Effects of Van Der Waals Forces on the Vibration of Stacked Multilayered Graphene/Black Phosphorus Heterostructures

2021 ◽  
pp. 2150115
Author(s):  
Dongchang Hou ◽  
Lifeng Wang ◽  
Yiqing Zhang
Keyword(s):  
Natural Frequencies ◽  
Van Der Waals ◽  
Black Phosphorus ◽  
Mode Shapes ◽  
Mesh Free ◽  
Mesh Free Method ◽  
Sequential Quadratic Programming Method ◽  
The Difference ◽  
Quadratic Programming Method ◽  
Vdw Interaction

In this paper, the vibration of a stacked multilayered graphene/black phosphorus (G/BP) heterostructure is investigated via the mesh-free method. The shape function and its derivatives are addressed by the moving least squares (MLS) approach. Optimization of the sequential quadratic programming method is adopted to calculate the distance between the arbitrary layers. Therefore, coefficients of the van der Waals (vdW) interaction between arbitrary layers of heterostructures are obtained. Then the frequencies and mode shapes of the multilayered G/BP heterostructure, considering the vdW interaction between arbitrary layers, are compared with considering only the vdW interaction among adjacent layers. The effects of the number of layers and aspect ratio of the G/BP heterostructure on the frequencies are investigated. The results demonstrate that coefficients of the vdW interaction, considering the arbitrary layers, are larger than those considering only adjacent layers. The difference between natural frequencies considering arbitrary layers and those considering adjacent layers is not clear for the low-order cases. Alternatively, the difference between natural frequencies obtained considering arbitrary layers and those considering adjacent layers are obvious for high-order cases. This paper provides a useful method to optimize the vdW interaction between multilayered G/BP heterostructures and can adequately simulate their vibration behaviors.

Analytical Solution for Vibration of a Rotating Delaminated Composite Beam with End Mass

2016 ◽  
Vol 16 (06) ◽  
pp. 1550013 ◽  
Author(s):  
Ramazan-Ali Jafari-Talookolaei
Keyword(s):  
Analytical Solution ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Mode Shapes ◽  
Material Anisotropy ◽  
Rotating Speed ◽  
Multipliers Method ◽  
Free Mode ◽  
The Difference ◽  
Laminated Composite Beams

In this paper, the free vibration of rotating laminated composite beams (LCBs) with general lay-ups and single through-the-width delamination is analytically investigated. The Hamilton’s principle is used to derive the coupled governing differential equations and boundary conditions for the rotating delaminated beam, considering the effects of shear deformation, rotary inertia, material couplings (bending–tension, bending–twist and tension–twist couplings), and Poisson’s effect. Both the free mode and constrained mode assumptions are adopted. Analytical solution for the natural frequencies and mode shapes are presented by incorporating the constraint conditions using the Lagrange multipliers method. The accuracy is assured by the convergence of the natural frequencies, as well as by comparison with published results. The effects of various factors such as delamination parameter, fiber angle, hub radius, material anisotropy, end mass and rotating speed are studied in detail. The difference between the results based on the free mode and constrained mode assumptions is also investigated.

A Normalized Modal Eigenvalue Approach for Resolving Modal Interaction

1997 ◽  
Vol 119 (3) ◽  
pp. 647-650 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Monte Carlo ◽  
Eigenvalue Problem ◽  
Perturbation Analysis ◽  
Material Properties ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Modal Interaction ◽  
Eigenvalue Approach ◽  
The Difference

Modal interaction refers to the way that the modes of a structure interact when its geometry and material properties are perturbed. The amount of interaction between the neighboring modes depends on the closeness of the natural frequencies, the mode shapes, and the magnitude and distribution of the perturbation. By formulating the structural eigenvalue problem as a normalized modal eigenvalue problem, it is shown that the amount of interaction in two modes can be simply characterized by six normalized modal parameters and the difference between the normalized frequencies. In this paper, the statistical behaviors of the normalized frequencies and modes are investigated based on a perturbation analysis. The results are independently verified by Monte Carlo simulations.

scholarly journals A Normalized Modal Eigenvalue Approach for Resolving Modal Interaction

