kg.mg = 20 kg. and k, = 100 kg = 200; Use the modal analysis approach calculate and plot the motions X X, cach on a separate plot and save them as JPEG images Do not forget to add the axes labels and the title of each plot. The initial conditions on the displacement and velocity are X = 1.X -1 and 0, = 0. Take a time interval of your choice that displays the graphs clearly. Steps in Solving Equation (4.54) by Modal Analysis 1. Calculate M12 2. Calculate R-M K M the mass-normalized stiffness matrix 2. Calculate the symmetric eigenvalue problem for R to get and 4. Normalize and form the matrix P = 5. Cakulate SM-pand S py 6. Calculate the modal initial conditions ) = S (0) =S z Substitute the components of 0) and inte equations (4.16) and (4.67) to get the solution in modal coordinate in X Multiply by to get the solution - Se. Note that is the matrix of mode shapes and Pis the matrix of eigen vectors ky + k -; 0 k ki + k 0 k Problem 1 (50%) For a multi-degree of freedom system that contains 2 masses and 2 springs, whose values are respectively m, = 10 kg, m2 = 20 kg, and k, = 100 k, = 200; Use the modal analysis approach to calculate and plot the motions X1, X2 each on a separate plot and save them as JPEG images. Do not forget to add the axes labels and the title of each plot. The initial conditions on the displacement and velocity are x 10 = 1, xzo = -1, and vio = 0,020 = 0. Take a time interval of your choice that displays the graphs clearly. 10 = Voprio t to sin(ase + tan sonra 1:) = Vario t sin(x + tan even Steps in Solving Equation (4.54) by Modal Analysis 1. Calculate M-1/2 2. Calculate R = M RKM" the mass-normalized stiffness matrix. 3. Calculate the symmetric eigenvalue problem for K to get and 4. Normalize v; and form the matrix P = 2. 5. Calculate S = M-TP and Sl= PMR 6. Calculate the modal initial conditions:(0) = S'xt(0) = S - 7. Substitute the components of (0) and (0) into equations (4.66 and (4.67) to get the solution in modal coordinate r(t). X. Multiply rid) by S to get the solution (1) = S(). Note that is the matrix of mode shapes and P is the matrix of eigenvectors 0 [ki + k k 0 Ik kz + k3 kg x = o -A k + ks MATLAR 2015 PLOTS APS EDITOR PUBLISM VEW Init - 3 Section Compare - Go To - Comment 95 Breakpoints Rou nd Aance Run and O Program Files MATLAB MATLAR Product Server 2015 Problem 1 (50%) 10 For a multi-degree of freedom system that contains 2 masses and 2 springs, whose values are respectively m, - 10 kg.mg = 20 kg. and k, = 100 kg = 200; Use the modal analysis approach calculate and plot the motions X X, cach on a separate plot and save them as JPEG images Do not forget to add the axes labels and the title of each plot. The initial conditions on the displacement and velocity are X = 1.X -1 and 0, = 0. Take a time interval of your choice that displays the graphs clearly. Steps in Solving Equation (4.54) by Modal Analysis 1. Calculate M12 2. Calculate R-M K M the mass-normalized stiffness matrix 2. Calculate the symmetric eigenvalue problem for R to get and 4. Normalize and form the matrix P = 5. Cakulate SM-pand S py 6. Calculate the modal initial conditions ) = S (0) =S z Substitute the components of 0) and inte equations (4.16) and (4.67) to get the solution in modal coordinate in X Multiply by to get the solution - Se. Note that is the matrix of mode shapes and Pis the matrix of eigen vectors ky + k -; 0 k ki + k 0 k Problem 1 (50%) For a multi-degree of freedom system that contains 2 masses and 2 springs, whose values are respectively m, = 10 kg, m2 = 20 kg, and k, = 100 k, = 200; Use the modal analysis approach to calculate and plot the motions X1, X2 each on a separate plot and save them as JPEG images. Do not forget to add the axes labels and the title of each plot. The initial conditions on the displacement and velocity are x 10 = 1, xzo = -1, and vio = 0,020 = 0. Take a time interval of your choice that displays the graphs clearly. 10 = Voprio t to sin(ase + tan sonra 1:) = Vario t sin(x + tan even Steps in Solving Equation (4.54) by Modal Analysis 1. Calculate M-1/2 2. Calculate R = M RKM" the mass-normalized stiffness matrix. 3. Calculate the symmetric eigenvalue problem for K to get and 4. Normalize v; and form the matrix P = 2. 5. Calculate S = M-TP and Sl= PMR 6. Calculate the modal initial conditions:(0) = S'xt(0) = S - 7. Substitute the components of (0) and (0) into equations (4.66 and (4.67) to get the solution in modal coordinate r(t). X. Multiply rid) by S to get the solution (1) = S(). Note that is the matrix of mode shapes and P is the matrix of eigenvectors 0 [ki + k k 0 Ik kz + k3 kg x = o -A k + ks