Vibration #3: The Human Vocal Chords

Introduction:  “The larynx is located in the throat and contains the vocal chords and glottis. With the exhalation of breath, the diaphragm forces air up through cartilage "horn" of the larynx by contracting. The air moves through the vocal chords, which are situated in the muscular vibrating folds of the larynx, and the glottis, the space formed between them. By stretching the vocal chords, adjusting the tension and varying the air pressure through the glottis, the pitch of our voice is adjusting, tuning higher or lower. A lower sound requires a longer column of air and is felt in the chest, a higher sound uses a shorter column of air and is felt in the nose and head.”  (http://md.essortment.com/vocalchordanat_rzii.htm)

In this example you will execute modal analysis of the vocal chords  and find their natural frequency for a person with these given anatomical dimensions.

 

Physical Problem: The chords are free to vibrate within the two flaps when air rushes past them, however, they are firmly attached to the larynx on the circumference of the circle.

Problem Description:

·         The chords have dimensions and orientation as shown in the figure.

·         They are approximately 2mm thick.

Assume the circumference of the vocal chords are connected to the larynx and are completely fixed in all degrees of freedom. The chord material is assumed to be solid and material properties are constant and isotropic.

·         Young’s Modulus = 6.7e7

·         Poisson’s Ratio = 0.1

·         Density = 898

 

·         Objective:

            To determine the natural frequencies of vibration

            To generate animations of these vibrations.

Figure:

 

 

The cylinder that defines the membrane that forms the vocal chords is 2 mm thick.  It has a radius of 0.025 m.

The triangular prism that defines the air column in the center of the vocal chords is positioned at (0, -0.025), has a radius of 0.048 m, set at an angle of 90° and has a depth of 0.015m.

 

 

 

mesh size of 0.002

 

IMPORTANT: Convert all dimensions and forces into SI units.

·         Create the cylindrical solid defining the basic shape of the vocal chords.

·         Create the triangular prism that defines the air channel between the vocal chords.

·         Subtract this volume from the cylinder you first created such that the final vocal chord shape remains.

·         Define the Material Properties of the vocal chords. (Hint: The Elastic Modulus, Poison’s Ratio and the density of the vocal chords is important to define)

·         Define the Element Properties as a Tet 10 node 92 Structural Solid.

·         Mesh the vocal chords. (Do so by setting the global size of the elements to 0.002.)

·         Apply the boundary conditions. (Displacement of zero on all the outer areas of the vocal chords.  These are the areas that would technically be connected to your throat. )

·         Solve for the natural frequencies of vibration of the vocal chords. (Use a modal analysis using the Block Lanczos Mode Extraction method and solve for 5 modes.)

·         List the nodal frequencies of vibration for the vocal chords.

·         From the results obtained, read the first set, then animate the mode shape using 60 frames with a 0.03 second time delay between frames.  Be sure to show the DOF Solution with both the Deformed and Undeformed Edge.  This will properly demonstrate the vibration patterns in the vocal chords.

·         Plot the nodal solutions to use as screenshots and compare with the answers below.

 (These are the results you should expect:  *Note: Your results may be slightly different due to “mesh uniqueness” but this difference should only be VERY small.)

 

(Modes of vibration:)

First

 

Second

 

Third

 

Fourth

 

Fifth