On viscoelastic transient response of magnetically imperfect functionally graded nanobeams

The transient response of a functionally graded material (FGM) orthotropic strip with a piezoelectric coating weakened by multiple cracks is investigated. The system is subjected to out-of-plane mechanical and in-plane electrical loading. The properties of the nonhomogeneous substrate are assumed to vary exponentially along the thickness and the energy dissipation is modeled by viscous damping. In this study, the rate of the gradual change of the shear moduli, mass density, and damping constant are assumed to be same. At first, the transient response of a Volterra-type dislocation in an FGM orthotropic strip is obtained analytically. Imposing a distributed dislocation density on the crack surface and using the Fourier and Laplace integral transforms, the problem is reduced to a system of singular integral equations for a substrate weakened by multiple cracks in the form of Cauchy singularity; which are solved numerically to obtain the dynamic stress intensity factors at the crack tips. Finally, the effects of the geometrical parameters, material properties, viscous damping and cracks arrangement on the dynamic fracture behavior of the interacting cracks are studied.

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Three-dimensional semi-analytical solutions for the transient response of functionally graded material cylindrical panels with various boundary conditions

Journal of Low Frequency Noise Vibration and Active Control ◽

10.1177/1461348419855807 ◽

2019 ◽

Vol 39 (4) ◽

pp. 1002-1023

Author(s):

Xu Liang ◽

Yu Deng ◽

Xue Jiang ◽

Zeng Cao ◽

Yongdu Ruan ◽

...

Keyword(s):

Analytical Solution ◽

Boundary Conditions ◽

Transient Response ◽

Functionally Graded Material ◽

Analytical Method ◽

Composite Structures ◽

Outer Radius ◽

Functionally Graded ◽

Cylindrical Panels ◽

Graded Material

In this paper, a 3D semi-analytical method is proposed by introducing the Durbin’s Laplace transform, as well as its numerical inversion method, state space approach and differential quadrature method to analyse the transient behaviour of functionally graded material cylindrical panels. Moreover, to investigate the effectiveness of the proposed semi-analytical solution, four boundary conditions are used to undertake the analyses. Comparing the proposed approach with other theoretical methods from the literatures, we see better agreements in the natural frequencies. Besides, the semi-analytical solution acquires nearly the same transient response as those obtained by ANSYS. Convergence studies indicate that the proposed method has a quick convergence rate with growing sample point numbers along the length direction, so do layer numbers increase along the radial direction. The effects of thickness/outer radius ratio, length/outer radius ratio and functionally graded indexes are also studied. When carbon nanotube is added to functionally graded material cylindrical panel, the composite structures have been reinforced greatly. The proposed 3D semi-analytical method has high accuracy for the analysis of composite structures. This study can serve as a foundation for solving more complicated environments such as fluid–structure interaction of flexible pipe or thermal effect analysis of functionally graded material in aerospace field.

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