Engineering Transactions, 6, 3, pp. 497-512, 1958

Wymuszone Drgania Tłumione Powłoki Obrotowe

M. Lawina

Contains considerations concerning forced damped vibration of a shell of revolution of any form, the vibration provoking normal forces being of an arbitrary type. In order  to take the damping into account, the Sorokin hypothesis is used. The equations of amplitude distribution (1.2) are integrated asymptotically. The vibration forcing action is represented as a superposition of partial actions according to the Eq. (2.1). For the n-th component of the vibration exciting force, the displacements are represented in the form (2.2) containing separate intensity functions and variability functions; the former may be represented in turn in the form of a series (2.3) in powers of the small parameter h-the relative thickness of the shell.
With such expansion, the integration of the equations (1.2) reduces a certain concrete example. The solutions of these systems yield successive approximations of the functions of displacement intensity (2.3). The first two approximations may be determined knowing the operators L0, N0, L1, N1, appearing as coefficients in the system of equations. The forms of these operators are given in the Tables 3, 4, 5 and 6.
The final remarks concern certain matters important in practice concerning the problem considered.

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M. Lawina, Dyskusja wpływu tłumienia na postać drgań skrętnych tarczy, Referat wygl. na Konf, ZMOC IPPT PAN, 1957.