Structural Dynamics Characteristic Roots

Finding the the natural frequencies of a continuous beam, plate, membrane or even an acoustical volume requires solving for the eigenvalue roots of a characteristic equation, which may contain trigonometric or Bessel functions.

Matlab provides an fzero function which can be used for this purpose. The fzero command is a function file. The algorithm, created by T. Dekker, uses a combination of bisection, secant, and inverse quadratic interpolation methods.

Here is a script which demonstrates this function: vibration_roots.m

The script has options for the following equations:

f(x)=Bessel Jo
f(x)=Bessel J1
f(x)=Bessel J2
f(x)=Bessel (Jn+1(x)/Jn(x)) + (In+1(x)/In(x)) -2x/(1-mu)

* * *

The roots may also be found via the Newton-Raphson method as shown in: Newrap.pdf

* * *

See also:

Beam Natural Frequencies

Bessel Functions in Vibration Analysis

* * *

– Tom Irvine

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s