Consider the vibration isolation problem from base excitation. Instead of modeling the isolator as a spring and damper placed parallel to each other, model the isolator using the standard linear model. k ∞∞∞∞∞∞∞∞∞0 m base k₁ motion Develop an expression for the displacement transmissibility of the isolator in terms of the normalized forcing frequency, damping ratio, and the ratio of the two spring constants: y = k₁/k Discuss the influence of the stiffness ratio on the performance of the isolator. For a damping ratio of 0.01 and stiffness ratio of 0.05, use the transmissibility curve to find the effective damping ratio of the isolator (this is equivalent to having a spring and damper in parallel). Can the equivalent damping ratio reproduce the transmissibility curve accurately? Discuss. Provide one specific application where it is necessary to use the standard linear model.

Consider the vibration isolation problem from base excitation. Instead of modeling the isolator as a spring and damper placed parallel to each other, model the isolator using the standard linear model. k ∞∞∞∞∞∞∞∞∞0 m base k₁ motion Develop an expression for the displacement transmissibility of the isolator in terms of the normalized forcing frequency, damping ratio, and the ratio of the two spring constants: y = k₁/k Discuss the influence of the stiffness ratio on the performance of the isolator. For a damping ratio of 0.01 and stiffness ratio of 0.05, use the transmissibility curve to find the effective damping ratio of the isolator (this is equivalent to having a spring and damper in parallel). Can the equivalent damping ratio reproduce the transmissibility curve accurately? Discuss. Provide one specific application where it is necessary to use the standard linear model.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

Consider the vibration isolation problem from base excitation. Instead of modeling the isolator as a spring
and damper placed parallel to each other, model the isolator using the standard linear model.
k
m
base
k₁ motion
Develop an expression for the displacement transmissibility of the isolator in terms of the normalized forcing
frequency, damping ratio, and the ratio of the two spring constants:
y = k₁/k
Discuss the influence of the stiffness ratio on the performance of the isolator.
For a damping ratio of 0.01 and stiffness ratio of 0.05, use the transmissibility curve to find the effective
damping ratio of the isolator (this is equivalent to having a spring and damper in parallel). Can the equivalent
damping ratio reproduce the transmissibility curve accurately? Discuss.
Provide one specific application where it is necessary to use the standard linear model.

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