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Published byTamsin Summers Modified over 6 years ago
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Part I β Basics (1) Geometric model: - interconnected model elements
(2) DOFs of a geometric model (3) FBDs of model elements (4) Elemental equations (5) Energy storage and dissipation (6) Obtain model parameters (7) Obtain simplified equivalent systems hw1~hw4. Also, examples in notes.
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Part II β SDOF systems 2.1 Free vibration of undamped system
(1) Obtain math model (hw4) π 2 π¦ + π π π¦=0 (2) Solution for the vibration (hw5) (3) System property and application (hw5) - the natural frequency: Examples in notes.
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2.2 Free vibration of damped system (1) Obtain math model (hw6)
π 2 π¦ + π 1 π¦ + π π π¦=0 or π¦ +2π π π π¦ + π π 2 π¦=0 π π = π π / π and π= 1 2 π π π 1 π 2 (2) Solution for the vibration (hw7) underdamped: π¦ π‘ =π΄ π βπ π π π‘ sin( π π π‘+π) critically damped: π¦ π‘ = (π΄ 1 + π΄ 2 π‘) π β π π π‘ overdamped: π¦ π‘ = π΄ 1 π π 1 π‘ + π΄ 2 π π 2 π‘ (3) System property and application (hw7) For underdamped systems: π π , π ~( π π , πΏ) relations
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2.3 Harmonically excited vibration
(1) Obtain math model (hw8) π 2 π¦ + π 1 π¦ + π π π¦=β(π‘) or π¦ +2π π π π¦ + π π 2 π¦=πΈπ ππππ‘ (2) Solution for the vibration (hw8) π¦ π‘ = π¦ β π‘ + π¦ π (π‘) π¦ β (π‘) same expression as π¦(π‘) in 2.2, different π΄ 1 , π΄ 2 π¦ π π‘ =ππ ππ(ππ‘+π) Y by Eq. (M): π= πΈ/ π π (1β π 2 ) 2 + (2ππ) 2 1/2 π by Eq. (P): π=β π‘ππ 2 β1 2ππ 1β π 2 (3) Application (hw9) π,π ~ πΈ, π ~( π π , π) relations
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