Free vibration analysis of thin rotating cylindrical shells using wave propagation approach

Sun, Shupeng; Cao, Dengqing; Chu, Shiming

doi:10.1007/s00419-012-0701-x

Cited by 38 publications

(10 citation statements)

References 35 publications

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“…To validate the nonlinear dynamic model shown in (26), a comparison is conducted between the frequencies calculated by the corresponding linear system and those available in open literature, as shown in Table 1. Between the lowest two nondimensional frequencies (i.e., 1 and 2 ), (1) 1 is the lower one and corresponding to the forward wave frequency and (2) 2 is the higher one and corresponding to the backward wave frequency, as shown in literature [5]. It can be seen from Table 1 that good agreement is achieved.…”

Section: Numerical Results and Discussionsupporting

confidence: 65%

“…The reduced model given by (55) is actually a 2-DOF gyroscopic system with cubic nonlinearities. The information related to in-plane vibrations ( and V) is still included in the reduced model, because the present model reduction only (1,1) 0.0131 0.0191 0.0131 0.0191 (1,2) 0.0045 0.0093 0.0043 0.0091 (1,3) 0.0074 0.0110 0.0073 0.0109 (1,4) 0.0125 0.0153 0.0125 0.0154 (1,5) 0.0185 0.0208 0.0186 0.0209 neglects vibration mode predominated by in-plane vibrations. However, the previous studies in the model simplification directly neglect in-plane vibrations ( and V) to obtain the 2-DOF system.…”

Section: Reduced-order Modelmentioning

confidence: 99%

“…Also they systematically analyzed the effects of centrifugal and Coriolis forces. Subsequently, some researchers proposed several analytical and numerical methods to study the dynamic characteristics of rotating shells, such as Fourier series expansion approach [4], wave propagation method [5], discrete singular convolution method [6,7], harmonic reproducing kernel particle approach [8],…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Dynamic Modeling and Model Reduction Strategy for Rotating Thin Cylindrical Shells

Sun

Liu

2019

Complexity

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properly cited.Nonlinear dynamic modeling and model reduction strategy are studied in this paper for a rotating thin cylindrical shell. The nonlinear dynamic model is first established in terms of ordinary differential equations, in which the effects of Coriolis and centrifugal forces are considered, as well as the initial hoop tension due to rotation. This model describes both the in-plane vibrations and the flexural vibration and reflects the coupling effects of those deformations. Based on this original model, a novel model reduction strategy is proposed to reduce the degrees of freedom by neglecting vibration modes predominated by in-plane vibrations. Meanwhile, for the reduced-order model, the in-plane vibrations' contributions to the rotating shell's response are still preserved. To validate the dynamic model and the model reduction strategy, comparisons and simulations are carried out. Subsequently, nonlinear dynamic behaviors are investigated preliminarily by analyzing the rotating cylindrical shell's amplitude-frequency responses under different excitation levels.

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Section: Numerical Results and Discussionsupporting

confidence: 65%

Section: Reduced-order Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear Dynamic Modeling and Model Reduction Strategy for Rotating Thin Cylindrical Shells

Sun

Liu

2019

Complexity

Self Cite

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“…Since the present CNTs has been expressed in the form of differential equation, so a simple and efficient method commonly known as wave propagation approach (WPA) is employed to solve such type of differential equation. This approach has been used widely and successively for studying shell vibrations (see Sun et al, 2013;Ramezani and Ahmadian, 2009;Xuebin, 2008;Zhang et al, 2001). Forms of three modal displacement functions u(x, θ, t), v(x, θ, t) and w(x, θ, t) are assumed such that they split the independent variables.…”

Section: Theoretical Formationmentioning

confidence: 99%

Vibration analysis of single-walled carbon nanotubes using wave propagation approach

Hussain

2017

Mech. Sci.

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Abstract. In this paper, influence of boundary conditions on free vibrations of single-walled carbon nanotubes (SWCNTs) is examined. The Flügge's shell dynamical equations are utilized for governing vibrations for carbon nanotubes. The wave propagation approach (WPA) is engaged to determine vibration frequency equation in standard eigenvalue form. The axial modal dependence is measured by the complex exponential functions implicating the axial modal numbers. These numbers are associated with boundary conditions specified at edges of a carbon nanotube. Computer programming is performed to obtain solutions of vibration frequency equation. In our new investigation, the vibration frequency spectra are obtained and analyzed for various physical parameters e.g., length and thickness-to-radius ratio. A number of results are presented to influence of different boundary conditions on SWCNTs. They are shown graphically and have been compared with those available in the literature.

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“…Before this, present method has been successively used for the study of shell vibrations [25][26][27]. The axial coordinate and time variable are denoted by x, t correspondingly and the circumferential coordinate signifies by θ.…”

Section: Applications Of the Wave Propagation Approachmentioning

confidence: 99%

Vibrational Behavior of Single-Walled Carbon Nanotubes Based on Donnell Shell Theory Using Wave Propagation Approach

Hussain¹

2018

Novel Nanomaterials - Synthesis and Applications

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This chapter is concerned with the vibration analysis of single-walled carbon nanotubes (SWCNTs). This analysis is based on the Donnell thin shell theory. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in SWCNTs. The axial modal dependence is measured by the complex exponential functions implicating the axial modal numbers. Vibration frequency spectra are gained and evaluated for physical parameter like length-to-diameter ratios. The dimensionless frequency is also investigated in armchair and zigzag SWCNTs with in-plane rigidity and mass density per unit lateral area for armchair and zigzag SWCNTs. These frequencies of the SWCNTs are computed with the aid of the computer software MATLAB. These results are compared with those obtained using molecular dynamics (MD) simulation and the results are somewhat in agreement.

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Free vibration analysis of thin rotating cylindrical shells using wave propagation approach

Cited by 38 publications

References 35 publications

Nonlinear Dynamic Modeling and Model Reduction Strategy for Rotating Thin Cylindrical Shells

Nonlinear Dynamic Modeling and Model Reduction Strategy for Rotating Thin Cylindrical Shells

Vibration analysis of single-walled carbon nanotubes using wave propagation approach

Vibrational Behavior of Single-Walled Carbon Nanotubes Based on Donnell Shell Theory Using Wave Propagation Approach

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