2Vibration of Discrete Systems: Brief Review


The number of degrees of freedom of a vibrating system is defined by the minimum number of displacement components required to describe the configuration of the system during vibration. Each system shown in Fig. 2.1 denotes a single‐degree‐of‐freedom system. The essential features of a vibrating system include: (i) a mass m, producing an inertia force: images; (ii) a spring of stiffness k, producing a resisting force: kx; and (iii) a damping mechanism that dissipates the energy. If the equivalent viscous damping coefficient is denoted as c, the damping force produced is images.

Five schematic diagrams marked (a) to (e) depicting Single-degree-of-freedom systems with stiffness k and mass m.

Figure 2.1 Single‐degree‐of‐freedom systems.

2.1.1 Free Vibration

In the absence of damping, the equation of motion of a single‐degree‐of‐freedom system is given by


where images is the force acting on the mass and images is the ...

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