**TRISTANO MANACORDA**
*Sulle vibrazioni trasversali di un filo elastico
*

**Pages** 115-127

**Received:** 4 June 1993

**AMS Classification :** 73D35

**Abstract**
Experimental results prove that the fundamental frequency of the transverse
vibrations of an elastic string with fixed ends is a function of the tension which
approaches a finite limit as the tension tends to the infinity. The Mooney-Rivlin's constitutive
law for the tension as a function of the stretch is, in this sense, adequate, but the frequency
does not tend to the limit monotonically increasing, but rather it attains a maximum value for
a finite value of the stretch, thereafter tending to the limit monotonically decreasing. A constitutive law
proposed by Signorini is more satisfactory. In fact, if the values of the coefficients are conveniently
restricted in the range which assure that the elastic potential is positive definite, the frequency will
tend to a finite limit in a monotonical way.