Transmissibility Ratio Calculator

✖Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system.ⓘ Maximum Displacement [K]			+10% -10%
✖Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched.ⓘ Stiffness of Spring [k]			+10% -10%
✖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%
✖Applied Force is the force that is intentionally applied to a system to induce or maintain mechanical vibrations.ⓘ Applied Force [F_a]			+10% -10%

✖Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis.ⓘ Transmissibility Ratio [ε]

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Transmissibility Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force
ε = (K*sqrt(k^2+(c*ω)^2))/F_a
This formula uses 1 Functions, 6 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.
Maximum Displacement - (Measured in Meter) - Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system.
Stiffness of Spring - (Measured in Newton per Meter) - Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched.
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.
Applied Force - (Measured in Newton) - Applied Force is the force that is intentionally applied to a system to induce or maintain mechanical vibrations.

STEP 1: Convert Input(s) to Base Unit

Maximum Displacement: 0.8 Meter --> 0.8 Meter No Conversion Required
Stiffness of Spring: 60000 Newton per Meter --> 60000 Newton per Meter No Conversion Required
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
Applied Force: 2500 Newton --> 2500 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε = (K*sqrt(k^2+(c*ω)^2))/F_a --> (0.8*sqrt(60000^2+(9000.022*0.200022)^2))/2500

Evaluating ... ...

ε = 19.2086399991543

STEP 3: Convert Result to Output's Unit

19.2086399991543 --> No Conversion Required

FINAL ANSWER

19.2086399991543 ≈ 19.20864 <-- 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

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Verified by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

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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 Formula

LaTeX Go

Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force
ε = (K*sqrt(k^2+(c*ω)^2))/F_a

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?

Transmissibility Ratio calculator uses Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force to calculate the Transmissibility Ratio, Transmissibility Ratio formula is defined as a measure of the ratio of the amplitude of the force transmitted to the foundation to the amplitude of the force applied to the system, providing insight into the vibration isolation efficiency in mechanical systems. Transmissibility Ratio is denoted by ε symbol.

How to calculate Transmissibility Ratio using this online calculator? To use this online calculator for Transmissibility Ratio, enter Maximum Displacement (K), Stiffness of Spring (k), Damping Coefficient (c), Angular Velocity (ω) & Applied Force (F_a) and hit the calculate button. Here is how the Transmissibility Ratio calculation can be explained with given input values -> 19.20864 = (0.8*sqrt(60000^2+(9000.022*0.200022)^2))/2500.

FAQ

What is Transmissibility Ratio?

Transmissibility Ratio formula is defined as a measure of the ratio of the amplitude of the force transmitted to the foundation to the amplitude of the force applied to the system, providing insight into the vibration isolation efficiency in mechanical systems and is represented as ε = (K*sqrt(k^2+(c*ω)^2))/F_a or Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force. Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system, Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched, 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 & Applied Force is the force that is intentionally applied to a system to induce or maintain mechanical vibrations.

How to calculate Transmissibility Ratio?

Transmissibility Ratio formula is defined as a measure of the ratio of the amplitude of the force transmitted to the foundation to the amplitude of the force applied to the system, providing insight into the vibration isolation efficiency in mechanical systems is calculated using Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force. To calculate Transmissibility Ratio, you need Maximum Displacement (K), Stiffness of Spring (k), Damping Coefficient (c), Angular Velocity (ω) & Applied Force (F_a). With our tool, you need to enter the respective value for Maximum Displacement, Stiffness of Spring, Damping Coefficient, Angular Velocity & Applied Force 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 Maximum Displacement, Stiffness of Spring, Damping Coefficient, Angular Velocity & Applied Force. We can use 3 other way(s) to calculate the same, which is/are as follows -

Transmissibility Ratio = Force Transmitted/Applied Force
Transmissibility Ratio = (Magnification Factor*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Stiffness of Spring
Transmissibility Ratio = Magnification Factor*sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2)

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