1996 ◽  
Author(s):  
Ming-Ta Yang ◽  
Jerry H. Griffin
Keyword(s):  
Monte Carlo ◽  
Eigenvalue Problem ◽  
Perturbation Analysis ◽  
Material Properties ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Modal Interaction ◽  
Eigenvalue Approach ◽  
The Difference

Modal interaction refers to the way that the modes of a structure interact when its geometry and material properties are perturbed. The amount of interaction between the neighboring modes depends on the closeness of the natural frequencies, the mode shapes, and the magnitude and distribution of the perturbation. By formulating the structural eigenvalue problem as a normalized modal eigenvalue problem, it is shown that the amount of interaction in two modes can be simply characterized by six normalized modal parameters and the difference between the normalized frequencies. In this paper, the statistical behaviors of the normalized frequencies and modes are investigated based on a perturbation analysis. The results are independently verified by Monte Carlo simulations.

Modal Characteristic of Cantilevered Beams and Plates: A Study of Transition From Beam-Like to Plate-Like Behaviour

1999 ◽  
Author(s):  
K. Tangchaichit ◽  
S. O. Oyadiji
Keyword(s):  
Transition Point ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Fe Analysis ◽  
Mode Shapes ◽  
Structural Components ◽  
Cantilevered Plates ◽  
The Difference ◽  
Cantilevered Beams ◽  
High Length

Abstract The paper presents the finite element (FE) analysis of the free vibrations of cantilevered aluminium alloy beams and plates of 5mm thickness and of length-to-breadth ratios ranging from a ratio of 20 for a beam down to a ratio of 0.25 for a plate. The analysis was carried out using the ABAQUS FE programme. For each ratio, a total of 20 natural frequencies and mode shapes were predicted. The objective of the paper was to demonstrate that a transition zone for beam-like to plate-like behaviour of structural components can be approximately defined for various length-to-breadth ratios. It is shown that the frequency parameters of cantilevered plates asymptotically approach the frequency parameters of cantilevered beams at high length-to-breadth ratios. In addition, it is shown that at the transition point for beam-like to plate-like behaviour, which occurs at small length-to-breadth ratios, the difference between the frequency parameters of cantilevered beams is less than the frequency parameters of cantilevered plates about 3 %.

Vibration-Based Damage Detection in Structural Members Utilizing Finite Elements and Evolutionary Algorithms

2006 ◽  
Author(s):  
Amir Poursamad
Keyword(s):  
Finite Elements ◽  
Damage Detection ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Fe Model ◽  
Structural Members ◽  
Vibration Data ◽  
Detection Approach ◽  
The Difference ◽  
Extent Of Damage

Presented within this paper is the application of finite elements method combined with an evolutionary algorithm to the problem of damage detection in structural members using vibration data. The objective is to identify the position of the damage in structure, and to estimate the extent of the damage. To describe the damage, finite element method (FEM) is used here and the damage is modeled as a reduction in the stiffness of the associated element. Using this model, the effect of damage on the vibration characteristics of the structure is studied. The problem of damage detection is then formulated as an optimization problem. The decision variables are the position of damaged element and the extent of damage. The objective function is considered as the difference between measured natural frequencies and those obtained from FE model of the structure. Only natural frequencies are adopted here, because the measurement of mode shapes is usually accompanied by larger amount of error. The proposed damage detection approach is verified and assessed using a simulated cantilever Euler-Bernoulli beam.

Dynamic Seismic Analysis of Long Segmented Lifelines

1979 ◽  
Vol 101 (1) ◽  
pp. 10-20 ◽  
Author(s):  
I. Nelson ◽  
P. Weidlinger
Keyword(s):  
Ground Motion ◽  
Ir Spectrum ◽  
Natural Frequencies ◽  
Seismic Analysis ◽  
Time History ◽  
Mode Shapes ◽  
Maximum Difference ◽  
Spectral Techniques ◽  
The Difference ◽  
Interference Response

The difference in ground motion along a lifeline, the incoherent motion, is an essential component of the input. A long, straight, segmented pipe, with each link attached to the ground via a spring and dashpot is subjected to incoherent ground motion caused by a phase delay. The equations governing the axial response of the system are developed. Modal decomposition is used and closed form expressions are given for the natural frequencies and mode shapes. Examples are given showing the center joint displacement time history when the lifeline is subjected to earthquake loading. Spectral techniques can be used to bound the motion with the Interference Response (IR) spectrum. This spectrum is the maximum difference in motion (response) of two adjacent points which are excited by a difference in ground input. It is seen that the IR spectrum is a useful tool in the dynamic analysis of lifelines over a broad range of parameters.

