Vibration Frequencies and Modes of a Z-Shaped Beam With Variable Folding Angles

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
W. Zhang ◽  
W. H. Hu ◽  
D. X. Cao ◽  
M. H. Yao
Keyword(s):  
Numerical Simulations ◽  
Mode Shapes ◽  
Geometrical Parameters ◽  
Morphing Aircraft ◽  
Shaped Beam ◽  
Out Of Plane ◽  
Folding Wing ◽  
Fixed Structure ◽  
Theoretical Results ◽  
Equations Of Motions

In this paper, we investigate the vibration characteristics of a Z-shaped beam with variable folding angles which is used to model a folding wing of a morphing aircraft under the condition of a fixed structure. The governing equations of motions for the Z-shaped beam are formulated. For a specific set of material and geometrical parameters, the first three in-plane and the first two out-of-plane linear frequencies of the Z-shaped beam are theoretically calculated, and validated by the experiments and numerical simulations. Additionally, the theoretical mode shapes at a fixed folding angle are compared to the experimental results and the finite element simulations. The theoretical results agree well with numerical simulations and experiments. The results obtained in this paper are helpful for designing and controlling Z-shaped beam structures, and can also be used as a basis to study the nonlinear dynamics of these structures.

FOCUSING LIGHT WITH TYPICAL SUBWAVELENGTH PATTERNED METALLIC STRUCTURES

2012 ◽  
Vol 26 (22) ◽  
pp. 1250144 ◽  
Author(s):  
ZHEN GUO ◽  
LIANSHAN YAN ◽  
KUNHUA WEN ◽  
XIANGANG LUO
Keyword(s):  
Boundary Condition ◽  
Numerical Simulations ◽  
Geometrical Parameters ◽  
Metallic Structures ◽  
Theoretical Results ◽  
Focusing Properties

Two typical subwavelength nano-lenses, nano-slits and nano-grooves, are investigated based on the diffraction and electromagnetic boundary condition. Detailed and systematic analyses for the focusing properties of the two structures with different geometrical parameters are carried out. Theoretical results agree well with those in the numerical simulations and experiments. Compared to the nano-grooves, nano-slits with appropriate geometrical parameters show higher efficiency and better focusing performance.

On the kinetics of Hadamard-type fractional differential systems

2020 ◽  
Vol 23 (2) ◽  
pp. 553-570 ◽  
Author(s):  
Li Ma
Keyword(s):  
Differential Operator ◽  
Numerical Simulations ◽  
Type Inequality ◽  
The Other ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Kinetics Of ◽  
Theoretical Results

AbstractThis paper is devoted to the investigation of the kinetics of Hadamard-type fractional differential systems (HTFDSs) in two aspects. On one hand, the nonexistence of non-trivial periodic solutions for general HTFDSs, which are considered in some functional spaces, is proved and the corresponding eigenfunction of Hadamard-type fractional differential operator is also discussed. On the other hand, by the generalized Gronwall-type inequality, we estimate the bound of the Lyapunov exponents for HTFDSs. In addition, numerical simulations are addressed to verify the obtained theoretical results.

scholarly journals A numerical investigation on impulse-induced nonlinear longitudinal waves in pantographic beams

2021 ◽  
pp. 108128652110108
Author(s):  
Emilio Turco ◽  
Emilio Barchiesi ◽  
Francesco dell’Isola
Keyword(s):  
Numerical Simulations ◽  
Mechanical Response ◽  
Integration Scheme ◽  
Present Contribution ◽  
Longitudinal Waves ◽  
Deformation Regime ◽  
Impulsive Loads ◽  
Unit Cells ◽  
Statics And Dynamics ◽  
Equations Of Motions

