Vibration of Rectangular Single-Layered Black Phosphorus

2017 ◽  
Author(s):  
Yiqing Zhang ◽  
Lifeng Wang
Keyword(s):  
Orthotropic Plate ◽  
Md Simulation ◽  
Natural Frequencies ◽  
Black Phosphorus ◽  
Fast Fourier Transformation ◽  
Layered Crystal ◽  
Practical Applications ◽  
Vibration Properties ◽  
Plate Models ◽  
Excellent Property

Two-dimensional layered crystal material black phosphorus (BP) has attracted extensive attention due to its excellent property and practical applications. Single-layered BP has a characteristic puckered structure which leads to two anisotropic in-plane directions. The vibration properties of this puckered structure material would be very interesting. Thermal vibration of a rectangular single-layered BP is studied by using continuum orthotropic plate models together with molecular dynamics (MD) simulation. Five elastic constants including two bending moduli, two Poisson’s ratios, and one shear modulus of BP are calculated by using MD method. The natural frequencies of BP are obtained by orthotropic plate models and MD simulation via fast Fourier transformation (FFT). The result of MD simulation shows that continuum orthotropic plate models can predict the natural frequencies well.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

scholarly journals Ambient Vibration Tests of an Arch Dam with Different Reservoir Water Levels: Experimental Results and Comparison with Finite Element Modelling

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Sergio Vincenzo Calcina ◽  
Laura Eltrudis ◽  
Luca Piroddi ◽  
Gaetano Ranieri
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Water Levels ◽  
Arch Dam ◽  
Experimental Results ◽  
Ambient Vibration ◽  
Reservoir Water ◽  
Ambient Vibration Tests ◽  
Vibration Properties ◽  
Vibration Tests

This paper deals with the ambient vibration tests performed in an arch dam in two different working conditions in order to assess the effect produced by two different reservoir water levels on the structural vibration properties. The study consists of an experimental part and a numerical part. The experimental tests were carried out in two different periods of the year, at the beginning of autumn (October 2012) and at the end of winter (March 2013), respectively. The measurements were performed using a fast technique based on asynchronous records of microtremor time-series. In-contact single-station measurements were done by means of one single high resolution triaxial tromometer and two low-frequency seismometers, placed in different points of the structure. The Standard Spectral Ratio method has been used to evaluate the natural frequencies of vibration of the structure. A 3D finite element model of the arch dam-reservoir-foundation system has been developed to verify analytically determined vibration properties, such as natural frequencies and mode shapes, and their changes linked to water level with the experimental results.

VIBRATION-BASED STRUCTURAL DAMAGE DETECTION UNDER VARYING TEMPERATURE CONDITIONS

2013 ◽  
Vol 13 (05) ◽  
pp. 1250082 ◽  
Author(s):  
XIAO-QING ZHOU ◽  
WEN HUANG
Keyword(s):  
Damage Detection ◽  
Structural Damage ◽  
Natural Frequencies ◽  
Environmental Changes ◽  
Model Updating ◽  
Modal Testing ◽  
Structural Damage Detection ◽  
Vibration Data ◽  
Temperature Conditions ◽  
Vibration Properties

In vibration-based structural damage detection, it is necessary to discriminate the variation of structural properties due to environmental changes from those caused by structural damages. The present paper aims to investigate the temperature effect on vibration-based structural damage detection in which the vibration data are measured under varying temperature conditions. A simply-supported slab was tested in laboratory to extract the vibration properties with modal testing. The slab was then damaged and the modal testing was conducted again, in which the temperature varied. The modal data measured under different temperature conditions were used to detect the damage with a two-stage model updating technique. Some damage was falsely detected if the temperature variation was not considered. Natural frequencies were then corrected to those under the same temperature conditions according to the relation between the temperature and material modulus. It is shown that all of the damaged elements can be accurately identified.

