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Vibration equations of the coupled torsional, longitudinal, and lateral vibrations of the propeller shaft at the ship stern

Firouzi Jabbar, Ghassemi Hassan, Vakilabadi Karim Akbari

Zeszyty Naukowe Akademii Morskiej w Szczecinie

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2020

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nr 61 (133)

121--129

EN

A propeller shaft generally experiences three linear forces and three moments, the most important of which are thrust, torque, and lateral forces (horizontal and vertical). Thus, we consider 4DOFs (degrees of freedom) of propeller shaft vibrations. This paper is presented to obtain the vibration equations of the various coupled vibrations of the propeller shaft at the stern of a ship (including coupled torsional-axial, torsional-lateral, axial-lateral, torsional-axial, and lateral vibrations). We focused on the added hydrodynamic forces (added mass and added damping forces) due to the location of the propeller behind the ship. In this regard, the 4DOFs of the coupled vibration (torsional-longitudinal and lateral vibrations in the horizontal and vertical directions) equations of shaft and propeller systems located behind a ship were extracted with and without added mass and damping forces. Also, the effect of mass eccentricity was considered on vibrations occurring at the rear of the ship.

2

Acoustical diagnostics of cracks in beam like structures

Majkut L.

Archives of Acoustics

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2006

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Vol. 31, No. 1

17-28

EN

In this paper, the acoustical symptoms of a constructional element with an edge non-propagating crack on the example of a cantilever beam are searched. In this work the influence of a crack on flexural natural frequency was analysed. The crack is substituted by a rotational spring, which flexibility is calculated using the Castigliano theorem and the laws of the fracture mechanics. In this work the changes in the first and second natural frequency of the flexural vibrations are showed as a function of location and depth of the crack. The acoustic signal measured with a microphone placed above the beam is used for diagnostic systems. Changes in the natural frequency cannot be used for the identification of a small crack (the depth is less than 10% of beam height). For the detecting of a smaller crack, the effect of coupled different modes of vibration is presented. The paper presents a modelling and analysis algorithm for cracked Euler-Bernoulli beams by considering the coupling between the bending and axial vibration modes. The analysis of the coupled vibrations showed that additional resonance frequencies appeared in the acoustic spectrum.

3

Wibroakustyczne symptomy pęknięcia belki.

Majkut L.

Zagadnienia Eksploatacji Maszyn

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2005

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Vol. 40, nr 4

165-181

PL

Praca dotyczy wpływu poprzecznego pęknięcia (jego głębokości i lokalizacji) na parametry charakterystyk dynamicznych elementu konstrukcyjnego na przykładzie belki wspornikowej. Wykazano, że typowe metody identyfikacji pęknięcia oparte na pomiarze zmiany częstości drgań własnych czy amplitud drgań wymuszonych (giętnych bądź wzdłużnych) pozwalają na diagnostykę pęknięć o głębokości większej niż 10% wysokości belki. Do wykrywania pęknięć o mniejszej głębokości wykorzystano efekt sprzęgania się różnych form drgań. Udowodniono, że źródłem sprzężenia jest pęknięcie. Wykazano, że fakt sprzęgania się drgań wpływa nieznacznie na zmianę częstości drgań własnych czy amplitudę drgań wymuszonych monoharmonicznie oraz, że w przypadku elementu konstrukcyjnego z pęknięciem drgania poprzeczne wymuszone poprzecznymi siłami zewnętrznymi generują również drgania wzdłużne mimo tego, że wymuszenia na tych kierunkach nie działają. Symptomem diagnostycznym pęknięcia może być również pojawienie się dodatkowych prążków (częstości rezonansowych) w zarejestrowanym widmie sygnału drganiowego.

EN

In this paper, the vibroacoustical symptoms of constructional element with an edge nonpropagating crack on the example of the cantilever beam are searched. At work the influence of crack on flexural and longitudinal natural frequency and changes forced vibrations amplitudes was analysed. The crack is substituted by rotational or longitudinal spring, which flexibility is calculated by using Castigliano theorem and laws of the fracture mechanics. At work the changes in first and second natural frequency the flexural and longitudinal vibrations as function of location and depth of the crack are showed. These changes can be used for diagnostic systems. Changes in forced vibration amplitudes can be also used for diagnostic systems. These changes in the flexural and longitudinal monoharmonic vibrations as function of location and depth of the crack are showed. Changes in natural frequency and forced vibration amplitudes can be used for identification of small crack (depth in less than 10% of beam height). To detecting of smaller crack the effect of coupled the different modes of vibration is presented. The paper presents a modelling and analysis algorithm for cracked Euler-Bernoulli beams by considering the coupling between the bending and axial vibration modes. The analysis of the coupled vibrations showed that the additional resonance frequencies in the vibration spectra appeared.