A unified Fourier series solution for vibration analysis of FG-CNTRC cylindrical, conical shells and annular plates with arbitrary boundary conditions

Qin, Bin; Zhong, Rui; Wang, Tiantian; Wang, Qingshan; Xu, Yong-ge; Hu, Zehua

doi:10.1016/j.compstruct.2019.111549

Cited by 83 publications

(15 citation statements)

References 42 publications

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“…Through the description of the moderately thick composite laminated cylindrical shell, the displacement resultant of the shell is shown by the middle surface displacements and rotation variables, expressed as [2,[49][50][51][52][53][54][55]:…”

Section: Kinematic Relations and Stress Resultantsmentioning

confidence: 99%

Free Vibration Analysis of Closed Moderately Thick Cross-Ply Composite Laminated Cylindrical Shell with Arbitrary Boundary Conditions

Shi

Wang

et al. 2020

Materials

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A semi-analytic method is adopted to analyze the free vibration characteristics of the moderately thick composite laminated cylindrical shell with arbitrary classical and elastic boundary conditions. By Hamilton’s principle and first-order shear deformation theory, the governing equation of the composite shell can be established. The displacement variables are transformed into the wave function forms to ensure the correctness of the governing equation. Based on the kinetic relationship between the displacement variables and force resultants, the final equation associated with arbitrary boundary conditions is established. The dichotomy method is conducted to calculate the natural frequencies of the composite shell. For verifying the correctness of the present method, the results by the present method are compared with those in the pieces of literatures with various boundary conditions. Furthermore, some numerical examples are calculated to investigate the effect of several parameters on the composite shell, such as length to radius ratios, thickness to radius ratios and elastic restrained constants.

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Section: Kinematic Relations and Stress Resultantsmentioning

confidence: 99%

Free Vibration Analysis of Closed Moderately Thick Cross-Ply Composite Laminated Cylindrical Shell with Arbitrary Boundary Conditions

Shi

Wang

et al. 2020

Materials

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“…This theory provides an accurate, efficient and versatile analytical method for vibration analysis and design of rigidflexible structures. The theory is also expected to be extended to other analytical vibrational models such as membranes [72] , plates [73][74][75][76][77][78] , shells [79][80][81] , solids [82] for the vibration and buckling analysis [83,84] by using associated techniques, e.g., [85][86][87] . Besides, the analytical nature of this proposed method facilitates the consideration of uncertainties that may occur during the manufacturing and assembly procedure, such as the uncertainties in rigid bodies (mass, rotatory inertia), the beam sections [88][89][90] (Young's modulus, density, cross section and etc), their connections (relative positions) and more complex engineering problems [91] .…”

Section: Discussionmentioning

confidence: 99%

An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

Xiang

Sun

Banerjee

et al. 2021

Mechanical Systems and Signal Processing

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An exact dynamic stiffness method is proposed for the free vibration analysis of multi-body systems consisting of flexible beams and rigid bodies. The theory is sufficiently general in that the rigid bodies can be of any shape or size, but importantly, the theory permits connections of the rigid bodies to any number beams at any arbitrary points and oriented at any arbitrary angles. For beam members, a range of theories including the Bernoulli-Euler and Timoshenko theories are applied. The assembly procedure for the beam and rigid body properties is simplified without resorting to matrix inversion. The difficulty generally encountered in computing the problematic J0 count when applying the Wittrick-Williams algorithm for modal analysis has been overcome. Applications of different beam theories for both axial and bending vibrations have enabled the examination of the role played by rigid-body parameters on the multibody system's dynamic behaviour. Some exact benchmark results are provided and compared with published results and with finite element solutions. This research provides an exact and highly efficient analysis tool for multibody system dynamics which is for the free vibration analysis, ideally suited for optimization and inverse problems such as modal parameter identification.

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“…For instance, by setting one or some of the k τ (τ = u, w, ϕ, φ, ν) at certain values, the elastic boundary conditions can be conveniently obtained. More information about the penalty terms to handle the boundary conditions can be found in previous investigations [27][28][29][30][31]. Consequently, the variational form for a CLCB subjected to arbitrary boundary conditions is…”

Section: Variational Formulation For Curved Beammentioning

confidence: 99%

Free Vibration Analysis of Curved Laminated Composite Beams with Different Shapes, Lamination Schemes, and Boundary Conditions

et al. 2020

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A general formulation is considered for the free vibration of curved laminated composite beams (CLCBs) with alterable curvatures and diverse boundary restraints. In accordance with higher-order shear deformation theory (HSDT), an improved variational approach is introduced for the numerical modeling. Besides, the multi-segment partitioning strategy is exploited for the derivation of motion equations, where the CLCBs are separated into several segments. Penalty parameters are considered to handle the arbitrary boundary conditions. The admissible functions of each separated beam segment are expanded in terms of Jacobi polynomials. The solutions are achieved through the variational approach. The proposed methodology can deal with arbitrary boundary restraints in a unified way by conveniently changing correlated parameters without interfering with the solution procedure.

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A unified Fourier series solution for vibration analysis of FG-CNTRC cylindrical, conical shells and annular plates with arbitrary boundary conditions

Cited by 83 publications

References 42 publications

Free Vibration Analysis of Closed Moderately Thick Cross-Ply Composite Laminated Cylindrical Shell with Arbitrary Boundary Conditions

Free Vibration Analysis of Closed Moderately Thick Cross-Ply Composite Laminated Cylindrical Shell with Arbitrary Boundary Conditions

An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

Free Vibration Analysis of Curved Laminated Composite Beams with Different Shapes, Lamination Schemes, and Boundary Conditions

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