PERUVIAN ENGINEER/GUITARIST EMPLOYS FINITE ELEMENT ANALYSIS TO MAKE STUDYING CONCERT GUITAR MORE AFFORDABLE

The names even sound exotic and expensive: Ramirez, Manuel Contreras, Dieter Hopf, Raimundo. Classical guitars can cost as little as $300 for a bottom-end student model, but the type of instrument that a musician truly can be proud to play costs at least $5,000.

Virgilio Alejandro Peña Haro wants to change all that. A renaissance man of sorts, the Peruvian Peña Haro is an accomplished classical and concert guitarist, as well as a civil engineer and anthropologist. Working to add philanthropist to his curriculum vita, Peña Haro used finite element analysis software from Algor, Inc., to design a guitar that costs less money, but sacrifices nothing in sound. He hopes his new composite plastic guitar will open up the world of classical/concert guitar to more young people in Peru and worldwide.

Peña Haro, now 26, began his affair with the guitar when he was a youngster living in Lima. That’s when he started studying classical guitar at the Bach Institute of Music in Lima and later at Conservatorio Nacional de Música, also in Lima. He has taken classes studying the masters of the instrument - Christopher Parkening (shown below), Carlos Barbosa-Lima, John Williams - and has performed as a solo artist, in duets and with orchestras around the world.

Peruvian engineer Virgilio Alejandro Peña Haro used Algor software to design a classical guitar made of a composite plastic. The guitar, which sacrifices nothing in sound quality, sells for about $400 in Peru -  much less expensive than the several thousands of dollars a wooden guitar like the one above played by international celebrity Christopher Parkening would cost.

Even with such a passion for the sound of his fingers on guitar strings, Peña Haro also found a second love in civil engineering. He came to engineering out of necessity, realizing that he would not be able to support himself financially with his music.

"I had to study something formal to be able to work, due to the pressures of my country and, overall, my parents," Peña Haro said.

He decided to pursue a master’s degree in structural engineering, which became the missing link between his musical and analytical passions: his master’s thesis involved his guitar.

"That was the beginning of my relationship with finite element analysis and with Algor," Peña Haro said. "I wanted to know, ‘Why can we not give students a guitar with good sound production at a low price?’. Why not help the manufacturers obtain a design for the instrument in less time than it normally takes them?"

Quality classical/concert guitars are expensive with Peña Haro’s costing $8,000. That high cost mainly is a matter of material and craftsmanship, according to Peña Haro. Woods such as Baltic pine, ebony and rosewood are expensive and delicate to work with. Guitarcrafters first make the guitar body and then determine whether it meets the high sound standards of a classical/concert guitar. Any wasted time or materials along the way contribute to the high cost.

Dynamic Behavior and Sound Emission

As a starting point, Peña Haro decided to search for the relationship between the dynamic behavior of materials and the sound made by a guitar built with traditional materials. He started with a static stress analysis to determine whether the tension of the guitar strings would play a role.

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 precision 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 (top and bottom of the body), Baltic pine (outside border of the body) and ebony (neck). The material properties for each wood were provided partly by engineers studying abroad, but also determined through a combination of physical and virtual testing, a strategy Peña Haro learned in a previous issue of Algor’s newsletter, Algor Design World.

The procedure calls for simple physical tests that produce a measurable displacement. Next, the engineer models the physical test carefully in Algor and analyzes the model, taking a best guess for Young’s modulus. The engineer compares the displacement obtained from the analysis with the displacement obtained from the experiment and repeats the process until the results match.

The static load 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 significant factors in the sound the guitar ultimately produces. Displacements along the body of the guitar, caused by plucking the strings, also proved inconsequential for Peña Haro. The greatest displacements occurred along the length of the neck (Figure 1), which tolerates bending because it is made of ebony, he said.

Peña Haro first performed a natural frequency analysis on his finite element model (Guitar 1) to determine the frequency at which the resonance box (the body) started to vibrate. Simulating a guitarist holding the neck of the guitar and depressing strings over the resonance box, he determined that the top of the resonance box begins vibrating at a frequency of 279.7 Hertz (Figure 3). The bottom of the resonance box vibrates at 311.04 Hertz.

Figure 3: Algor analysis shows displacement from vibration.

He modeled two more guitars. Guitar 2 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. Guitar 3 had no border wood, but had the same internal structure as the original Guitar 1. Dynamic analysis revealed natural frequencies of 230.56 and 277.23, for the front and back covers of Guitar 2, and 256.49 and 292.49 for the same sides in Guitar 3.

Peña Haro took those results a bit further, determining the center of gravity of his three guitars. Next, he 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 among the three. Guitar 3 was next and Guitar 2 had the smallest acoustic intensity. What Peña Haro deduced from those results was that natural frequency and acoustic intensity level vary according to what’s inside the resonance box. He attributed that change to the fact that the internal structure of the resonance box controls the center of gravity of the guitar.

With that knowledge in hand, Peña Haro used Algor’s EAGLE to automate a design optimization process allowing him to perform a series of analyses in hours that otherwise could have taken him days. EAGLE is a programming language for parametric design and analysis that links various Algor programs, taking a model through repetitive analyses. He 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 around $400 each in Peru. Peña Haro is looking for investors to help him manufacture an additional 1,000 guitars and begin sharing them with the world.

Peña Haro’s analysis results have been accepted for presentation at the NAFEMS World Congress 2001 in Italy. NAFEMS is an international organization founded in 1983 to promote the safe and reliable use of finite element and related technology.