Tire Vibrations

1977 ◽  
Vol 5 (4) ◽  
pp. 202-225 ◽  
Author(s):  
G. R. Potts ◽  
C. A. Bell ◽  
L. T. Charek ◽  
T. K. Roy
Keyword(s):  
Natural Frequencies ◽  
Standing Waves ◽  
Resonant Mode ◽  
Mode Shapes ◽  
Resonant Vibrations ◽  
Resonant Frequencies ◽  
Radial Tire ◽  
Analysis Techniques ◽  
Thin Ring ◽  
Good Agreement

Abstract Natural frequencies and vibrating motions are determined in terms of the material and geometric properties of a radial tire modeled as a thin ring on an elastic foundation. Experimental checks of resonant frequencies show good agreement. Forced vibration solutions obtained are shown to consist of a superposition of resonant vibrations, each rotating around the tire at a rate depending on the mode number and the tire rotational speed. Theoretical rolling speeds that are upper bounds at which standing waves occur are determined and checked experimentally. Digital Fourier transform, transfer function, and modal analysis techniques used to determine the resonant mode shapes of a radial tire reveal that antiresonances are the primary transmitters of vibration to the tire axle.

Dynamic model for high-speed rotors based on their experimental characterization

2017 ◽  
Vol 2 (4) ◽  
pp. 25
Author(s):  
L. A. Montoya ◽  
E. E. Rodríguez ◽  
H. J. Zúñiga ◽  
I. Mejía
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Experimental Characterization ◽  
Rotating Systems ◽  
Computing Performance ◽  
The Impact ◽  
Stiffness Distribution ◽  
Good Agreement

Rotating systems components such as rotors, have dynamic characteristics that are of great importance to understand because they may cause failure of turbomachinery. Therefore, it is required to study a dynamic model to predict some vibration characteristics, in this case, the natural frequencies and mode shapes (both of free vibration) of a centrifugal compressor shaft. The peculiarity of the dynamic model proposed is that using frequency and displacements values obtained experimentally, it is possible to calculate the mass and stiffness distribution of the shaft, and then use these values to estimate the theoretical modal parameters. The natural frequencies and mode shapes of the shaft were obtained with experimental modal analysis by using the impact test. The results predicted by the model are in good agreement with the experimental test. The model is also flexible with other geometries and has a great time and computing performance, which can be evaluated with respect to other commercial software in the future.

scholarly journals Spatially Resolved Experimental Modal Analysis on High-Speed Composite Rotors Using a Non-Contact, Non-Rotating Sensor

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4705
Author(s):  
Julian Lich ◽  
Tino Wollmann ◽  
Angelos Filippatos ◽  
Maik Gude ◽  
Juergen Czarske ◽  
...  
Keyword(s):  
High Speed ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Fiber Reinforced ◽  
Structural Dynamic ◽  
Spatially Resolved ◽  
Glass Fiber Reinforced ◽  
Vibration Responses ◽  
And Performance

Due to their lightweight properties, fiber-reinforced composites are well suited for large and fast rotating structures, such as fan blades in turbomachines. To investigate rotor safety and performance, in situ measurements of the structural dynamic behaviour must be performed during rotating conditions. An approach to measuring spatially resolved vibration responses of a rotating structure with a non-contact, non-rotating sensor is investigated here. The resulting spectra can be assigned to specific locations on the structure and have similar properties to the spectra measured with co-rotating sensors, such as strain gauges. The sampling frequency is increased by performing consecutive measurements with a constant excitation function and varying time delays. The method allows for a paradigm shift to unambiguous identification of natural frequencies and mode shapes with arbitrary rotor shapes and excitation functions without the need for co-rotating sensors. Deflection measurements on a glass fiber-reinforced polymer disk were performed with a diffraction grating-based sensor system at 40 measurement points with an uncertainty below 15 μrad and a commercial triangulation sensor at 200 measurement points at surface speeds up to 300 m/s. A rotation-induced increase of two natural frequencies was measured, and their mode shapes were derived at the corresponding rotational speeds. A strain gauge was used for validation.

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