Parametric Instability of a Rotating Axially Loaded FG Cylindrical Thin Shell Under Both Axial Disturbances and Thermal Effects

Parametric instability of a rotating functionally graded (FG) cylindrical thin shell with axial compression under various boundary conditions is studied in this article. In particular, the shell is subjected to both axial periodic displacement disturbances and a thermal environment. The initial hoop tension and Coriolis effects due to rotation are also considered. The coupled dynamic equations of the shell under multiple conditions are formulated based on Love’s thin-shell theory. The instability boundaries of the shell with different boundary conditions considering thermal factors, axial disturbances, and other system parameters are obtained analytically under the case of primary and combination resonance; numerical illustrations are also given. It is found that high temperature weakens the stability of the system, while axial disturbances show stronger influence on the instability regions of the shell compared to other parameters such as thermal factors and the angular rotation velocity.

Vibrational Study of Fluid-Filled Functionally Graded Cylindrical Shells Resting on Elastic Foundations

Vibrational characteristics of functionally graded cylindrical shells filled with fluid and placed on Winkler and Pasternak elastic foundations are investigated. Love's thin-shell theory is utilized for strain-displacement and curvature-displacement relationships. Shell dynamical equations are solved by using wave propagation approach. Natural frequencies for both empty and fluid-filled functionally graded cylindrical shells based on elastic foundations are determined for simply-supported boundary condition and compared to validate the present technique. Results obtained are in good agreement with the previous studies. It is seen that the frequencies of the cylindrical shells are affected much when the shells are filled with fluid, placed on elastic foundations, and structured with functionally graded materials. The influence of Pasternak foundation is more pronounced than that of Winkler modulus.

Vibrations of Partially Fluid-Filled Functionally Graded Cylindrical Shells

In this study, the free vibration of partially fluid-filled functionally graded material (FGM) cylindrical shells with arbitrary boundary conditions has been investigated using the Rayleigh-Ritz method. The analysis has been carried out with strain-displacement relations from Love’s thin shell theory and the contained fluid is assumed irrotational, incompressible and inviscid. The Rayleigh-Ritz method is based on the energy parameters, so after determining the kinetic and potential energies of FGM shell filled with fluid, the eigenvalue problem has been obtained. To demonstrate the validity and accuracy of the obtained theoretical results, comparison has been made with the previous published results and also with the finite element results for the empty and partially fluid-filled shells. Finally, the effects of fluid level and power-law exponent on natural frequencies of partially fluid-filled FGM shells have been investigated.

Frequency analysis of functionally graded material cylindrical shells with various volume fraction laws

In the current paper a frequency analysis is performed for functionally graded material (FGM) circular cylindrical shells. A comparative study of shell frequencies is given for algebraic polynomial, exponential, and trigonometric volume fraction laws. An FGM shell considered here is structured from two materials. Love's thin shell theory is utilized for strain-displacement and curvature-displacement relations. The Rayleigh-Ritz method is employed to derive the frequency equation in the form of eigenvalue problem. Natural frequencies are evaluated for a shell with simply supported edge conditions. The axial modal dependence is approximated by circular trigonometric functions. Theoretical results are compared with those available in the literature for the validity of the present methodology.