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Vibrations of Timoshenko beams of two-parameter elastic soil

Auciello N. M.

Engineering Transactions

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2008

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Vol. 56, iss. 3

187-200

EN

In this paper the influence of the two-parameter elastic soil on the dynamic behavior of abeam with variable cross-section is examined, in the presence of conservative axial loads. The beams are assumed to follow the well-known Timoshenko hypotheses, in order to take into ac-count bot h the rotary inertia and shear deformation effect. The Rayleigh-Ritz approach is used and Boundary Characteristic Orthogonal Polynomials are chosen as trial functions; (BCOPs method [2]). The theory is concisely presented in a matrbc form, so that the contribution of the rotary inertia and of the soil can be easily recognized. Various examples and comparisons are illustrated, in order to emphasize the influence of the soil properties and of the beam taper ratio. Finally, the results are also compared with the results given by other authors, using exact and approximate approaches.

2

The vibration of rectangular orthotropic plate with massive inclusions

Sukhorolsky M., Shopa T.

Computer Assisted Mechanics and Engineering Sciences

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2008

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Vol. 15, No. 3/4

369-376

EN

The problem on proper and forced vibrations of the loosely leant rectangular orthotropic plate with massive circular inclusion is considered in the paper. The flexure of the plate is described by modified equations of Timoshenko's theory of plates. Numerical solution of the problem is found by the indirect method of boundary elements based on the sequential approach to constructing generalized functions and on collocation method. The problem can be generalized on the case of arbitrary located inclusion and the arbitrary number of them. The influence of the mass of the massive circular inclusion on the proper frequencies of the plate is investigated.

3

Drgania belki Timoshenki-Kelvina

Cabański J.

Zeszyty Naukowe. Mechanika / Akademia Techniczno-Rolnicza w Bydgoszczy

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1999

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Z. 44 (221)

29-37

PL

W pracy przedstawiono analityczną metodę rozwiązania zagadnienia drgań swobodnych i wymuszonych belki Timoshenki. Założono, że belka jest wykonana z materiału lepko-sprężystego opisanego modelem reologicznym Voigta-Kelvina. W opracowanej metodzie użyto reguł operatorowych przedstawionych w pracy [2]. Istotą tej metody jest rozdzielenie zmiennych w przestrzeni zespolonej oraz własność ortogonalności zespolonych wektorów drgań własnych. Rozwiązania uzyskano w postaci uogólnionych szeregów Fouriera.

EN

In this paper an analytical method of solving the free and forced vibration problems of Timoshenko beam is presented. It's assumed, that the beam is carried out from a viscoelastic material, which is descriebed by the rheology Voigt-Kelvin model. The besis of the elaborate method are the operator principles [2]. The essence of this method is separation of variables in the conjugate space and the property of orthogonality of complex eigenvector of free vibration. The solution in the generalize form of the Fourier's series is obtained.

4

Free vibration of the system of two Timoshenko beams coupled by a viscoelastic interlayer

Cabańska-Płaczkiewicz K.

Engineering Transactions

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1999

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Vol. 47, iss. 1

21-37

EN

In this paper the uniform analytical method [3] has been used for solving a problem of free vibrations of continuous sandwich beam with damping. External layers are modelled as Timoshenko beams, while the internal layer possesses the characteristics of a viscoelastic, one-directional Winkler foundation. The phenomenon of free vibration has been descibed using a homogenous system of coupled partial differential equations. After separation of variables in the system of differential equations, the boundary problem has been solved and four complex sequences have been obtained : the sequences of frequencies, and the sequences of vibration modes. Then, the property of orthogonality of complex free vibration modes has been demonstrated. The free vibration problem has been solved for arbitrarily assumed initial conditions.