Nonlocal Approaches for the Vibration of Lattice Plates Including Both Shear and Bending Interactions

2018 ◽  
Vol 18 (07) ◽  
pp. 1850094 ◽  
Author(s):  
F. Hache ◽  
N. Challamel ◽  
I. Elishakoff
Keyword(s):  
Natural Frequencies ◽  
Scale Effects ◽  
Dynamical Behavior ◽  
Mindlin Plate ◽  
Length Scale ◽  
Small Length ◽  
Simply Supported ◽  
Small Length Scale ◽  
Plate Models ◽  
Scale Coefficient

The present study investigates the dynamical behavior of lattice plates, including both bending and shear interactions. The exact natural frequencies of this lattice plate are calculated for simply supported boundary conditions. These exact solutions are compared with some continuous nonlocal plate solutions that account for some scale effects due to the lattice spacing. Two continualized and one phenomenological nonlocal UflyandMindlin plate models that take into account both the rotary inertia and the shear effects are developed for capturing the small length scale effect of microstructured (or lattice) thick plates by associating the small length scale coefficient introduced in the nonlocal approach to some length scale coefficients given in a Taylor or a rational series expansion. The nonlocal phenomenological model constitutes the stress gradient Eringen’s model applied at the plate scale. The continualization process constructs continuous equation from the one of the discrete lattice models. The governing partial differential equations are solved in displacement for each nonlocal plate model. An exact analytical vibration solution is obtained for the natural frequencies of the simply supported rectangular nonlocal plate. As expected, it is found that the continualized models lead to a constant small length scale coefficient, whereas for the phenomenological nonlocal approaches, the coefficient, calibrated with respect to the element size of the microstructured plate, is structure-dependent. Moreover, comparing the natural frequencies of the continuous models with the exact discrete one, it is concluded that the continualized models provide much more accurate results than the nonlocal Uflyand–Mindlin plate models.

Combinations for the Free Vibration Behaviors of Anisotropic Rectangular Plates Under General Edge Conditions

1999 ◽  
Author(s):  
Yoshihiro Narita
Keyword(s):  
Free Vibration ◽  
Structural Design ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Technical Information ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Plate Models ◽  
Edge Conditions ◽  
Anisotropic Rectangular Plates

Abstract The free vibration behavior of rectangular plates provides important technical information in structural design, and the natural frequencies are primarily affected by the boundary conditions as well as aspect and thickness ratios. One of the three classical edge conditions, i.e., free, simple supported and clamped edges, may be used to model the constraint along an edge of the rectangle. Along the entire boundary with four edges, there exist a wide variety of combinations in the edge conditions, each yielding different natural frequencies and mode shapes. For counting the total number of possible combinations, the present paper introduces the Polya counting theory in combinatorial mathematics, and formulas are derived for counting the exact numbers. A modified Ritz method is then developed to calculate natural frequencies of anisotropic rectangular plates under any combination of the three edge conditions and is used to numerically verify the numbers. In numerical experiments, the number of combinations in the free vibration behaviors is determined for some plate models by using the derived formulas, and are corroborated by counting the numbers of different sets of the natural frequencies that are obtained from the Ritz method.

Unstable Motion of a Floating Structure in Surface Waves

2011 ◽  
Author(s):  
Hongmei Yan ◽  
Yuming Liu ◽  
Yile Li
Keyword(s):  
Natural Frequencies ◽  
Wave Structure ◽  
The Body ◽  
Body Motion ◽  
Irregular Waves ◽  
Nonlinear Instability ◽  
Physical Factors ◽  
Floating Structure ◽  
Practical Applications ◽  
Sum Frequency

Unstable resonant heave and pitch motions of a floating deep draft platform, under the action of a regular wave with the frequency equal to the sum of the heave and pitch natural frequencies, can be developed by nonlinear instability (Liu, Yan & Yung 2010). The instability is associated with difference-frequency interactions between the body motion and the ambient wave. In this work, we study the effect of the nonlinear instability upon floating platforms with relatively shallow drafts whose wave damping at heave/pitch natural frequencies may not be small. Direct time-domain numerical simulations of wave-structure interactions, which can take into account different levels of nonlinearity effects, are applied to understand the characteristics of the unstable coupled heave/pitch (or heave/roll) resonant motion and its dependence on the key physical factors. In particular, it is found that such a nonlinear instability at other wave conditions involving sum-frequency interactions between the body motion and the ambient wave can also occur. For practical applications, long-time nonlinear simulations with irregular waves are also performed. The results show that depending on the sea conditions and damping in the system, the unstable resonant motion associated with the nonlinear instability can be significant for platforms with shallow drafts.

