12/00 mechanical engineering: input output

input/output

composites in concert

Classical guitars can cost as little as $300 for a student model, but for a concert musician the instrument costs at least $5,000.

Virgilio Alejandro Peña Haro wants to change all that. An accomplished classical and concert guitarist, as well as a civil engineer and anthropologist, Peña Haro used finite element analysis software from Algor Inc. of Pittsburgh to arrive at a composite construction intended to make the concert guitar available to more people.

Peña Haro studied classical guitar at the Bach Institute of Music in Lima, Peru, and later at Conservatorio Nacional de Música. He has performed as a solo artist and with orchestras around the world.

Peña Haro also studied engineering. His master's degree work in structural engineering became the missing link between his musical and analytical passions: his master's thesis involved his guitar.

"I wanted to know, 'Why can we not give students a guitar with good sound production at a low price?' " Peña Haro said.

Professional classical concert guitars are expensive: Peña Haro's cost $8,000. The cost is mainly a matter of material and craftsmanship. Woods such as Baltic pine, ebony, and rosewood are expensive and delicate. Craftsmen first make the body, then determine if it meets standards of a classical concert guitar. Any waste of time or materials along the way contributes to the cost.

Using Autodesk's AutoLISP programming language, Peña Haro designed a classical concert guitar for finite element analysis. He imported the CAD solid model into Superdraw III, Algor's finite element model building tool, and created a mesh of plate elements.

To keep his model and analysis as true to a real guitar as possible, Peña Haro assigned material properties to his guitar corresponding to rosewood, for the top and bottom of the body; to Baltic pine, for the outside border of the body; and to ebony, for the neck. The material properties were provided partly by engineers studying abroad, but also determined through a combination of physical and virtual testing.

The procedure calls for simple physical tests that produce a measurable displacement. The engineer models the physical test in the software and analyzes the model. The engineer tweaks the model until its results conform with those of the experiment.

The static load that Peña Haro applied to the model represented the tension of the guitar strings and an estimated 1.5 kilograms representing the weight of the arm of the person playing the guitar. That weight was applied to the border of the guitar frame. The total tension of a tuned guitar was determined in an acoustic laboratory.

Peña Haro determined that stresses caused by the tension of the strings and the weight of a player's arm are not key factors in the sound the guitar produces. Displacements along the body of the guitar, caused by plucking the strings, also proved inconsequential.

With the static stress analysis complete, Peña Haro set about his dynamic analysis to determine the relationship between structural behavior and acoustic response.

Peña Haro decided to investigate changes to the internal structure of the instrument. He performed a natural frequency analysis on his finite element model to determine the frequency at which the resonance box, the body, started to vibrate. Simulating a guitarist holding the guitar's neck and depressing strings over the resonance box, he determined the top of the resonance box begins vibrating at a frequency of 279.7 Hz. The bottom of the resonance box vibrates at 311.04 Hz.

He modeled two more guitars. The second had no thin strips of border wood that attach the top and bottom of the resonance box to the frame of the guitar and also was without reinforcing bars inside the resonance box. The third had no border wood, but had the same internal structure as the original guitar. Dynamic analysis revealed natural frequencies of 230.56 and 277.23 Hz, for the front and back covers of Guitar 2, and 256.49 and 292.49 Hz for the same sides in Guitar 3.

Peña Haro did an acoustic analysis of his three models to determine the level of acoustic intensity—their sound and how loud that sound is—by inputting frequencies representing the 64 notes in eight octaves.

Guitar 1, the traditional model, had the greatest acoustic intensity of the three. Guitar 3 was next and Guitar 2 had the smallest acoustic intensity. Peña Haro deduced that natural frequency and acoustic intensity vary according to what's inside the resonance box.

With that knowledge in hand, Peña Haro used Eagle, a programming language for parametric design and analysis that links various Algor programs. It can shorten the time to run a series of repetitive analyses to hours instead of a couple of days.

Peña Haro arrived at a plastic compound much cheaper to work with than the woods of traditional concert guitars. The new composite plastic guitars began selling in February for approximately $400 each in Peru. Peña Haro is currently looking for investors to help him manufacture 1,000 guitars.

Virgilio Alejandro Peña Haro studied his finite element model to determine the relationship between structural behavior and acoustic response.