On determination of stationary states for systems of thin-walled elements at propagation of harmonic disturbances

Acoustic bulletin, Vol. 3 1, (2000) p.61-72
The problems on determination of stationary states at harmonic motions are considered for shells with stiffening elements such as the additional supports of a plate or shell type. There are outlined the features of statement of mentioned problems at using the two-dimensional shell theory with consideration of a shift. Developed general arrangement of the solution is grounded on usage of a method of forces at replacement of the unknown contact stresses by statically equivalent systems of local loadings. To describe the stationary states there were constructed the systems of vector functions, which are the nontrivial solutions of nonclassical problems on eigenvalues, and the last ones find a frequency eigenspectrum of vibration of system as a whole. For constructed systems of functions the properties of orthogonality are proved, and a functional space is underlined, in which they have the property of completeness. The general arrangement is implemented with application of both decompositions with respect to natural vibration modes of separate system components and the numerically-analytical methods. The examples of calculations for concrete mechanical systems are given. It is established that the most precise values of natural frequencies can be obtained only at satisfying all conditions of matched deforming for the basic shell and the support elements. In the case of plates it gives in necessity to involve the complete systems of differential equations featuring not only the bending, but also the extension-compression of plates. At a rigid joint of the basic shell and the support elements only mentioned approach allows to describe a configuration of stationary states of system in proper way.
stationary state, the shell with stiffeners, statically equivalent system of the local loads, non-classical eigenvalue problem