scholarly journals Vibration analysis of rotating rings with complex support stiffnesses

2018 ◽  
Vol 237 ◽  
pp. 01010
Author(s):  
Fuchun Yang ◽  
Yue Zhang ◽  
Hailong Li
Keyword(s):  
Differential Operators ◽  
Natural Frequencies ◽  
Frequency Separation ◽  
Vibration Modes ◽  
Governing Equations ◽  
Nodal Diameter ◽  
Vibration Properties ◽  
Matrix Differential Operators ◽  
Matrix Differential ◽  
Space Matrix

Vibration characteristics of rotating rings with complex support stiffnesses are studied. The complex stiffnesses of the rotating ring include discrete stiffnesses and partially distributed stiffnesses. The governing equations are established by Hamilton’s principle. The governing equations are cast in matrix differential operators and discretized using Galerkin’s method. The eigenvalue problem is dealt with state space matrix and the natural frequencies and vibration modes are obtained. The properties of natural frequencies and vibration modes of rotating rings are studied. The results illustrate that frequency separation and frequency veering happen with the increase of rotation speed. The vibration modes are not dominated by only one nodal diameter while dominated by several nodal diameters because the discrete and partially distributed stiffnesses disrupt the axisymmetry of rotating rings. The influences of several parameters to vibration properties of rotating rings are also investigated.

scholarly journals Enhanced Energy Harvesting of Flexural Waves in Elastic Beams by Bending Mode of Graded Resonators

2021 ◽  
Vol 8 ◽  
Author(s):  
Jacopo Maria De Ponti ◽  
Luca Iorio ◽  
Emanuele Riva ◽  
Francesco Braghin ◽  
Alberto Corigliano ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
Natural Frequencies ◽  
Elastic Beam ◽  
Flexural Waves ◽  
Vibration Energy Harvesting ◽  
Micro Fabrication ◽  
Wave Propagation Direction ◽  
Practical Applications ◽  
Bending Mode ◽  
Definition Of

We show efficient elastic energy transfer and wave confinement through a graded array of resonators attached to an elastic beam. Experiments demonstrate that flexural resonators of increasing lengths allow to reduce wave scattering and to achieve the rainbow effect with local wavefield amplifications. We show that the definition of a monotonically decreasing distribution of the natural frequencies of the resonators along the wave propagation direction, is the preferable choice to increase the energy efficiency of the system. The proposed configuration is suitable for micro-fabrication, envisaging practical applications for micro-scale vibration energy harvesting.

ANALYTICAL AND EXPERIMENTAL INVESTIGATION ON THE FREE VIBRATION OF SUBMERGED STIFFENED STEEL PLATE

2021 ◽  
Vol 160 (A2) ◽  
Author(s):  
S S Rezvani ◽  
M S Kiasat
Keyword(s):  
Numerical Solution ◽  
Fourier Transformation ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Steel Plate ◽  
Added Mass ◽  
Fast Fourier Transformation ◽  
Stiffened Plate ◽  
Transformation Functions ◽  
Stiffened Steel

The approach developed in this paper applies to vibration analysis of rectangular stiffened plate coupled with fluid. It is obvious that the natural frequencies of a submerged structure are less than those of in vacuum and these are due to the effect of added mass of water to the structure. This paper focuses on the experimental, analytical and numerical solution of natural frequencies of submerged stiffened plate. The analytical solution based on the deflection equation of submerged orthotropic plate, Laplace’s equation and Rayleigh's method in vibration analysis. By used the FEM software the numerical results for natural frequencies are derived. The natural frequencies of the stiffened plate are obtained practically by using Fast Fourier Transformation functions (FFT) in experimental analysis. Experimental results demonstrate the validity of analytical and numerical solution and results.

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