scholarly journals Numerical Investigation of Discrepancies Between Two-Dimensional and Three-Dimensional Acoustic Metamaterials

2021 ◽  
Vol 8 ◽  
Author(s):  
Wenchao Jin ◽  
Hui Guo ◽  
Pei Sun ◽  
Yansong Wang ◽  
Tao Yuan
Keyword(s):  
Band Structure ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Experimental Models ◽  
Mode Shapes ◽  
Periodic Lattice ◽  
Two Dimensional ◽  
Acoustic Metamaterials ◽  
Band Structures ◽  
Practical Applications

In order to get insight information of the band structure of acoustic metamaterials (AMMs) in condensed matter, periodic lattice structures are analyzed using Bloch’s theorem. Typical approaches of the band structure computation methods, topology optimization, and tunable abilities cannot overcome the gap between the two-dimensional (2D) AMMs theoretical and three-dimensional (3D) specimens’ experimental data yet. In this work, the variation in the results of the band structure obtained from the 2D mathematical model computed with respect to the 3D experimental models, and related cause of the variation is explored. The band structures and mode shapes of the 2D AMMs, quasi-2D models, and 3D specimen models are followed to reveal the boundary conditions and source for the observed differences in band structures. The cause for the discrepancies is verified by using the finite element method (FEM) with corresponding boundary conditions. It is found that outcomes from computational data of the 2D AMMs model are diverted significantly by means of bandgap, band structure, and stress distribution in counterparts of the 3D specimen model. This approach can provide assistance for computing the band structure of 2D AMMs for practical applications.

A Spectral-Tchebychev Solution for Three-Dimensional Vibrations of Parallelepipeds Under Mixed Boundary Conditions

2012 ◽  
Vol 79 (5) ◽  
Author(s):  
Sinan Filiz ◽  
Bekir Bediz ◽  
L. A. Romero ◽  
O. Burak Ozdoganlar
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Mixed Boundary ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mixed Boundary Conditions ◽  
Integral Form ◽  
Mode Shapes ◽  
Different Boundary Conditions ◽  
Practical Applications

Vibration behavior of structures with parallelepiped shape—including beams, plates, and solids—are critical for a broad range of practical applications. In this paper we describe a new approach, referred to here as the three-dimensional spectral-Tchebychev (3D-ST) technique, for solution of three-dimensional vibrations of parallelepipeds with different boundary conditions. An integral form of the boundary-value problem is derived using the extended Hamilton’s principle. The unknown displacements are then expressed using a triple expansion of scaled Tchebychev polynomials, and analytical integration and differentiation operators are replaced by matrix operators. The boundary conditions are incorporated into the solution through basis recombination, allowing the use of the same set of Tchebychev functions as the basis functions for problems with different boundary conditions. As a result, the discretized equations of motion are obtained in terms of mass and stiffness matrices. To analyze the numerical convergence and precision of the 3D-ST solution, a number of case studies on beams, plates, and solids with different boundary conditions have been conducted. Overall, the calculated natural frequencies were shown to converge exponentially with the number of polynomials used in the Tchebychev expansion. Furthermore, the natural frequencies and mode shapes were in excellent agreement with those from a finite-element solution. It is concluded that the 3D-ST technique can be used for accurate and numerically efficient solution of three-dimensional parallelepiped vibrations under mixed boundary conditions.

scholarly journals Transformation Between 2D and 3D Covalent Organic Frameworks via Reversible [2+2] Cycloaddition

2020 ◽  
Author(s):  
Thaksen Jadhav ◽  
Yuan Fang ◽  
Cheng-Hao Liu ◽  
Afshin Dadvand ◽  
Ehsan Hamzehpoor ◽  
...  
Keyword(s):  
Band Structure ◽  
Absorption Edge ◽  
Room Temperature ◽  
Three Dimensional ◽  
Cross Linking ◽  
Two Dimensional ◽  
Covalent Organic Frameworks ◽  
Doping Behavior ◽  
2D Polymers ◽  
2D And 3D

We report the first transformation between crystalline vinylene-linked two-dimensional (2D) polymers and crystalline cyclobutane-linked three-dimensional (3D) polymers. Specifically, absorption-edge irradiation of the 2D poly(arylenevinylene) covalent organic frameworks (COFs) results in topological [2+2] cycloaddition cross-linking the π-stacked layers in 3D COFs. The reaction is reversible and heating to 200°C leads to a cycloreversion while retaining the COF crystallinity. The resulting difference in connectivity is manifested in the change of mechanical and electronic properties, including exfoliation, blue-shifted UV-Vis absorption, altered luminescence, modified band structure and different acid-doping behavior. The Li-impregnated 2D and 3D COFs show a significant ion conductivity of 1.8×10<sup>−4</sup> S/cm and 3.5×10<sup>−5</sup> S/cm, respectively. Even higher room temperature proton conductivity of 1.7×10<sup>-2</sup> S/cm and 2.2×10<sup>-3</sup> S/cm was found for H<sub>2</sub>SO<sub>4</sub>-treated 2D and 3D COFs, respectively.

