Experimental Vibration Analysis of a Loudspeaker Enclosure
Tom Zarembka, Purdue University, Mechanical Engineering Technology
401 North Grant Street, West Lafayette, IN, 47907-2021
Introduction
Speaker design is a function of both theoretical knowledge and applied experience. Designing a superior loudspeaker takes
the application of speaker design theory and prior trial and error design experience. Because the driver is firmly mounted to
the enclosure, the movement of the speaker cone, along with the pressure created within the enclosure, excites vibration of
the enclosure walls. These vibrations produce unwanted noises that disrupt the desired response of the speaker system.
Using simple braces mounted on the interior walls of the enclosure has been the typical attempt to solve this problem, but the
trial and error process typically used is not the most effective solution.
The purpose of this project is to develop an engineering approach to bracing design. Vibration analysis of a speaker enclosure
is used to measure the natural vibration response. The results are used to create a systematic procedure to design effective
braces.
Measurements and Analysis
First, a single, air suspension enclosure was designed and built according to Thiele and Small specifications for frequency
response and low frequency performance. A single input (fixed impact), multiple output (roving accelerometer) vibration
measurement system was used. With the accelerometers in place at specified locations on the enclosure, the enclosure was
impacted with a modal impact hammer. The acceleration data was collected in the form of MATLAB® array data using MRIT
(multiple reference impact testing) data acquisition software. The accelerometers were moved to the next position and the
process was repeated for the whole enclosure.
The data acquisition program was used to transfer the time domain acceleration data from the accelerometers into the
frequency domain in the form of frequency response functions (FRFs). The FRF is the ratio of the displacement response on
the enclosure wall to the input force from the impact hammer. From the FRFs, the resonant or modal frequencies were
determined. Also, using the FRFs and X-Modal2 software, animated mode shapes of the enclosure walls were created. The
transformation between the analytical model and the frequency domain is described in more detail below.
SDOF Mathematical Model
MDOF Experimental Model
A single degree of freedom (SDOF) vibration system is
represented by the mass/spring/damper model in Figure 1.
The speaker system can be represented as a sum of
individual SDOF models, resulting in a multiple degree of
freedom (MDOF) model. The FRF of the top panel of the
enclosure, which is the experimental MDOF response of
the enclosure, is shown in Figure 2. Modal frequencies
and mode shapes are determined from the location of the
peaks and the relative magnitudes of each accelerometer.
Figure 1: SDOF Analytical Model
From this, Newtonian laws are applied resulting in the time
domain expression in Equation 1. A Fourier transform
produces the frequency domain expression in Equation 2.
m&x&(t ) + cx& (t ) + kx (t ) = f (t )
(1)
X(ω) = H(ω) * F(ω)
(2)
The compliance H(ω) is the ratio of the output X(ω) to the
input F(ω) as a function of frequency, or the FRF.
Figure 2: MDOF Experimental FRF for Top Panel
Results
The significant modal frequencies determined were 60 Hz, 240 Hz, 325 Hz, 480 Hz, and 682 Hz. These frequencies displayed
the greatest amount of wall movement. Different types of wall movement were observed, including whole wall movement, half
wall movement in and out of phase, and quarter wall movement off and on center of the walls. There was also considerable
torsion movement in the lower frequencies. The vibration modes that have the most effect on sound reproduction are modes
with the most whole and half wall section movement. At 240 Hz, the mode shape displays a strong breathing mode. This
produces a noticeably stronger sound radiation response, because the sound is amplified across the entire area of the wall. At
480 Hz, the mode shape displays a dipole configuration, where one half of the wall moves independently of the other. This
produces a two-tone sound radiation response. Below are pictures of the left and right panels at 240 Hz and 480 Hz. These
pictures display both a whole wall movement and dipole movement.
Figure 2: Left and Right Panel Mode Shapes at 240 and 480 Hz
The acoustic cavity modes of the air inside the enclosure were also quickly analyzed in this project. A cavity mode analysis
provides the modal frequencies of the air within the enclosure. Based on the enclosure dimensions, the first cavity resonant
frequency was calculated to be 466 Hz, assuming a one-dimensional plane wave model of the air inside the enclosure. The
466 Hz cavity mode is close to the measured enclosure vibration frequency of 480 Hz. In this case, the first cavity mode within
the enclosure may be coupled with the movement of the wall, and further create sound disturbances.
Conclusions and Ongoing Work
Experimental modal analysis was used to characterize the free response (modal frequencies and mode shapes) of the
speaker enclosure. The vibration modes having the most effect on sound reproduction were determined to be the 235 Hz
breathing mode and the 480 Hz dipole mode. Also, to determine the effect the air has within the enclosure, an estimate of the
acoustic cavity modes and coupling was made. Because the calculated first cavity mode was 466 Hz, it may couple with the
480 Hz modal frequency in creating sound disturbances. Braces will be designed for locations on the enclosure that display
maximum wall movement, on the center of maximum wall deflection from these combined effective modes. The vibrations will
be moved to higher frequencies when bracing is applied, and will be replaced by vibrations that have less amplitude of
movement. Bracing design will be validated with operational vibration and sound reproduction testing. The validation phase of
the project will be completed in the Spring 2004 semester.
Acknowledgements
Professor Heather Cooper, P.E. – Faculty Advisor, Mechanical Engineering Technology, Purdue University
Professor Douglas Adams, PhD – Herrick Research Facility Advisor, Mechanical Engineering, Purdue University
References
Dickason, V. The Loudspeaker Design Cookbook, Peterborough, New Hampshire: Audio Amateur Press, 2000.
Dossing, O. Structural Testing, Part 1: Mechanical Mobility Measurements, Denmark: Bruel & Kjaer, 1988.
Dossing, O. Structural Testing, Part 2: Modal Analysis and Simulation, Denmark: Bruel & Kjaer, 1988.