Natural frequencies and vibration modes of tank's protective capacitance with weld defects under axial static load
Keywords:thin shell, weld defect, finite element method, nonlinear behavior, natural frequency and vibration modes, axial static load
The natural frequencies and vibration modes of tank's protective capacitance with welded joints defects under axial static load are determined in order to construct a diagnostic model and monitor of the welded joints defects propagation. Computer simulation of capacitance dynamic behavior using the computer finite element analysis system NASTRAN was performed. The design model in the form of a cylindrical thin-walled shell with allowance for belts from weld rolled sheet was built. Weld defects as two through horizontal cracks located in the welds between the first and second shell belts were presented. The crack width was equaled to the rolled sheets diameter. For assessing the effect of crack propagation on the shell dynamic characteristics the crack length increased until a single continuous crack. The defects in the form of through cracks allowed to generalize different weld defects types and predict the shell critical state. Determination of capacitance natural frequencies and vibration modes under axial static load was performed in two stages. At the first stage, the capacitance stress-strain state in a nonlinear formulation was investigated and a total stiffness matrix (linear and geometric) was formed. The nonlinear static problem as a finite element approximation of the Lagrange possible displacements principle was formulated. The Newton-Raphson stepwise loading method (Nonlinear Static) was used. The natural frequencies and vibration modes were determined by by the Lanczos method (Param Modes) on solving the eigenvalue problem. The effect of weld defects and axial static action on the capacitance dynamic characteristics was evaluated. The results showed that the presence of cracks and an their length increase reduced the values of the natural frequencies. The static action of an axial compressive load on a thin shell wall can both reduce and increase its rigidity, thereby changing its natural frequency and vibration modes. According to the authors, consideration of such a load should be present in the dynamic calculations of thin shells, especially under stochastic loads (wind, seismic, etc.).
Afanasyev N.N. Statisticheskaya teoriya ustalostnoy prochnosti meterialov (Statistical theory of fatigue strength of materials). - Kiev: Publishing house of the Academy of Sciences of the Ukrainian SSR, 1953 . – 105 p.
Bazhenov V.A., Gulyar O.I., Piskunov S.O., Sakharov O.S. Napivanalitychnyi metod skinchennykh elementiv v zadachakh ruinuvannia prostorovykh til (The semi-analitical method of scanned elements in the problems of ruining spacious spaces): Monograph - Kiev: KNUBA, 2005. –298 p.
Bazhenov V.A., Vabishchevich M.O., Solodey I.I., Chepurnaya E.A. O poluanaliticheskom metode konechnyih elementov v dinamicheskih zadachah lineynoy mehaniki razrusheniya(On the semi-analytical finite element method in dynamic problems of linear fracture mechanics) // Applied Mechanics. – 2018. – T. 54, No. 5. – S. 35-46.
Bolotin V.V. Statisticheskie metodyi v stroitelnoy mehanike (Statistical Methods in Structural Mechanics). – M .: Gostroyizdat, 1961 . – 202 p.
Grigorenko A.Ya., Borisenko M.Yu., Boychuk E.V., Prigoda A.P. Chislennoe opredelenie chastot i form svobodnyih kolebaniy tolstostennoy tsilindricheskoy obolochki (Numerical determination of frequencies and forms of free vibrations of a thick-walled cylindrical shell) // Prikladnaya mehanika. – 2018. – T. 54, # 1. – S. 90-100.
Guz A.N. Neklassicheskie problemyi mehaniki razrusheniya: k 50-letiyu issledovaniy (obzor). I. (Non-classical problems of fracture mechanics: to the 50th anniversary of research (review)) // Prikladnaya mehanika. – 2019.– 55, #2. – S. 8-72.
Kurkin S.A. Prochnost svarnyih tonkostennyih sosudov, rabotayuschih pod davleniem. (Strength of welded thin-walled pressure vessels) – M.: Mashinostroenie, 1976. – 184 s.
Matvienko Yu.G. Modeli i kriterii mehaniki razrusheniya (Fracture Mechanics Models and Criteria). – M.: FIZMATLIT, 2006. – 328 s.
Oryinyak I. V. Prochnost truboprovodov s defektami (Strength of pipelines with defects). – K.: Nauk. dumka, 2012. – 445 s.
Prochnost svarnyih soedineniy pri peremennyih nagruzkah. AN USSR. In-t elektrosvarki im. E.O. Patona. Pod red. V.I. Trufyakova.(Strength of welded joints at variable loads. Academy of Sciences of the Ukrainian SSR. Institute of Electric Welding named after E.O. Paton. Ed. V.I. Trufyakova)– Kiev: Naukova dumka, 1990.– 256 s.
Rudakov K.N. FEMAP 10.2.0. Geometricheskoe i konechno-elementnoe modelirovanie konstruktsiy. (Geometric and finite element modeling of structures) – K.: KPI (2011), 317 c.
Timoshenko S.P., Voynovskiy-Kriger S. Plastinki i obolochki (Plates and shells). – M., 1963. – 636 s.
Adams D. Health Monitoring of Structural Materials and Components. Methods with Applications, John Wiley & Sons Ltd., 2007.
Balageas D., Fritzen C.-P., Gemes A. Structural Health Monitoring, John Wiley & Sons Ltd., 2006.
Bazhenov V.А., Luk’yanchenko О.О., Kostina О.О., Gerashchenko О.V. Probabilistic Approach to Determination of Reliability of an Imperfect Supporting Shell//Strength of Materials: Volume 46, Issue 4 (2014), Page 567-574.
Bouraou N.I., Luk’yanchenko О.О., Tsybulnik S.A., Shevchuk D.V. Vibration Condition Monitoring of the Vertical Steel Tanks // Vibrations in Physical Systems Vol. 27 (2016), рр. 53-60.
Bouraou N., Rupich S., Lukianchenko O., Kostina O. Monitoring of the Crack Propagation in Welded Joint of the Tank Using Multi-Class Recognition // Vibrations in Physical Systems (02.2018).
Luk’yanchenko О.О., Kostina О.V., Bouraou N.I., Kuz’ko O.V. Investigation of Static and Dynamic Characteristics of Complex Thin-Walled Shell Structure with Cracks. – Strength of Materials:Volume 48, Issue 3 (2016), pp. 401-410.
Shen T., Wan F., Song B., Wu Y. Damage location and identification of the wing structure with Probabilistic Neural Network, Proc. of Prognostics and System Health Management Conf., IEEE Xplore Digital Library (2011).
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