Separation of the 3D stress state of a loaded plate into two-dimensional tasks: bending and symmetric compression of the plate

2021 ◽  
Vol 103 (3) ◽  
pp. 53-62
Author(s):  
Victor Revenko ◽  
Andrian Revenko
Keyword(s):  
Boundary Conditions ◽  
Harmonic Functions ◽  
Three Dimensional ◽  
Partial Solution ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Normal Stresses ◽  
Equilibrium Equations ◽  
Dimensional Boundary ◽  
The Right

The three-dimensional stress-strain state of an isotropic plate loaded on all its surfaces is considered in the article. The initial problem is divided into two ones: symmetrical bending of the plate and a symmetrical compression of the plate, by specified loads. It is shown that the plane problem of the theory of elasticity is a special case of the second task. To solve the second task, the symmetry of normal stresses is used. Boundary conditions on plane surfaces are satisfied and harmonic conditions are obtained for some functions. Expressions of effort were found after integrating three-dimensional stresses that satisfy three equilibrium equations. For a thin plate, a closed system of equations was obtained to determine the harmonic functions. Displacements and stresses in the plate were expressed in two two-dimensional harmonic functions and a partial solution of the Laplace equation with the right-hand side, which is determined by the end loads. Three-dimensional boundary conditions were reduced to two-dimensional ones. The formula was found for experimental determination of the sum of normal stresses via the displacements of the surface of the plate.

scholarly journals A New Two-Dimensional Mutual Coupled Logistic Map and Its Application for Pseudorandom Number Generator

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Xuan Huang ◽  
Lingfeng Liu ◽  
Xiangjun Li ◽  
Minrong Yu ◽  
Zijie Wu
Keyword(s):  
Statistical Tests ◽  
Chaotic Map ◽  
Logistic Map ◽  
Security Analysis ◽  
Three Dimensional ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Number Generator ◽  
Two Dimensional ◽  
Practical Applications

Given that the sequences generated by logistic map are unsecure with a number of weaknesses, including its relatively small key space, uneven distribution, and vulnerability to attack by phase space reconstruction, this paper proposes a new two-dimensional mutual coupled logistic map, which can overcome these weaknesses. Our two-dimensional chaotic map model is simpler than the recently proposed three-dimensional coupled logistic map, whereas the sequence generated by our system is more complex. Furthermore, a new kind of pseudorandom number generator (PRNG) based on the mutual coupled logistic maps is proposed for application. Both statistical tests and security analysis show that our proposed PRNG has good randomness and that it can resist all kinds of attacks. The algorithm speed analysis indicates that PRNG is valuable to practical applications.

scholarly journals Projection of compact fractal sets: application to diffusion-limited and cluster-cluster aggregates

2008 ◽  
Vol 15 (4) ◽  
pp. 695-699 ◽  
Author(s):  
F. Maggi
Keyword(s):  
Fractal Dimension ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Cohesive Sediment ◽  
Mathematical Approach ◽  
Two Dimensional ◽  
Atmospheric Sciences ◽  
Practical Applications ◽  
Fractal Sets ◽  
Diffusion Limited

Abstract. The need to assess the three-dimensional fractal dimension of fractal aggregates from the fractal dimension of two-dimensional projections is very frequent in geophysics, soil, and atmospheric sciences. However, a generally valid approach to relate the two- and three-dimensional fractal dimensions is missing, thus questioning the accuracy of the method used until now in practical applications. A mathematical approach developed for application to suspended aggregates made of cohesive sediment is investigated and applied here more generally to Diffusion-Limited Aggregates (DLA) and Cluster-Cluster Aggregates (CCA), showing higher accuracy in determining the three-dimensional fractal dimension compared to the method currently used.

scholarly journals Dynamic Response of a Thick Piezoelectric Circular Cylindrical Panel: An Exact Solution

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Atta Oveisi ◽  
Mohammad Gudarzi ◽  
Seyyed Mohammad Hasheminejad
Keyword(s):  
Steady State ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Cylindrical Panel ◽  
Mode Shapes ◽  
Steady State Response ◽  
Two Dimensional ◽  
Finite Element Software ◽  
State Response ◽  
Thick Shells

One of the interesting fields that attracted many researchers in recent years is the smart structures. The piezomaterials, because of their ability in converting both mechanical stress and electricity to each other, are very applicable in this field. However, most of the works available used various inexact two-dimensional theories with certain types of simplification, which are inaccurate in some applications such as thick shells while, in some applications due to request of large displacement/stress, thick piezoelectric panel is needed and two-dimensional theories have not enough accuracy. This study investigates the dynamic steady state response and natural frequency of a piezoelectric circular cylindrical panel using exact three-dimensional solutions based on this decomposition technique. In addition, the formulation is written for both simply supported and clamped boundary conditions. Then the natural frequencies, mode shapes, and dynamic steady state response of the piezoelectric circular cylindrical panel in frequency domain are validated with commercial finite element software (ABAQUS) to show the validity of the mathematical formulation and the results will be compared, finally.

