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
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.
Music and Engineering
Peña Haro, now 26, began his affair with the guitar when he was a youngster
living in Lima. Thats 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
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 masters degree in structural
engineering, which became the missing link between his musical
and analytical passions: his masters thesis involved his
"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
Haros 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
Using Autodesks AutoLISP programming language, Peña Haro
designed a classical/concert guitar for finite element analysis. He imported the
CAD solid model into Superdraw III, Algors 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 Algors
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 Youngs 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
Peña Haro determined that stresses caused by the tension of the strings and
the weight of a players 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.
Figure 1: Algor analysis
shows effect of loads on the neck of a guitar.
|Whats on the Inside?
With the static stress analysis complete, Peña Haro set about
his dynamic analysis to determine the relationship between
structural behavior and acoustic response.
Considering that the shape of the guitar body does not change
significantly from guitar to guitar, Peña Haro decided to
investigate changes to the internal structure of the instrument.
Specifically, he set his sights on the complex assembly of
reinforcing bars on the surfaces inside the guitar (Figure 2).
Figure 2: Algors
Superdraw was used to build this finite element model of a
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
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
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
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 whats 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 Algors 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 Haros 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