Vibrational analysis damped systems

The boundary conditions established by the machine design determine the freedom of movement permitted within the machine-train. A basic understanding of this concept is essential for vibration analysis. Free vibration refers to the vibration of a damped (as well as undamped) system of masses with motion entirely influenced by their potential energy. Forced vibration occurs when motion is sustained or driven by an applied periodic force in either damped or undamped systems. The following sections discuss free and forced vibration for both damped and undamped systems. 

Lutes LD, Sarkani S (2004) Random vibrations - analysis of structural and mechanical vibrations. Elsevier, Boston Michaelov G, Sarkani S, Lutes LD (1999a) Spectral characteristics of nonstationary random processes - a critical review. Struct Saf 21 223-244 Michaelov G, Sarkani S, Lutes LD (1999b) Spectral characteristics of nonstationary random processes -response of a simple oscillator. Struct Saf 21 245-267 Muscolino G (1991) Nonstationary pre-envelope covariances of nonclassically damped systems. J Sound Vib 149 107-123... 

Figure P14.8 also shows the error norm, ej, versus the number of Ritz vectors (from Problem 14.7). The error is smaller when Ritz vectors are used, because they are derived from the force distribution. Ritz vectors are useful for dynamic analysis of large systems with classical damping, since the vibration properties of the system can be obtained by solving, a smaller eigenvalue problem of order 7, instead of original eigenvalue problem of size N. It must be noted that the resulting frequencies and mode shapes are approximations to the...

---