Green's function boundary conditions in two-dimensional and three-dimensional atomistic simulations of dislocations

1998 ◽  
Vol 77 (1) ◽  
pp. 231-256 ◽  
Author(s):  
S. Rao ◽  
C. Hernandez ◽  
J. P. Simmons ◽  
T. A. Parthasarathy ◽  
C. Woodward
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Green's Function ◽  
Three Dimensional ◽  
Atomistic Simulations ◽  
Two Dimensional

Contact Temperature in Dry Bearings. Three Dimensional Theory and Verification

1981 ◽  
Vol 103 (2) ◽  
pp. 243-251 ◽  
Author(s):  
A. Floquet ◽  
D. Play
Keyword(s):  
Fourier Transform ◽  
Boundary Conditions ◽  
Experimental Verification ◽  
Three Dimensional ◽  
Contact Temperature ◽  
3D Analysis ◽  
New Work ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Infra Red

Boundary conditions were arbitrarily specified in an earlier two dimensional (2D) analysis of contact temperature. In this new work a general three dimensional (3D) Fourier transform solution is obtained from which for specific cases, the boundary conditions can be estimated. Further, experimental verification of 3D analysis was performed using infra-red technique.

Three-Dimensional Vibrations of Truncated Hollow Cones

1995 ◽  
Vol 1 (2) ◽  
pp. 145-158 ◽  
Author(s):  
Arthur W. Leissa ◽  
Jinyoung So
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Ritz Method ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Arbitrary Boundary ◽  
Conical Shells ◽  
Hole Radius ◽  
Geometric Boundary

This work presents a three-dimensional (3-D) method of analysis for determining the free vibration frequencies and corresponding mode shapes of truncated hollow cones of arbitrary thickness and having arbitrary boundary conditions. It also supplies the first known numerical results from 3-D analysis for such problems. The analysis is based upon the Ritz method. The vibration modes are separated into their Fourier components in terms of the circumferential coordinate. For each Fourier component, displacements are expressed as algebraic polynomials in the thickness and slant length coordinates. These polynomials satisfy the geometric boundary conditions exactly. Because the displacement functions are mathematically complete, upper bound values of the vibration frequencies are obtained that are as close to the exact values as desired. This convergence is demonstrated for a representative truncated hollow cone configuration where six-digit exactitude in the frequencies is achieved. The method is then used to obtain accurate and extensive frequencies for two sets of completely free, truncated hollow cones, one set consisting of thick conical shells and the other being tori having square-generating cross sections. Frequencies are presented for combinations of two values of apex angles and two values of inner hole radius ratios for each set of problems.

Study of the Effect of Boundary Conditions on Residual Stresses in Welding Using Element Birth and Element Movement Techniques

2003 ◽  
Vol 125 (4) ◽  
pp. 432-439 ◽  
Author(s):  
Ihab F. Z. Fanous ◽  
Maher Y. A. Younan ◽  
Abdalla S. Wifi
Keyword(s):  
Residual Stresses ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Welding Process ◽  
Computation Time ◽  
The Other ◽  
Two Dimensional ◽  
The Media ◽  
Three Dimensional Models ◽  
Element Movement

The structure in which the welding process is performed highly affects the residual stresses generated in the welding. This effect is simulated by choosing the appropriate boundary conditions in modeling the welding process. The major parameters of the boundary conditions are the method by which the base metal is being fixed and the amount of heat being applied through the torch. Other parameters may include the coefficients of thermal heat loss from the plate which may simulate the media in which the welding is taking place. In modeling the welding process, two-dimensional forms of approximation were developed in analyzing most of the models of such problem. Three-dimensional models analyzing the welding process were developed in limited applications due to its high computation time and cost. With the development of new finite element tools, namely the element movement technique developed by the authors, full three-dimensional analysis of the welding process is becoming in hand. In the present work, three different boundary conditions shall be modeled comparing their effect on the welding. These boundary conditions shall be applied to two models of the welding process: one using the element birth technique and the other using the element movement technique showing the similarity in their responses verifying the effectiveness of the latter being accomplished in a shorter time.

Sign in / Sign up

Export Citation Format

Share Document