Question

A $300-\mathrm{kg}$ machine is placed at the end of a cantilever beam of length $1.8 \mathrm{~m}$, elastic modulus $200 \times 10^9 \mathrm{~N} / \mathrm{m}^2$, and moment of inertia $1.8 \times 10^{-5} \mathrm{~m}^4$. When the machine operates at $1000 \mathrm{r} / \mathrm{min}$, it has a steady-state amplitude of $0.8 \mathrm{~mm}$. What is the machine's steady-state amplitude when a $30-\mathrm{kg}$ absorber of damping coefficient $650 \mathrm{~N}-\mathrm{s} / \mathrm{m}$ and stiffness $1.5 \times 10^5 \mathrm{~N} / \mathrm{m}$ is added to the end of beam?

   A $300-\mathrm{kg}$ machine is placed at the end of a cantilever beam of length $1.8 \mathrm{~m}$, elastic modulus $200 \times 10^9 \mathrm{~N} / \mathrm{m}^2$, and moment of inertia $1.8 \times 10^{-5} \mathrm{~m}^4$. When the machine operates at $1000 \mathrm{r} / \mathrm{min}$, it has a steady-state amplitude of $0.8 \mathrm{~mm}$. What is the machine's steady-state amplitude when a $30-\mathrm{kg}$ absorber of damping coefficient $650 \mathrm{~N}-\mathrm{s} / \mathrm{m}$ and stiffness $1.5 \times 10^5 \mathrm{~N} / \mathrm{m}$ is added to the end of beam?

Theory and problems of mechanical vibrations

S. Graham Kelly 1st Edition

Chapter 8, Problem 33

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Step 1

The natural frequency ($\omega_n$) of the system can be calculated using the formula: $\omega_n = \sqrt{\frac{k}{m}}$ where $k$ is the stiffness of the beam and $m$ is the total mass at the end of the beam. Show more…

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A $300-\mathrm{kg}$ machine is placed at the end of a cantilever beam of length $1.8 \mathrm{~m}$, elastic modulus $200 \times 10^9 \mathrm{~N} / \mathrm{m}^2$, and moment of inertia $1.8 \times 10^{-5} \mathrm{~m}^4$. When the machine operates at $1000 \mathrm{r} / \mathrm{min}$, it has a steady-state amplitude of $0.8 \mathrm{~mm}$. What is the machine's steady-state amplitude when a $30-\mathrm{kg}$ absorber of damping coefficient $650 \mathrm{~N}-\mathrm{s} / \mathrm{m}$ and stiffness $1.5 \times 10^5 \mathrm{~N} / \mathrm{m}$ is added to the end of beam?

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