scholarly journals Design of Energy Absorbing Metamaterials Using Stochastic Soft-Wall Billiards

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1798
Author(s):  
Valery Pilipchuk
Keyword(s):  
Mode Shapes ◽  
Potential Wells ◽  
One Dimensional ◽  
Artificial Materials ◽  
Chaotic Mode ◽  
Propagating Waves ◽  
Soft Wall ◽  
Energy Absorbing ◽  
Physical Principles ◽  
Directional Trend

Physical principles for designing cellwise artificial materials with energy-absorbing/harvesting and wave guiding properties are discussed in the present work. We analyzed the evolution of waves in a one-dimensional lattice of 3D massive potential wells with light particles inside. The potential wells were coupled with elastic springs and represented soft-wall versions of the so-called stochastic billiards. A billiard could switch from repelling to the stadium type as the parameter of shape changed its sign from positive to negative. We found that certain shapes of the potential wells/containers provided a one-directional trend of the energy flow from the chain of containers into the chaotically moving light inclusions by increasing their total kinetic energy. As a result, propagating waves became trapped by giving rise to standing waves with chaotic mode shapes with decaying amplitudes.

scholarly journals Hierarchical mechanical metamaterials built with scalable tristable elements for ternary logic operation and amplitude modulation

2021 ◽  
Vol 7 (9) ◽  
pp. eabf1966
Author(s):  
Hang Zhang ◽  
Jun Wu ◽  
Daining Fang ◽  
Yihui Zhang
Keyword(s):  
Structural Diversity ◽  
Cell Number ◽  
Structural Elements ◽  
Ternary Logic ◽  
Stable States ◽  
One Dimensional ◽  
Logic Operation ◽  
Artificial Materials ◽  
Mechanical Metamaterials ◽  
Unit Cells

Multistable mechanical metamaterials are artificial materials whose microarchitectures offer more than two different stable configurations. Existing multistable mechanical metamaterials mainly rely on origami/kirigami-inspired designs, snap-through instability, and microstructured soft mechanisms, with mostly bistable fundamental unit cells. Scalable, tristable structural elements that can be built up to form mechanical metamaterials with an extremely large number of programmable stable configurations remains illusive. Here, we harness the elastic tensile/compressive asymmetry of kirigami microstructures to design a class of scalable X-shaped tristable structures. Using these structure as building block elements, hierarchical mechanical metamaterials with one-dimensional (1D) cylindrical geometries, 2D square lattices, and 3D cubic/octahedral lattices are designed and demonstrated, with capabilities of torsional multistability or independent controlled multidirectional multistability. The number of stable states increases exponentially with the cell number of mechanical metamaterials. The versatile multistability and structural diversity allow demonstrative applications in mechanical ternary logic operators and amplitude modulators with unusual functionalities.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

scholarly journals Numerical Modeling of the Interaction of Solitary Waves and Submerged Breakwaters with Sharp Vertical Edges Using One-Dimensional Beji & Nadaoka Extended Boussinesq Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mohammad H. Jabbari ◽  
Parviz Ghadimi ◽  
Ali Masoudi ◽  
Mohammad R. Baradaran
Keyword(s):  
Solitary Waves ◽  
Numerical Study ◽  
Time Integration ◽  
Boussinesq Equations ◽  
Linear Interpolation ◽  
Reflected Waves ◽  
One Dimensional ◽  
Propagating Waves ◽  
Linear Elements ◽  
Predictor Corrector

Using one-dimensional Beji & Nadaoka extended Boussinesq equation, a numerical study of solitary waves over submerged breakwaters has been conducted. Two different obstacles of rectangular as well as circular geometries over the seabed inside a channel have been considered in view of solitary waves passing by. Since these bars possess sharp vertical edges, they cannot directly be modeled by Boussinesq equations. Thus, sharply sloped lines over a short span have replaced the vertical sides, and the interactions of waves including reflection, transmission, and dispersion over the seabed with circular and rectangular shapes during the propagation have been investigated. In this numerical simulation, finite element scheme has been used for spatial discretization. Linear elements along with linear interpolation functions have been utilized for velocity components and the water surface elevation. For time integration, a fourth-order Adams-Bashforth-Moulton predictor-corrector method has been applied. Results indicate that neglecting the vertical edges and ignoring the vortex shedding would have minimal effect on the propagating waves and reflected waves with weak nonlinearity.

