WEEK-2: WEEK-2: Governing equation of SDOF Governing equation of SDOF

systemssystemsAssoc. Prof. Dr. Abdullah Assoc. Prof. Dr. Abdullah SeçginSeçgin

Governing equation (Equation of motion) of SDOF systemsa) 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.

Equation of motion

(Governing equation)

b) By Newton’s Second Law

System FBD

Free-Body Diagram (FBD)

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.

c

c

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

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

SOLVED DURIN

G THE C

LASS

Example: Show that the system’s equation of motion is

a) By equivalent energy method

b) By Newton method