In this module the equation of motion of continuous systems or distributed mass systems will be derived using both d'Alembert principle and extended Hamilton's principles. Different one-dimensional systems such as longitudinal vibration of rod, transverse vibration of string, torsional vibration of rod and transverse vibration of Euler-Bernoulli beams will be considered in this module.

Introduction to Continuous systems

In the previous modules we have studied about discrete mass system, which are modeled as single, two or multi-degrees of freedom systems. In these cases the system has a definite number of lumped masses, stiffness elements and damping elements. For example the cantilever beam with a tip mass as shown in Figure 10.1 is modeled as a single degree of freedom system with a spring and a mass. The stiffness k of the system was calculated using the following equation.