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Forced vibrations of a laminated cylindrical shell attached to a laminated beam by point elastic links

Andryushin V.A., Bagdasaryan A.A., Nedbai A.Ya.

#### Abstract:

We study multiply connected structures under the action of harmonic loading. On this basis, the following problems of practical importance may be investigated: to find the region of dangerous frequencies, to determine the relative level of stresses in a structure under these frequencies (this level of stresses is absolute when we know accurate values of parameters of the function of dissipation), to indicate the structural members that affect mostly on the stresses discussed above, to perform the analysis of fatigue and durability of structures. Thus, the problem of forced vibrations of structures is the up-to-date problem of great importance. Problems of forced vibrations of cylindrical shells are studied in some publications. The theory of complex internal friction is used in these papers to describe the function of dissipation. As a result, solutions of visco-elastic problems may be easily obtained. In the paper presented, we consider forced vibrations of a laminated cylindrical shell under harmonic loading. The shell is supported by a hole cylinder and attached to a laminated beam by point elastic links (springs). According to the hypothesis by Sorokin, we take into consideration visco-elastic properties of the cylinder, shell, and beam by introducing complex value moduli of elasticity. We represent components of stress-strain state of all the structural members of the system in the form of trigonometric series in terms of space coordinates. Considering not identical links located arbitrary, we can reduce the problem to a set of algebraic equations in amplitude values of forces in the springs. Considering identical links located regularly, we obtain a solution in the explicit form.

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