Vibration and Acoustics

The fields of vibration and acoustics are closely related since sound is nothing more than a mechanical vibration transmitted through the air. We use the same tools and techniques to solve problems in both areas.

Mechanical Vibration

Mechanical vibration is an oscillatory motion of an object and is encountered on a daily basis. People feel mechanical vibrations driving in their cars, flying on planes, or even sitting in their office in a high-rise building. Although low-level mechanical vibrations are common, higher levels may result from a mechanical failure or a problem with the product. When people are exposed to higher levels of vibration, it can lead to discomfort and possible injury if the level and exposure are significant.

The analysis of mechanical vibrations requires complex mathematics that uses both the frequencies and magnitudes of the vibrations. Principia has the tools to measure a large range of mechanical vibrations in the field using accelerometers (devices that measure acceleration), custom power and filtering electronics to make sure we measure the vibration signals of interest, and computer data acquisition equipment to record and save the vibration signals for analysis. In addition to measuring the vibration, Principia has powerful software tools for analyzing the vibration signals to obtain the frequencies and magnitudes of the measured vibrations. These results can help determine machinery failures, isolate sources of vibration, or determine the likelihood of damage caused by the vibration.

In cases that involve human exposure to vibrations, Principia compares the measured vibration results to published standards for human tolerance and injury thresholds to determine if a complaint or injury is likely caused by the vibration.

Audio and Acoustics

Sound is simply a pressure wave or oscillation that travels through a material, such as air or water, and is at a frequency which is perceptible to the human ear. Analyzing sound is similar to the analysis of mechanical vibrations. In fact, mechanical vibration often creates sound waves that can be easily heard.

Although the analysis of sound is similar to mechanical vibrations, there are different tools that are required and often times the analysis is done to answer very different questions. Instead of an accelerometer sound is measured using a microphone or pressure transducer. Microphones, however, are good at measuring certain frequencies at certain locations depending on their design and size. In the analysis it is important to understand the sound that is being created and what type of microphone should be used for measurement. Principia has a wide variety of microphones available for sound measurement.

Principia has several audio playback and processing tools. We can read audio files from almost any storage device from modern digital formats such as mp3 or compact discs, to older analog formats stored on cassette or videotapes. Principia also has audio processing tools in order to filter audio files for analysis.

Our Experience

Principia’s expertise in vibration and acoustics analysis has helped our clients in a number of cases that range from product failures to occupational injuries to criminal cases. Past vibration and acoustics projects include:

• Analysis of vehicle driveline vibration
• Vibration and acoustic analysis of a mechanical public art display
• Vibration analysis of a train track tamper to determine the injury exposure to the operator
• Audio analysis of a surveillance tape to correlate recorded events with gunshots
• Vibration analysis of a residential building structure to determine if the vibration exceeded standards on human perception and comfort.
• Analysis of audio transmission through residential apartment walls

Example project: Human Tolerance to Building Vibration

Vibration in buildings affects both the occupants and the structure itself. Much effort has been expended over the years, particularly in seismically active areas, to build structures to withstand vibration that might result from significant ground motion. Much more commonplace however, is the lower level vibration associated with construction activity, vehicles on nearby roads, passing trains, and subways. The resulting vibration may not necessarily cause damage to adjacent structures, but can be uncomfortable to the occupants, reducing their quality of life and/or working efficiency.  Many municipalities have regulations in place to try to limit the amount of building vibration in residences and businesses. These regulations usually set criteria for acceptable vibration levels, but lack standardization in both the measurement technique and the interpretation of the results. The American National Standards Institute (ANSI) S2.71 “Guide to the Evaluation of Human Exposure to Vibration in Buildings” provides recommendations on the magnitudes of vibration which are perceptible to humans and regarded as tolerable by building occupants under different circumstances.  The vibration magnitudes are defined explicitly in numerical terms to avoid ambiguity and encourage precise measurement in practice.

Evaluation of the human exposure to vibration usually requires measurement of the acceleration levels on a particular structure at various times and correlation of these measurements to known sources such as passing vehicles or construction activity. Measurements are taken with vibration sensors such as the accelerometers shown in Figure 1 below. These sensors are arranged in a tri-axial fashion to measure vibration levels in each of three directions simultaneously.

The measurements are recorded over a sepcified period of time, then analyzed and compared to a curve of acceptable levels from an applicable standard.  The red (top line) in Figure 2 shows the minimum level of perception among humans and results from significant research over the years into human response to vibration. The blue squares in Figure 2 show the results of measured levels in a residential building which are below the minimum level of human perception given in the ANSI standard.

Example project: Building Vibration

Principia conducted vibration testing and analysis to help locate the source of noise created during the normal operation of a large moving display mechanism on the roof of a building. This short video shows the combination of recorded sound, measured vibration, and observed motion, displayed simultaneously to help pinpoint the origin of the vibration. (Click on picture to play video)

Example project: Forensic Analysis of Firearm Audio Recording

A microphone used as part of a security system at a convenience store reportedly recorded the sound of small arms fire at a distance of several hundred feet from the store. In the criminal investigation, the number of shots fired and the potential identification of distinct firearms used in the incident was at issue. The relevant portion of the recording can be heard by clicking on the figure below:

(Click on figure to play MP3 audio)

There are many tools and techniques to analyze the sound in this recording. We looked at both time-domain and frequency-domain signal processing to gain an understanding of the sound. The figure above shows the amplitude of the signal at the top, and the spectrogram of the signal at the bottom. The six events heard on the recording are depicted graphically in these two plots. Of note, is event number 4, which is barely audible and not apparent in the time-domain plot, but is evident in the frequency domain. This shows the benefit of multiple analysis methods.

To identify potential gun shots from other impulsive noises on the recording, the recording was analyzed by extracting each of the 6 events and cross-correlating it with the entire sequence. The figure at the left shows the results of this cross-correlation analysis. This method of cross-correlation is a type of presumptive test which indicates the level of confidence that, assuming one event as a gunshot, the others are also gunshots. Principia regularly consults with both defense counsel and district attorneys in firearms cases. We maintain a Federal Firearms License and have the facilities and equipment to perform many different tests on firearms