Evaluation of methods for analysis of multi-degree-of-freedom systems with damping

A general review of various methods for studying the behavior of linear lumped parameter systems with viscous damping is presented. Five methods are discussed. These are: (1) Normal Mode Technique (2) Ho\u27s Method (3) Impedance Method (4) Graphical Technique (5) A Method for Reducing Degrees-of-freedom. For solution of vibration problems by the Normal Mode Technique, the systems are classified as (1) classically damped or (2) non-classically damped. It is shown that the classically damped systems are relatively easy to solve. For non-classically damped systems, the method proposed by K. A. Foss has been employed. This method is quite complex, but does provide an exact solution in most cases. In Holzer\u27s Method, equations for both undamped and damped systems are derived. A sample table is presented which is employed to solve these equations. Systems having dampers between masses as well as between the masses and ground have been discussed. Also branched systems have been treated. In the Impedance Method, the four-pole parameters of a mass, spring and damper are derived and the formulas for solving tandem and parallel connections are presented. In the Graphical Technique, procedures for arranging the equations of motion in a form suitable for graphical solution are outlined. Application of this method to branched systems is discussed. In the Method for Reducing Degrees-of-Freedom, two problems are presented to illustrate the use of this method. The results obtained have been compared with exact solutions. Advantages and disadvantages of each of these methods are discussed on a comparative basis. A sample problem is solved by all of these methods and the results are compared. Suggestions for further work are mode --Abstract, page ii-iii