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Transient response of functionally graded non-uniform cylindrical helical rods
Yavuz C. Cuma,Faruk Firat Calim 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.40 No.4
This paper have the objective of investigating forced vibration behaviour of axially functionally graded cylindrical helices with variable cross-section. An algorithm is developed in order to solve corresponding problems. The ordinary differential equations governing the dynamic behaviour of cylindrical helices are determined in Laplace domain by using Timoshenko beam theory. Then transfer matrix method is implemented for the solution, including shear and axial deformation effects. Obtained results are transferred to time domain using Durbin’s modified numerical inverse algorithm for Laplace transform. A benchmark problem has been solved to check the accuracy of developed algorithm then a parametric study is conducted considering the effects of material gradient index ( ), section variation parameter ( ) and number of active turns ( ). Results are compared with solutions attained from ANSYS for verification
Mehmet Bugra Ozbey,Yavuz Cetin Cuma,Ibrahim Ozgur Deneme,Faruk Firat Calim Techno-Press 2024 Advances in nano research Vol.16 No.4
This paper investigates the dynamic behavior of a simply supported viscoelastic plate made of functionally graded carbon nanotube reinforced composite under dynamic loading. Carbon nanotubes are distributed in 5 different shapes: U, V, A, O and X, depending on the shape they form through the thickness of the plate. The displacement fields are derived in the Laplace domain using a higher-order shear deformation theory. Equations of motion are obtained through the application of the energy method and Hamilton's principle. The resulting equations of motion are solved using Navier's method. Transforming the Laplace domain displacements into the time domain involves Durbin's modified inverse Laplace transform. To validate the accuracy of the developed algorithm, a free vibration analysis is conducted for simply supported plate made of functionally graded carbon nanotube reinforced composite and compared against existing literature. Subsequently, a parametric forced vibration analysis considers the influence of various parameters: volume fractions of carbon nanotubes, their distributions, and ratios of instantaneous value to retardation time in the relaxation function, using a linear standard viscoelastic model. In the forced vibration analysis, the dynamic distributed load applied to functionally graded carbon nanotube reinforced composite viscoelastic plate is obtained in terms of double trigonometric series. The study culminates in an examination of maximum displacement, exploring the effects of different carbon nanotube distributions, volume fractions, and ratios of instantaneous value to retardation times in the relaxation function on the amplitudes of maximum displacements.