D'Alembert Principle in Structural Dynamics

Dynamics of Structures

Structural Engineering Simplified

Chapter 1. Undamped Single Degree of Freedom System

Chapter 1

1.1 Degrees of Freedom Concept 1.2 Dalembert Principle 1.3 Springs 1.4 Developing the Eq. of Motion 1.5 What is Phase?1.6 Free Vibration Animation 1.7 Examples

1.2 Dalembert Principle

FIgure 1.2.1 A car moving with acceleration a

Dynamic Equilibrium and Inertial Force

Dynamic Equilibrium is the state of a system where all the dynamic forces acting on the system are balanced by Inertial Force (which is a fictitios force applied againist its motion direction)

In this example

As the vehicle engine produces a force F_e that propels the car forward to overcome the frictional forces F_f, an inertial force F_i is developed opposite to the vehicle motion.The same result can be obtained by applying Newton's second law.