This contribution presents the results of a campaign of numerical simulations aimed at better understanding the propagation of longitudinal waves in pantographic beams within the large-deformation regime. Initially, we recall the key features of a Lagrangian discrete spring model, which was introduced in previous works and that was tested extensively as capable of accurately forecasting the mechanical response of structures based on the pantographic motif, both in statics and dynamics. Successively, a stepwise integration scheme used to solve equations of motions is briefly discussed. The key content of the present contribution concerns the thorough presentation of some selected numerical simulations, which focus in particular on the propagation of stretch profiles induced by impulsive loads. The study takes into account different tests, by varying the number of unit cells, i.e., the total length of the system, spring stiffnesses, the shape of the impulse, as well as its properties such as duration and peak amplitude, and boundary conditions. Some conjectures about the form of traveling waves are formulated, to be confirmed by both further numerical simulations and analytical investigations.

scholarly journals A Stochastic SIR Epidemic System with a Nonlinear Relapse

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Ali El Myr ◽  
Abdelaziz Assadouq ◽  
Lahcen Omari ◽  
Adel Settati ◽  
Aadil Lahrouz
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Stochastic Perturbations ◽  
Sir Epidemic ◽  
Spread Model ◽  
Stochastic Sir ◽  
Theoretical Results

We investigate the conditions that control the extinction and the existence of a unique stationary distribution of a nonlinear mathematical spread model with stochastic perturbations in a population of varying size with relapse. Numerical simulations are carried out to illustrate the theoretical results.

scholarly journals Evaluation of Stiffness and Dynamic Properties of a Mine Shaft Steelwork Structure through In Situ Tests and Numerical Simulations

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 664
Author(s):  
Jacek Jakubowski ◽  
Przemysław Fiołek
Keyword(s):  
Numerical Simulations ◽  
Dynamic Properties ◽  
Vertical Motion ◽  
Load Test ◽  
Mode Shapes ◽  
Dynamic Amplification Factor ◽  
In Situ Tests ◽  
Mine Shaft ◽  
Numerical Investigations

A mine shaft steelwork is a three-dimensional frame that directs the vertical motion of conveyances in mine shafts. Here, we conduct field and numerical investigations on the stiffness and dynamic properties of these structures. Based on the design documentation of the shaft, materials data, and site inspection, the steelwork’s finite element model, featuring material and geometric non-linearities, was developed in Abaqus. Static load tests of steelwork were carried out in an underground mine shaft. Numerical simulations reflecting the load test conditions showed strong agreement with the in situ measurements. The validated numerical model was used to assess the dynamic characteristics of the structure. Dynamic linear and non-linear analyses delivered the natural frequencies, mode shapes, and structural response to dynamic loads. The current practices and regulations regarding shaft steelwork design and maintenance do not account for the stiffness of guide-to-bunton connections and disregard dynamic factors. Our experimental and numerical investigations show that these connections provide considerable stiffness, which leads to the redistribution and reduction in bending moments and increased stiffness of the construction. The results also show a high dynamic amplification factor. The omission of these features implicates an incorrect assessment of the design loads and can lead to over- or under-sized structures and ultimately to shortened design working life or failure.

scholarly journals Confinement of Vibrations in Variable-Geometry Nonlinear Flexible Beam

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
W. Gafsi ◽  
F. Najar ◽  
S. Choura ◽  
S. El-Borgi
Keyword(s):  
Passive Control ◽  
Inverse Eigenvalue Problem ◽  
Beam Dynamics ◽  
Mode Shapes ◽  
Physical Parameters ◽  
Geometrical Parameters ◽  
Flexible Beam ◽  
Beam Model ◽  
Nonlinear Frequency ◽  
Nonlinear Beam

In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differential equation that describes the beam dynamics. The nonlinear frequency response curves of the beam are approximated using the differential quadrature method and the finite difference method. We confirm that using the linear model, the strategy of vibration confinement remains valid for the nonlinear beam.

