Help w/ using Blevins formula for natural frequency of a cylinder

AI Thread Summary
The discussion focuses on using Blevins' formula to calculate the natural frequency of a hollow cylinder, specifically seeking clarification on determining mass per unit length (m) and the area moment of inertia (I). For a thin-walled cylinder, the correct formula for mass per unit length is derived from the area multiplied by the mass per unit volume, specifically using the outer diameter, wall thickness, and density. Participants debate the appropriate formula for I, with two options presented: one based on the outer and inner diameters and another for thin-walled tubes. The need for precise definitions and correct formulas is emphasized to ensure accurate calculations. Overall, the thread seeks to clarify these key parameters for effective application of the formula.
GenSoft3d
Messages
31
Reaction score
0
I came across this formula by Blevins for calculating the natural frequency of a hollow cylinder and was hoping that someone could answer a question I have for calculating the mass per unit length (m). Here's the formula:

f = A/(2*pi*L^2)*sqrt(E*I/m)

A= 9.87 for first mode
I = Area Moment of Inertia (m^4)
m= Mass per Unit Length (kg/m)


In this formula what equation should I use to determine the m (mass per unit length) for a thin-walled cylinder? Also, does I = pi/64*(d^4-di^4) in this case?
 
Last edited:
Physics news on Phys.org
Does anyone have any insight on this? In the original data where I found this formula it states that "m = mass per unit length of beam (kg/m)". I take it that it's not referring to the mass density of the beam itself but rather the mass per unit length as described. If so then is this actually the area X the mass per unit volume (i.e., PI*d*t*density)?

As for the I (Area Moment of Inertia) I have found two formulas but can someone tell me which is the correct one to use for this application? Here's what I've found:

I = PI * (OD^4 - ID^4)/64

I = PI*d^3*t/8 (for a thin wall round tube)

Any help would be greatly appreciated.
 
This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'
Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
Back
Top