A mass matrix is a mathematical representation of the distribution of mass in a multi-degree-of-freedom (MDOF) torsional system. It is used in structural analysis to calculate the response of a structure to external forces and loads.
A stiffness matrix is a mathematical representation of the stiffness of each degree of freedom in a MDOF torsional system. It is a square matrix that relates the displacements and forces at each degree of freedom in the system.
Mass and stiffness matrices are used to solve the equations of motion for a MDOF torsional system. By applying external forces and loads to the system, the equations of motion can be solved to determine the system's response, including displacements, velocities, accelerations, and internal forces.
Mass and stiffness matrices are calculated using the mass and stiffness properties of each element in the system. These properties, such as mass, length, and stiffness, are combined using mathematical equations to create the mass and stiffness matrices for the entire system.
One limitation is that mass and stiffness matrices assume linear behavior of the system, which may not always accurately reflect the true behavior of a structure. Additionally, the accuracy of the results depends on the accuracy of the input parameters used to calculate the matrices. Nonlinear behavior and incorrect input parameters can lead to inaccurate results.