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Various aspects of damped vibration, including the causes of damping, different damping models such as viscous, structural, and Coulomb damping, energy dissipation, and the solution of equations of motion. It also discusses practical applications and provides examples of viscous dampers. Students will gain a comprehensive understanding of damped vibration and its significance in mechanical systems.
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Topics: • Introduction to Damped Vibration
Damping Models - Viscous Damping - Energy Dissipation - Damping Parameters - Structural Damping - Coulomb Damping - Solution of Equations of Motion - Logarithmic Decrement - Practical Applications
Vibrating systems can encounter damping in various ways like
Intermolecular friction - Sliding friction - Fluid resistance 2. Damping estimation of any system is the most difficult process in any vibration analysis 3. The damping is generally complex and generally for mechanical systems it is so small to compute Fluid resistantdamper x
Topics: • Introduction to Damped Vibration
Damping Models - Viscous Damping - Energy Dissipation - Damping Parameters - Structural Damping - Coulomb Damping - Solution of Equations of Motion - Logarithmic Decrement - Practical Applications
Occurs when system vibrates in a viscous medium Obeys Newton's law of viscosity The damping force is given by dv dz τ μ = For the given viscousdashpot.. c – damping constant
Topics: • Introduction to Damped Vibration
Damping Models - Viscous Damping - Energy Dissipation - Damping Parameters - Structural Damping - Coulomb Damping - Solution of Equations of Motion - Logarithmic Decrement - Practical Applications
d W V β = 2 d W cw V k η π = = Specific dampingcapacity Loss coefficient The damping properties of the system can be compared using parameterslike β and η Specific damping capacity: Ratio of Energy loss per cycle to the max PE of system Loss coefficient :^ Ratio of energy loss per radian to max PE of system Hence using parameters like β and η we can compare two systems for which we don’t know the value of c
Equation of motion for coulomb damping is
μ
Also Opposite sign to be used for + and – vevelocity Free body diagram
Solution is given by The decrease of is very important is important characteristics of coulomb damping 4 Δ For initial condition of x o displacement and zero input velocity
Now let us know how the solution of the equations of motion areeffected by the introduction of damping parameters. The generalized equation of motion is 0 Mx cx kx
= && & The viscous damping is more common or in other terms equivalentviscous damping is more commonly used in place. Hence using that in the analysis…
SDF viscous damping solutions Damped SDF and freebody diagram The eqn of motion isgiven by x(t)
Under damped
Undamped
Over damped
Critically damped ξ ξ ξ <1 =0 >1 = ξ Over damped The general solution becomes The solution will be non oscillatory and gradually comes to rest
Critically damped The general solution becomes For zero initial conditions
Door Damper
Topics: • Introduction to Damped Vibration
Damping Models - Viscous Damping - Energy Dissipation - Damping Parameters - Structural Damping - Coulomb Damping - Solution of Equations of Motion - Logarithmic Decrement - Practical Applications
The logarithmic decrement is the Natural log of Ratio of the SuccessiveDrops in the Amplitude It is used for the estimation of the value of of the system experimentally ξ For two points
