Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient Calculator

✖Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss.ⓘ Damping Coefficient [c]			+10% -10%
✖Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.ⓘ Angular Velocity [ω]			+10% -10%
✖Critical Damping Coefficient is the minimum amount of damping required to prevent oscillations in a mechanical system, resulting in a critically damped response.ⓘ Critical Damping Coefficient [c_c]			+10% -10%
✖Natural Circular Frequency is the number of oscillations per unit time of a vibrating system in a circular motion.ⓘ Natural Circular Frequency [ω_n]			+10% -10%

✖Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis.ⓘ Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient [ε]

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Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Transmissibility Ratio = (sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency)^2)))/sqrt(((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2)
ε = (sqrt(1+((2*c*ω)/(c_c*ω_n)^2)))/sqrt(((2*c*ω)/(c_c*ω_n))^2+(1-(ω/ω_n)^2)^2)
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Transmissibility Ratio - Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis.
Damping Coefficient - (Measured in Newton Second per Meter) - Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss.
Angular Velocity - (Measured in Radian per Second) - Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.
Critical Damping Coefficient - (Measured in Newton Second per Meter) - Critical Damping Coefficient is the minimum amount of damping required to prevent oscillations in a mechanical system, resulting in a critically damped response.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is the number of oscillations per unit time of a vibrating system in a circular motion.

STEP 1: Convert Input(s) to Base Unit

Damping Coefficient: 9000.022 Newton Second per Meter --> 9000.022 Newton Second per Meter No Conversion Required
Angular Velocity: 0.200022 Radian per Second --> 0.200022 Radian per Second No Conversion Required
Critical Damping Coefficient: 690000 Newton Second per Meter --> 690000 Newton Second per Meter No Conversion Required
Natural Circular Frequency: 0.19501 Radian per Second --> 0.19501 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε = (sqrt(1+((2*c*ω)/(c_c*ω_n)^2)))/sqrt(((2*c*ω)/(c_c*ω_n))^2+(1-(ω/ω_n)^2)^2) --> (sqrt(1+((2*9000.022*0.200022)/(690000*0.19501)^2)))/sqrt(((2*9000.022*0.200022)/(690000*0.19501))^2+(1-(0.200022/0.19501)^2)^2)

Evaluating ... ...

ε = 17.083354511296

STEP 3: Convert Result to Output's Unit

17.083354511296 --> No Conversion Required

FINAL ANSWER

17.083354511296 ≈ 17.08335 <-- Transmissibility Ratio

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Mechanical » Vibration Isolation and Transmissibility » Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< Vibration Isolation and Transmissibility Calculators

Maximum Displacement of Vibration using Force Transmitted

LaTeX Go Maximum Displacement = Force Transmitted/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))

Stiffness of Spring using Force Transmitted

LaTeX Go Stiffness of Spring = sqrt((Force Transmitted/Maximum Displacement)^2-(Damping Coefficient*Angular Velocity)^2)

Damping Coefficient using Force Transmitted

LaTeX Go Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity

Force Transmitted

LaTeX Go Force Transmitted = Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)

< Forced Vibration Calculators

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration

LaTeX Go Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio

Angular Velocity of Vibration using Force Transmitted

LaTeX Go Angular Velocity = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Damping Coefficient

Damping Coefficient using Force Transmitted

LaTeX Go Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity

Applied Force given Transmissibility Ratio

LaTeX Go Applied Force = Force Transmitted/Transmissibility Ratio

Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient Formula

LaTeX Go

What is meant by Vibration Isolation?

Vibration isolation is a commonly used technique for reducing or suppressing unwanted vibrations in structures and machines. With this technique, the device or system of interest is isolated from the source of vibration through insertion of a resilient member or isolator.

How to Calculate Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient?

Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient calculator uses Transmissibility Ratio = (sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency)^2)))/sqrt(((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2) to calculate the Transmissibility Ratio, Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient formula is defined as a measure of the ratio of the amplitude of the transmitted force to the original force in a mechanical system, providing insight into the system's ability to transmit vibrations. Transmissibility Ratio is denoted by ε symbol.

How to calculate Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient using this online calculator? To use this online calculator for Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient, enter Damping Coefficient (c), Angular Velocity (ω), Critical Damping Coefficient (c_c) & Natural Circular Frequency (ω_n) and hit the calculate button. Here is how the Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient calculation can be explained with given input values -> 17.13421 = (sqrt(1+((2*9000.022*0.200022)/(690000*0.19501)^2)))/sqrt(((2*9000.022*0.200022)/(690000*0.19501))^2+(1-(0.200022/0.19501)^2)^2).

FAQ

What is Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient?

Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient formula is defined as a measure of the ratio of the amplitude of the transmitted force to the original force in a mechanical system, providing insight into the system's ability to transmit vibrations and is represented as ε = (sqrt(1+((2*c*ω)/(c_c*ω_n)^2)))/sqrt(((2*c*ω)/(c_c*ω_n))^2+(1-(ω/ω_n)^2)^2) or Transmissibility Ratio = (sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency)^2)))/sqrt(((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2). Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss, Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations, Critical Damping Coefficient is the minimum amount of damping required to prevent oscillations in a mechanical system, resulting in a critically damped response & Natural Circular Frequency is the number of oscillations per unit time of a vibrating system in a circular motion.

How to calculate Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient?

Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient formula is defined as a measure of the ratio of the amplitude of the transmitted force to the original force in a mechanical system, providing insight into the system's ability to transmit vibrations is calculated using Transmissibility Ratio = (sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency)^2)))/sqrt(((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2). To calculate Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient, you need Damping Coefficient (c), Angular Velocity (ω), Critical Damping Coefficient (c_c) & Natural Circular Frequency (ω_n). With our tool, you need to enter the respective value for Damping Coefficient, Angular Velocity, Critical Damping Coefficient & Natural Circular Frequency and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Transmissibility Ratio?

In this formula, Transmissibility Ratio uses Damping Coefficient, Angular Velocity, Critical Damping Coefficient & Natural Circular Frequency. We can use 3 other way(s) to calculate the same, which is/are as follows -

Transmissibility Ratio = Force Transmitted/Applied Force
Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force
Transmissibility Ratio = (Magnification Factor*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Stiffness of Spring

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