WEEK-2: Governing equation of SDOF systems Assoc. Prof. Dr. Abdullah Seçgin

Governing equation (Equation of motion) of SDOF systems a) By equivalent energy method

Example: Find equivalent stiffness using “Equivalent energy method”

Example: Find equivalent mass using “Equivalent energy method”

Example: Find equation of motion of the following system by using Equivalent energy method.

b) By Newton’s Second Law Equation of motion (Governing equation)

Free-Body Diagram (FBD) System

Example: Find equation of motion of the following system by using Newton’s Second Law.

Example: Find equation of motion of the following system by using Newton’s Second Law.

Example: Find equation of motion of the following system by using Newton’s Second Law.

SOLVED DURING THE CLASS Example: Find governing equations by a) Equivalent energy b) Newton’s Second Law by defining equivalent mass, stiffness and damping constant SOLVED DURING THE CLASS

Do it yourself ! Do it yourself ! Example: Show that the system’s equation of motion is By equivalent energy method By Newton method Do it yourself ! Do it yourself !