Riv.Mat.Univ.Parma (5) 2 (1993)-Parte I


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.