1 Jiraphon Srisertpol, Ph.D School of Mechanical Engineering 2 Recommended reading : ... ก : กก, Pearson Education Indochina 2545 Singiresu S.Rao : Mechanical Vibration (Fourth Edition) ,Prentice Hall 2004. SI Edition Leonard Meirovitch : Fundamentals of Vibrations , Mc-Graw Hill 2001. Kelly S. Graham : Fundamentals of Mechanical Vibrations, Mc-Graw Hill 2000. 3 Introduction to Vibration and The Introduction to Vibration and The Introduction to Vibration and The Introduction to Vibration and The Free Response Free Response Free Response Free Response The Spring-Mass model Single –degree of freedom Simple harmonic motion Relationship between Displacement, Velocity and Acceleration Representations of harmonic motion 4 School of Mechanical Engineering 4
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Introduction to Vibration and The Free Responseeng.sut.ac.th/me/meold/1_2552/425304/Mechanical_Vibrations-1[1].pdf · SingiresuS.Rao: Mechanical Vibration (Fourth Edition) ,Prentice
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2004. SI Edition� Leonard Meirovitch : Fundamentals of Vibrations , Mc-Graw Hill 2001.� Kelly S. Graham : Fundamentals of Mechanical Vibrations,
Mc-Graw Hill 2000.
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Introduction to Vibration and The Introduction to Vibration and The Introduction to Vibration and The Introduction to Vibration and The Free ResponseFree ResponseFree ResponseFree Response� The Spring-Mass model
� Single –degree of freedom
� Simple harmonic motion
� Relationship between Displacement, Velocity and Acceleration
� Representations of harmonic motion
4School of Mechanical Engineering 4
5School of Mechanical Engineering 5 6
The Vibration of a Fixed-Fixed String
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The main mass and dynamic absorber at three
frequencies.
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Vibration Characteristics of a Vibration Characteristics of a Vibration Characteristics of a Vibration Characteristics of a SpringSpringSpringSpring
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Fundamental Fundamental Fundamental Fundamental TorsionalTorsionalTorsionalTorsional Mode of a Mode of a Mode of a Mode of a Valve Support Stand Valve Support Stand Valve Support Stand Valve Support Stand
Two degree of freedom systemTwo degree of freedom systemTwo degree of freedom systemTwo degree of freedom system
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Three degree of freedom systemThree degree of freedom systemThree degree of freedom systemThree degree of freedom system
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Infinite number of degree of freedom Infinite number of degree of freedom Infinite number of degree of freedom Infinite number of degree of freedom systemsystemsystemsystem
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���������� ก��������ก��ก������������ก���
� Discrete System (Lumped System)-��""�*�������ก'�#�/ก����$���(#�(/�/��+'�/�"��2�����������*��'�ก�/���#����
� Continuous System (Distributed System)- ��""�*��*'�/�"��2������)-������(���'�ก�/
Mathematical Model of Mathematical Model of Mathematical Model of Mathematical Model of MotorcycleMotorcycleMotorcycleMotorcycle� ����������ก."�'����*����+�*���/ • Single-degree of freedom model �*�.�/�����) b.
� ���#������$�����ก����(��+$/#+���������/� (Hysteretic Damping or
Structural Damping)
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DampingDampingDampingDamping
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Viscous DampingViscous DampingViscous DampingViscous DampingAll real systems dissipate energy when they vibrate. To account for this we must consider damping. The most simple form of damping (from a mathematical point of view) is called viscous damping. A viscous damper (or dashpot) produces a force that is proportional to velocity.
Damper (c)
( ) ( )cf cv t cx t= − = − ɺ x
fc
Mostly a mathematically motivated form, allowinga solution to the resulting equations of motion that predictsreasonable (observed) amounts of energy dissipation.