Ce 226 11415 Part 04 - Equiv Viscous Damping

8/10/2019 Ce 226 11415 Part 04 - Equiv Viscous Damping

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The energy input to an SDOF by imparting to it an initialdisplacement and initial velocity is given by

Recall he displacement response of a free vibration with initial displacement and velocity:

2.3 Energy in Free Vibration

This is the same as the input energy in Eq. 2.3.1. Therefore the total energy is

independent of time and is dependent only on the input energy. Hence, there is

conservation of energy during free vibration of a system without damping.


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The energy dissipated is proportional to the square of the amplitude of motion. It

is not a constant value for any given amount of damping and amplitude since the

energy dissipated increases linearly with the excitation frequency.


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In steady-state vibration, the energy input to the system due to the applied

force is dissipated in viscous damping. The external forcep(t) inputs energy tothe system which for each cycle is

Using Eq. 3.2.12:

Eq. 3.8.2 can be written as (see Derivation 3.6)

Hence, from Eq. 3.8.1 and 3.8.3, ED = EI

The preceding energy concepts help explain the growth of thedisplacement amplitude caused by harmonic force with = nuntil steady-state is attained as shown in Fig 3.2.2. For = n ,=90o and Eq. 3.8.2 gives

EI= po uo (3.8.4)


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. 3.8.2 ()

()

()


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, .., ,fl , .,

.


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(2)

damping ratio and damping coefficient c.


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.

() / 390 / 0.15 2600 /

() . 3..2

2

26

, 0.071 7.1%

/ 2 / 2 ( )

(1/4)(/)

(2 ) 2 / 2(0.071)(2600)/10 36.92 /

Ce 226 11415 Part 04 - Equiv Viscous Damping

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Transcript of Ce 226 11415 Part 04 - Equiv Viscous Damping