Engineering Transactions,

**8**, 4, pp. 765-779, 1960### Podstawowa Postać Drgań Walcowych Pokryć Kratowych

The problem under consideration is that of determining the fundamental mode of vibration of a cylindrical lattice roof.

Investigations are carried out assuming vertical motion of masses during vibration and without this assumption.

The assumption of the mode is of essential importance for the computation of natural frequency by means of the iteration method.

The roofs under investigation represent systems of many degrees of freedom and the determination of the vibration mode by means of known accurate methods requires considerable labour.

On the basis of the results of computation by means of the method of forces of less complicated roofs with smaller number of masses, a method is proposed for determining the fundamental frequency of roofs loaded with a considerable number of masses. This method enables us to determine the form of vibration of a lattice roof by assuming that the masses are concentrated along the generant of the cylindrical surface in the middle cross-section.

In order to relate each displacement component to one displacement component treated as a parameter, the assumption of vertical motion of the masses being rejected, the equation of kinematic chain is used. The variability of the ordinates along the covering is assumed to be represented by a half-wave of a sine curve.

The method proposed is verified by computing by means of the iteration method the natural frequencies of a cylindrical roof with 25 masses. It is found that the first approximation alone suffices to obtain results sufficiently accurate for the practice.

Investigations are carried out assuming vertical motion of masses during vibration and without this assumption.

The assumption of the mode is of essential importance for the computation of natural frequency by means of the iteration method.

The roofs under investigation represent systems of many degrees of freedom and the determination of the vibration mode by means of known accurate methods requires considerable labour.

On the basis of the results of computation by means of the method of forces of less complicated roofs with smaller number of masses, a method is proposed for determining the fundamental frequency of roofs loaded with a considerable number of masses. This method enables us to determine the form of vibration of a lattice roof by assuming that the masses are concentrated along the generant of the cylindrical surface in the middle cross-section.

In order to relate each displacement component to one displacement component treated as a parameter, the assumption of vertical motion of the masses being rejected, the equation of kinematic chain is used. The variability of the ordinates along the covering is assumed to be represented by a half-wave of a sine curve.

The method proposed is verified by computing by means of the iteration method the natural frequencies of a cylindrical roof with 25 masses. It is found that the first approximation alone suffices to obtain results sufficiently accurate for the practice.

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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

#### References

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A. LISOWSKI, Stateczność i drgania powłok w oparciu o wyniki badan modelowych, Rozpr. inzyn., 1, 6 (1958).

M. GIERSZEWSKI, Ramy - Obliczenia statyczne, Warszawa 1955.