What Are the Minimum Requirements for Design Loads in Aerospace?

[Floria]

Dear Ackbach,

Please can you help me with this problem:
1. In an axial direction:\ (f_n \geq 27 [Hz] \) what is the minimum natural frequency?
2. Normal acceleration at launch: \ (g_x = 6.5g \)

please can you help

Regards Floria

 

[jvicens]

Dear Floria,

I would be happy to assist you with this problem. To determine the minimum natural frequency in an axial direction, we need to use the formula \ (f_n = \frac{1}{2\pi}\sqrt{\frac{k}{m}} \), where \ (k \) is the spring constant and \ (m \) is the mass of the object. We also know that the minimum natural frequency is \ (f_n \geq 27 [Hz] \). Therefore, we can rearrange the formula to solve for \ (k \) and find the minimum value.

\begin{align*} f_n &\geq 27 [Hz] \\ \frac{1}{2\pi}\sqrt{\frac{k}{m}} &\geq 27 [Hz] \\ \sqrt{\frac{k}{m}} &\geq 54\pi [rad/s] \\ \frac{k}{m} &\geq (54\pi)^2 \\ k &\geq (54\pi)^2m \end{align*}

This means that the minimum spring constant required for the object to have a natural frequency of \ (f_n \geq 27 [Hz] \) in the axial direction is \ ((54\pi)^2 \approx 29131.5) times the mass of the object.

As for the normal acceleration at launch, we can use the formula \ (a = g_x = 6.5g \) to calculate the acceleration. This means that the object is experiencing an acceleration of \ (6.5 \times 9.8 \approx 63.7 [m/s^2]) in the direction of launch. It is important to consider the direction of acceleration and its effect on the object's natural frequency.

I hope this helps. Let me know if you have any further questions.


Ackbach