ABSTRACT
Vibration phenomenon, common in mechanical devices and structures [2,9], is undesirable in many
cases, such as machine tools. But this phenomenon is not always unwanted; for example, vibration is
needed in the operation of vibration screens. Thus, reducing or utilizing vibration is among the
challenging tasks that mechanical or structural engineers have to face. Vibration modeling has been used
extensively for a better understanding of vibration phenomena. The vibration modeling here implies a
process of converting an engineering vibration problem into a mathematical model, whereby the major
vibration characteristics of the original problem can be accurately predicted. The mathematical model of
vibration in its general sense consists of four components: a mass (inertia) term; a stiffness term; an
excitation force term; and a boundary condition term. These four terms are represented in differential
equations of motion for discrete (or, lumped-parameter) systems, or boundary value problems for
continuous systems. A damping term is included if damping effects are of concern. Depending on the
nature of the vibration problem, the complexity of the mathematical model varies from simple spring-
mass systems to multi-degree-of-freedom (DoF) systems; from a continuous system for a single
structural member (beam, rod, plate, or shell) to a combined system for a built-up structure; from a
linear system to a nonlinear system. The success of the mathematical model heavily depends on whether
or not the four terms mentioned before can represent the actual vibration problem. In addition, the
mathematical model must be sufficiently simplified in order to produce an acceptable computational
cost. The construction of such a representative and simple mathematical model requires an in-depth
understanding of vibration principles and techniques, extensive experience in vibration modeling, and
ingenuity in using vibration software tools. Furthermore, it also requires sufficient knowledge of the
vibration problem itself in terms of working conditions and specifications.
