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Structural Engineering and Mechanics
  Volume 73, Number 3, February10 2020 , pages 319-330

Effect of different viscoelastic models on free vibrations of thick cylindrical shells through FSDT under various boundary conditions
Hossein Daemi and Hamidreza Eipakchi

    This paper investigates the free vibrations of cylindrical shells made of time-dependent materials for different viscoelastic models under various boundary conditions. During the extraction of equations, the displacement field is estimated through the first-order shear deformation theory taking into account the transverse normal strain effect. The constitutive equations follow Hooke\'s Law, and the kinematic relations are linear. The assumption of axisymmetric is included in the problem. The governing equations of thick viscoelastic cylindrical shell are determined for Maxwell, Kelvin-Voigt and the first and second types of Zener\'s models based on Hamilton\'s principle. The motion equations involve four coupled partial differential equations and an analytical method based on the elementary theory of differential equations is used for its solution. Relying on the results, the natural frequencies and mode shapes of viscoelastic shells are identified. Conducting a parametric study, we examine the effects of geometric and mechanical properties and boundary conditions, as well as the effect of transverse normal strain on natural frequencies. The results in this paper are compared against the results obtained from the finite elements analysis. The results suggest that solutions achieved from the two methods are ideally consistent in a special range.
Key Words
    thick cylindrical shell; viscoelastic models; frequency analysis; first-order shear deformation theory; analytical solution; boundary conditions
Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, Iran

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