More Dynamical Properties Revealed from a 3D Lorenz-like System

2014 ◽  
Vol 24 (10) ◽  
pp. 1450133 ◽  
Author(s):  
Haijun Wang ◽  
Xianyi Li
Keyword(s):  
Numerical Simulations ◽  
Local Stability ◽  
Equilibrium Points ◽  
Heteroclinic Orbits ◽  
Mathematical Work ◽  
Chaotic Attractors ◽  
Heteroclinic Cycles ◽  
Homoclinic And Heteroclinic Orbits ◽  
Dynamical Properties ◽  
Theoretical Results

After a 3D Lorenz-like system has been revisited, more rich hidden dynamics that was not found previously is clearly revealed. Some more precise mathematical work, such as for the complete distribution and the local stability and bifurcation of its equilibrium points, the existence of singularly degenerate heteroclinic cycles as well as homoclinic and heteroclinic orbits, and the dynamics at infinity, is carried out in this paper. In particular, another possible new mechanism behind the creation of chaotic attractors is presented. Based on this mechanism, some different structure types of chaotic attractors are numerically found in the case of small b > 0. All theoretical results obtained are further illustrated by numerical simulations. What we formulate in this paper is to not only show those dynamical properties hiding in this system, but also (more mainly) present a kind of way and means — both "locally" and "globally" and both "finitely" and "infinitely" — to comprehensively explore a given system.

scholarly journals The Effect of Inner Reinforcing Cores on Natural Frequencies of the Lathe Tool Body

2013 ◽  
Vol 21 (Special-Issue) ◽  
pp. 186-192 ◽  
Author(s):  
Ladislav Rolník ◽  
Milan Naď
Keyword(s):  
Material Properties ◽  
Machine Tools ◽  
Structural Modification ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Geometrical Parameters ◽  
Structural Modifications ◽  
Modal Properties ◽  
Machine Productivity ◽  
Lathe Tool

Abstract The contribution is mainly focused on research and development of structural modification of machine tools, lathes in particular. The main aim of the modification is to change the modal properties (mode shapes, natural frequencies) of the lathe tool. The main objective of the contribution will be to formulate, mathematical analyse and evaluate the proposed methods and procedures for structural modifications of the tool, represented by beam body. A modification of modal properties by insertion of beam cores into beam body is studied in this paper. In this paper, the effect of material properties and geometrical parameters of reinforcing cores on natural frequencies of beam body is presented. The implementation will bring benefit on machine productivity, decreasing the machine tool wear and in many cases it will lead to better conditions in the cutting process.

DYNAMICS OF A PREY-DEPENDENT DIGESTIVE MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL

2012 ◽  
Vol 22 (04) ◽  
pp. 1250092 ◽  
Author(s):  
LINNING QIAN ◽  
QISHAO LU ◽  
JIARU BAI ◽  
ZHAOSHENG FENG
Keyword(s):  
Numerical Simulations ◽  
Analytical Method ◽  
Impulsive Control ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Period Doubling ◽  
Lambert W Function ◽  
Impulsive Effect ◽  
State Dependent ◽  
Theoretical Results

In this paper, we study the dynamical behavior of a prey-dependent digestive model with a state-dependent impulsive effect. Using the Poincaré map and the Lambert W-function, we find the analytical expression of discrete mapping. Sufficient conditions are established for transcritical bifurcation and period-doubling bifurcation through an analytical method. Exact locations of these bifurcations are explored. Numerical simulations of an example are illustrated which agree well with our theoretical results.

Dynamics of a stochastic three-species competitive model with Lévy jumps

2018 ◽  
Vol 11 (05) ◽  
pp. 1850075
Author(s):  
Yongxin Gao ◽  
Shiquan Tian
Keyword(s):  
Numerical Simulations ◽  
Critical Value ◽  
Persistence In The Mean ◽  
Competitive Model ◽  
Stability In Distribution ◽  
Parameters Analysis ◽  
The Mean ◽  
Lévy Jumps ◽  
White Noises ◽  
Theoretical Results

This paper is concerned with a three-species competitive model with both white noises and Lévy noises. We first carry out the almost complete parameters analysis for the model and establish the critical value between persistence in the mean and extinction for each species. The sufficient criteria for stability in distribution of solutions are obtained. Finally, numerical simulations are carried out to verify the theoretical results.

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