Nonlinear forced vibration analysis of functionally graded non-uniform cylindrical microbeams applying the semi-analytical solution

Employing an efficient numerical strategy, the nonlinear forced vibration analysis of composite cylindrical shells reinforced with single-walled carbon nanotubes (CNTs) is carried out. It is assumed that the distribution of CNTs along the thickness direction of the shell is uniform or functionally graded and the temperature dependency of the material properties is accounted. The governing equations are presented based on the first-order shear deformation theory along with von-Karman nonlinear strain-displacement relations. The vectorized form of energy functional is derived and directly discretized using numerical differential and integral operators. By the use of variational differential quadrature (VDQ) method, discretized nonlinear governing equations are obtained. Then, the time periodic differential operators are applied to perform the discretization procedure in time domain. Finally, the pseudo-arc length continuation method is employed to solve the nonlinear governing equations and trace the frequency response curve of the nanocomposite cylindrical shell. A comparison study is first presented to verify the efficiency and validity of the proposed numerical method. Comprehensive numerical results are then given to investigate the effects of the involved factors on the nonlinear forced vibration characteristics of the structure. The results show that the changes of fundamental vibrational mode shape have considerable effects on the frequency response curves of composite cylindrical shells reinforced with CNTs.

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Forced Vibration Analysis for a FGPM Cylindrical Shell

Shock and Vibration ◽

10.1155/2013/512847 ◽

2013 ◽

Vol 20 (3) ◽

pp. 531-550 ◽

Cited By ~ 7

Author(s):

Hong-Liang Dai ◽

Hao-Jie Jiang

Keyword(s):

Cylindrical Shell ◽

Forced Vibration ◽

Vibration Analysis ◽

Mechanical Load ◽

Functionally Graded ◽

Power Law Distribution ◽

Constituent Material ◽

Present Solution ◽

Functionally Graded Piezoelectric ◽

Forced Vibration Analysis

This article presents an analytical study for forced vibration of a cylindrical shell which is composed of a functionally graded piezoelectric material (FGPM). The cylindrical shell is assumed to have two-constituent material distributions through the thickness of the structure, and material properties of the cylindrical shell are assumed to vary according to a power-law distribution in terms of the volume fractions for constituent materials, the exact solution for the forced vibration problem is presented. Numerical results are presented to show the effect of electric excitation, thermal load, mechanical load and volume exponent on the static and force vibration of the FGPM cylindrical shell. The goal of this investigation is to optimize the FGPM cylindrical shell in engineering, also the present solution can be used in the forced vibration analysis of cylindrical smart elements.

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