Question 13.3.1: Design of a Vibration Absorber A certain machine with suppor...

System Dynamics

Design of a Vibration Absorber

A certain machine with supports has a measured natural frequency of 5 Hz. The machine will be subjected to a rotating unbalance force having an amplitude of 2 lb and a frequency of 4 Hz. Design a dynamic vibration absorber for this machine. The available clearance for the absorber’s motion is 0.5 in.

The "Step-by-Step Explanation" refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.
Our explanations are based on the best information we have, but they may not always be right or fit every situation.

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

This Question has been Answered.

Already have an account?

Related Answered Questions

Question: 13.2.2

Isolation of a Motor Often motors are mounted to a base with an isolator consisting of an elastic pad. The pad serves to reduce the motor’s rotating unbalance force transmitted to the base. A particular motor weighs 10 lb and runs at 3200 rpm. Neglect damping in the pad and calculate the pad ...

Verified Answer:

A 90% force reduction corresponds to a transmissib...

Question: 13.7.1

Root Locus of a Suspension Mode Consider the two-mass suspension model developed in Example 4.5.9 in Chapter 4, and shown again in Figure 13.7.1. The equations of motion are m1x1 = c1(x2 − x1) + k1(x2 − x1) m2x2 = −c1(x2 − x 1) − k1(x2 − x1) + k2(y − x2) We will use the following numerical values: ...

Verified Answer:

a. Transforming the equations of motion using zero...

Question: 13.6.1

Linearizing a Nonlinear Spring Model Suppose a particular nonlinear spring is described by (13.6.1) with k1 = 1400 N/m and k2 = 13000 N/m³. Determine its equivalent linear spring constant k for the two equilibrium positions corresponding to the following masses: a. m = 4 kg b. m = 14 kg In addition ...

Verified Answer:

The first step is to determine the equilibrium pos...

Question: 13.4.5

Sensitivity of Node Location For the vehicle in Example 13.4.4, investigate the sensitivity of the bounce and pitch node location to uncertainty in the parameter values ...

Verified Answer:

Rearrange the mode ratio expression to obtain [lat...

Question: 13.4.4

Locating Node Points Evaluate the mode shapes and mode frequencies of the vehicle shown in Figure 13.4.2 for the case: k1 = 1.6 × 10^4 N/m, k2 = 2.5 × 10^4 N/m, L1 = 1.5 m, L2 = 1.1 m, m = 730 kg, and IG = 1350 kg · m². ...

Verified Answer:

Dividing the characteristic equation (13.4.8) by m...

Question: 13.4.3

Pitch and Bounce Modes of a Vehicle Determine the mode shapes and mode frequencies of the vehicle shown in Figure 13.4.2. ...

Verified Answer:

The mode ratio can be found from either (13.4.5) o...

Question: 13.4.2

Nonsymmetric Modes Find and interpret the mode ratios for the system shown in Figure 13.4.1, for the case m1 = m, m2 = 3m, k1 = k, and k2 = k3 = 2k. ...

Verified Answer:

For this case, equation (3) in Example 13.4.1 beco...

Question: 13.4.1

Modes of Two Masses in Translation EXAMPLE 13.4.1 Find and interpret the mode ratios for the system shown in Figure 13.4.1, for the case m1 = m2 = m, k1 = k3 = k, and k2 = 2k. ...

Verified Answer:

The equations of motions for the system are [latex...

Question: 13.3.2

Sensitivity Analysis of Absorber Design Suppose the main mass in the system in Example 13.3.1 has the value m1 = 0.8 slug. Evaluate the sensitivity of the absorber design to variations in the input frequency. ...

Verified Answer:

The absorber values from the previous example are ...

Question: 13.2.3

Shaft Design with Rotating Unbalance Rotating machines such as pumps and fans must have their shafts supported by bearings, and often are enclosed in a housing. Suppose that the rotor (the rotating element) of a specific machine has mass of 300 kg and a measured unbalance of mu ε = 0.5 kg · m. The ...

Verified Answer:

First convert the speed into rad/s: 3500 rpm = 350...