![]() This mode, which has three nodal diameters (6 nodal lines around the circumference) and zero nodal circles, does not radiate sound nearly as well as the n=2 modes. As the bottle vibrates it looks like it has two regions which alternate between bulging outwards and compressing inwards. The mode shape designation (n=2,m=1) means that there are two nodal diameters (moving around the circumference you would find 2n=4 lines with no motion) and as you moved along the length of the bottle you would find zero (m-1) nodal circles. The first prominent vibrational mode of the bottle is essentially a breathing mode, similar to what is observed in a bell, wineglass, or baseball bat. The mode shapes identified in red correspond to the most prominent peaks in the frequency spectrum above. Looking at the measured mode shapes below might help. Actually, the integer m counts the number of anti-nodes (locations of maximum amplitude) so that the number of nodal circles is really m-1. The m integers representing nodal circles are evidenced by a line around the circumference - (a circle) at a fixed location along the length of the bottle - that does not move while the bottle is vibrating. On one side of a nodal line the bottle will be vibrating outwards, while on the other side of the nodal line the bottle is vibrating inwards. So, for a mode shape with n=2 if you traced a path around the circumference of the bottle you would encounter 4=2n lines (2 diameters = 2 pairs of lines on opposite sites of the bottle) where no vibration occurs. A nodal diameter indicates that there are two lines down the length of the bottle (on opposite sides of the bottle) which do not move while the rest of the bottle is vibrating. A node a location (a line on a 2-D surface, or a plane in a 3-D volume) where there is no vibration for a particular mode shape. Each mode shape is designated by a pair of integers, (n,m) where n represents the number of nodal diameters and m represents the number of nodal circles. In order to catalog the important mode shapes, I am using the modal designation which is most commonly used to describe the vibration of systems with cylindrical symmetry (cylinders, bells, drums, baseball bats). The natural frequencies and the animated mode shapes shown below. Software program STAR Modal to curve fit the frequency response functions in order to obtain Response Function, consisting of the ratio of acceleration to force, using a 2-channel frequency analyzer. I attached a small (0.5g) accelerometer to one of the locations near the base of the barrel portion of the bottle, and used a special force hammer to tap the bottle at each of the 106 locations along the length and around the circumference. The bottle was suspended from rubber bands - which allow the bottle to vibrate freely without significantly altering the damping or vibration amplitudes. The figures at left show the grid compared to the actual bottle. ![]() There are points every 0.5-inch along the length and every 1cm around the bottle. I marked the bottle with 106 points forming a grid representative of the shape of the bottle. I used experimental modal analysis to determine the vibrational mode shapes and frequencies for the bottle. But, the next three prominent peaks (at 3200 Hz, 4448 Hz, and 5632 Hz), which appear to dominate the "clink" sound, are the lowest frequency vibrational modes of the bottle, as we will see below. The peak at 1152 Hz is the next higher order acoustic mode inside the cavity. The almost imperceptible peak at 192 Hz is due to the Helmholtz mode, and is the same frequency that one would produce by blowing over the opening of the empty bottle. The frequency spectrum at right represents the sound obtained by holding an empty glass beer bottle lightly at the base, striking the neck with a small metal hammer, and recording the sound using a microphone. (I didn't want to clink two bottles together because then the sound would involve the vibrations of both bottles together). First I made a recording of the sound resulting from striking the neck of a beer bottle with a hard object. In response to a question regarding the sound made by clinking two beer bottles together I became curious and wondered what the vibrational mode shapes of a glass beer bottle look like. Vibrational Behavior of an Empty Beer Bottle The Experiment RussellĪnd may not used in other web pages or reports without permission. All text and images on this page are ©2004-2011 by Daniel A.
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