Solitary-wave solutions of nonlinear problems

1990 ◽  
Vol 331 (1617) ◽  
pp. 195-244 ◽  
Keyword(s):  
Fixed Point ◽  
Solitary Waves ◽  
Fixed Point Index ◽  
Fixed Point Theorems ◽  
Nonlinear Problems ◽  
One Dimensional ◽  
Propagating Waves ◽  
Model Equations ◽  
Permanent Form ◽  
General Method

A general method is presented for the exact treatment of analytical problems that have solutions representing solitary waves. The theoretical framework of the method is developed in abstract first, providing a range of fixed-point theorems and other useful resources. It is largely based on topological concepts, in particular the fixed-point index for compact mappings, and uses a version of positive-operator theory referred to Frechet spaces. Then three exemplary problems are treated in which steadily propagating waves of permanent form are known to be represented. The first covers a class of one-dimensional model equations that generalizes the classic Korteweg—de Vries equation. The second concerns two-dimensional wave motions in an incompressible but density-stratified heavy fluid. The third problem describes solitary waves on water in a uniform canal.

scholarly journals Interactions between Rotation and Pulsation

2004 ◽  
Vol 215 ◽  
pp. 404-413
Author(s):  
Rich Townsend
Keyword(s):  
Angular Momentum ◽  
Coriolis Force ◽  
Rossby Waves ◽  
Narrow Band ◽  
Rotating Stars ◽  
Stellar Rotation ◽  
Coriolis Forces ◽  
Wave Dynamics ◽  
Propagating Waves ◽  
Physical Principles

In this contribution, I will examine the interaction between stellar rotation and pulsation. I begin with a brief review of the non-rotating case, emphasizing the character of pulsations as azimuthally-propagating waves. I then go on to discuss how these waves are modified under the influence of the centrifugal and Coriolis forces. Through simple arguments, I outline the conditions under which each force can become significant in determining the wave dynamics. Particular attention is paid to the Coriolis force, since it is responsible for the formation of a waveguide, which confines the pulsation to a narrow band centered on the stellar equator. Using the example of a prograde sectoral pulsation mode, I explain the basic physical principles underlying this trapping.The Coriolis force is also responsible for the existence of Rossby waves, which are not found in non-rotating stars. I demonstrate how these waves may be understood in terms of a conservation law for angular momentum, and review their most important characteristics. I then examine how rotation modifies the frequencies of pulsation, and explain how observations of such modifications can provide information regarding a star's rotation rate. To conclude, I focus on the converse of the pulsation-rotation interaction: how the transport of angular momentum by pulsation might be important in determining the evolution of a star's rotation profile.

Axisymmetric waves in compressible Newtonian liquids contained in rigid tubes: steady-periodic mode shapes and dispersion by the method of eigenvalleys

1973 ◽  
Vol 58 (3) ◽  
pp. 595-621 ◽  
Author(s):  
H. A. Scarton ◽  
W. T. Rouleau
Keyword(s):  
Boundary Layer ◽  
Acoustic Waves ◽  
Mode Shapes ◽  
Periodic Mode ◽  
Rotational Mode ◽  
High Frequencies ◽  
Wide Range ◽  
Propagating Waves ◽  
New Type ◽  
Newtonian Liquids

In this paper the first thirty-two axisymmetric modes for steady-periodic waves in viscous compressible liquids contained in rigid, impermeable, circular tubes are calculated. These results end long speculation over the effects of viscosity on guided acoustic waves. Sixteen of the modes belong to a family of rotation-dominated modes whose existence was previously unknown. The thirty-two modes were computed for a wide range of frequencies, viscosities and wave-lengths.The modes were found through the use of the method of eigenvalleys, which also led to the discovery of backward-propagating waves, an exact analytical expression for the zeroth rotational mode eigenvalue, definitive boundaries between low and intermediate frequencies and between intermediate and high frequencies, and a new type of boundary layer, called a dilatational boundary layer.

Free Vibration of a Multilayered One-Dimensional Quasi-Crystal Plate

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Natalie Waksmanski ◽  
Ernian Pan ◽  
Lian-Zhi Yang ◽  
Yang Gao
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Crystal Plate ◽  
Mode Shapes ◽  
Sandwich Plates ◽  
One Dimensional ◽  
Propagator Matrix ◽  
Multilayered Plates

An exact closed-form solution of free vibration of a simply supported and multilayered one-dimensional (1D) quasi-crystal (QC) plate is derived using the pseudo-Stroh formulation and propagator matrix method. Natural frequencies and mode shapes are presented for a homogenous QC plate, a homogenous crystal plate, and two sandwich plates made of crystals and QCs. The natural frequencies and the corresponding mode shapes of the plates show the influence of stacking sequence on multilayered plates and the different roles phonon and phason modes play in dynamic analysis of QCs. This work could be employed to further expand the applications of QCs especially if used as composite materials.

