WHAT IS THE MEANING OF LUMPED MASS AND MASS MATRIX?
Lumped mass just means that you assume all the mass is concentrated in one rigid object. This means only the blocks have considered mass…the springs are assumed massless…instead of continuous mass of a coiled wire as it really is. Lumped elasticity is also important in vibration analysis. That means we assume only the springs are deformable and not the blocks. Matrices (plural of matrix) are tables of numbers used to organize our algebra of a problem. A mass matrix is the matrix that organizes all the involved masses. The stiffness matrix organizes all the k-values of all the springs. For the system that looks like this: FIXED}—-\/\/\ k1 /\/\/—–[m1]—-\/\/\/\/ k2 \/\/\/\/\—-[m2] The equations of motion derive as: -k1*x1 + k2*(x2 – x1) = m1*x1″ -k2*(x2 – x1) = m2*x2″ Organizing all to one side: m1*x1″ + k1*x1 – k2*(x2 – x1) = 0 m2*x2″ + k2*(x2 – x1) = 0 Organizing as a matrix equation: M*X” + K*X = 0 M = [ m1, 0] [ 0, m2] K = [ k1 + k2, -k2] [ -k2, … …
