Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems

On small vibrations of a damped Stieltjes string

“…Like in [9] we suppose the string to be a thread (i.e. a string of zero density) bearing a finite number of point masses.…”

“…, n − 1) and l n damped at the mass m n with the coefficient of damping α. The length of the interval between the left end of the string and the mass m n according to [9] is equal to R2n−2(0) R2n−3(0) . From (3.7) we obtain…”

“…2) the product l It is clear from (5.3) that n k=0 a k = l. According to [9] this fraction can be identified as the ratio of two polynomials the zeros of the numerator are the eigenvalues of an undamped Stieltjes string with fixed ends and the zeros of the denominator are the eigenvalues of the same string with the left end fixed and the right end free. The masses of this string are |b k | at distances a k .…”

“…a thread bearing point masses) was considered in [9] and [14] assuming absence of damping. The inverse problem, i.e.…”

“…These conditions are given in implicit form: the ratio of the corresponding characteristic polynomials should admit decomposition in continued fraction of a special type. The decomposition is an analogue to that in [9] based on the results of [28].…”