Complex Modal Extraction for Estimating Wave Parameters in One-Dimensional Media

2010 ◽  
Author(s):  
B. F. Feeny
Keyword(s):  
Group Velocity ◽  
Traveling Waves ◽  
Random Noise ◽  
Mode Shapes ◽  
Transient Wave ◽  
Wave Speeds ◽  
One Dimensional ◽  
Wave Numbers ◽  
Displacement Profile ◽  
Complex Modal

A method of complex orthogonal decomposition is applied to the extraction of modes from simulation data of multi-modal traveling waves in one-dimensional continua. The decomposition of a transient wave is performed on a nondispersive pulse. Complex wave modes are then extracted from a two-harmonic simulation of a dispersive medium. The wave frequencies and wave numbers are obtained by looking at the whirl of the complex modal coordinate, and the complex modal function, respectively, in the complex plane. From the frequencies and wave numbers, the wave speeds are then estimated, as well as the group velocity associated with the two waves. The group velocity is also extracted directly from a decomposition of the traveling envelope of the waveform. The observations from the first two examples are used to help interpret the decomposition of a simulation of the traveling waves produced by a Gaussian initial displacement profile in an Euler-Bernoulli beam. While such a disturbance produces a continuous spectrum of wave components, the sampling conditions limit the range of wave components (i.e. mode shapes and modal coordinates) to be extracted. Within this working range, the wave numbers and frequencies are obtained from the extraction, and compared to theory. The frequency distribution is then approximated. The results are robust to random noise.

Piezoelectric Modal Sensors for Two-Dimensional Structures

Aerospace ◽  
2004 ◽  
Author(s):  
Yuan-Fang Chou ◽  
Ming-Yi Yang
Keyword(s):  
Finite Element Analysis ◽  
Free Surface ◽  
Signal Strength ◽  
Mode Shapes ◽  
Two Dimensional ◽  
Surface Charges ◽  
Optimization Scheme ◽  
Element Analysis ◽  
One Dimensional ◽  
Orthogonal Property

Using the orthogonal property of eigenfunctions, piezoelectric modal sensors for one-dimensional members were created by shaping electrode patterns proportional to modal strains. However, it is not easy to apply the same concept to two-dimensional structures due to the difficulty in implementing location weight needed for signals. Therefore, nonlinear optimization scheme is employed in this paper to design modal sensors for two-dimensional structures. For a given electrode pattern, the signal contributed from each mode is found by integrating the corresponding free surface charges on the sensing electrode. Then the modal sensor is obtained by modifying electrode pattern to achieve required relative signal strength for different modes. Sensors that are capable to sense or filter out the signal generated by a specific mode can be developed. A two-dimensional aluminum plate coated with PZT layer is adopted as an example. Mode shapes are found with finite element analysis. Modal sensors are designed successfully and mode- reject filters are also demonstrated.

Molecular Motions in Halogen-Bridged One-Dimensional Pt Complexes, [PtII(en)2][PtIVX2(en)2](ClO4)4 (X = Cl, Br) Studied by 2H and 1H NMR

2002 ◽  
Vol 57 (6-7) ◽  
pp. 413-418 ◽  
Author(s):  
Noriyoshi Kimura ◽  
Toru Hachisuka ◽  
Yukitaka Nakano ◽  
Ryuichi Ikeda
Keyword(s):  
Relaxation Times ◽  
Lattice Relaxation ◽  
Energy Difference ◽  
Spin Lattice Relaxation ◽  
X Ray Diffraction ◽  
Potential Wells ◽  
One Dimensional ◽  
X Ray ◽  
Spin Lattice ◽  
H Nmr

2H and 1H NMR measurements were performed on crystalline [Pt(en)2][PtX2(en)2](ClO4)4 (X = Cl, Br), where the protonated and partially deuterated ethylenediamines (en’s), NH2(CH2)2NH2, NH2(CD2)2NH2 and ND2(CH2)2ND2 were used as ligands. Measurements of 2H and 1H NMR spin-lattice relaxation times showed the presence of motions of en chelate rings at the temperatures near the phase transitions, whereas broad 2H NMR spectra and the reported X-ray diffraction data showed no marked motions. These results were consistently explained by introducing the en puckering motion between highly asymmetric potential wells with an energy difference of 10 - 13 kJ mol-1. This difference was shown to be much larger than 2 - 5 kJ mol-1, reported for the iodo-complex, [Pt(en)2][PtI2(en)2](ClO4)4

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