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### DOMV No 2 RESPONSE OF LINEAR SDOF SYSTEMS TO GENERAL LOADING (2).pdf

• 1. Response of linear SDOF systems to general loading – use of superposition. Mass-Spring Damper System y is the displacement, in the downward direction, as a result of the force p(t) acting on m p(t) k c m y
• 2. An approach to constructing the general solution for arbitrary forcing
• 3. Linear systems satisfy the principle of superposition (in the Time and Frequency Domains) ?
• 4. Two special free-decay response functions The Unit Amplitude Free-Decay Function
• 5. So what does the UAFD function look like?
• 6. Two special free-decay response functions The Unit Velocity Free-Decay Function
• 7. So what does the UVFD function look like?
• 8. The free response to any set of initial conditions (from superposition) is: ( ) ( ) ( ) y y y t y y t cf UAFD UVFD =  +  0 0  ( )
• 9. The Impulse Response function h(t)
• 10. Impulse response Mass-Spring Damper System Consider a unit impulse h(t) applied to a mass- spring-damper system, with light (subcritical) damping parameter ξ (i.e. ξ << 1) and natural frequency ωn . How would it respond? h(t) 2ξωn y
• 11. The Impulse Response function (irf) h(t) (identical to the UVFD function)
• 12. To recap Two functions have been defined: the Unit Amplitude Free Decay Function: 𝑦(𝑡) = 𝑦UAFD(𝑡) and the Impulse Response Function h(t) (which is identical to the Unit Velocity Free Decay Function): 𝑦 𝑡 = h t = 𝑦UVFD 𝑡 We will see in the next lecture that only these two functions are needed to generate the general solution to the forced response of a SDOF system.
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