Multiple Scattering of Flexural Waves on Thin Plates

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Liang-Wu Cai ◽  
Stephen A. Hambric
Keyword(s):  
Multiple Scattering ◽  
Cross Section ◽  
Scattering Amplitude ◽  
Thin Plates ◽  
Flexural Waves ◽  
Gap Formation ◽  
Numerical Examples ◽  
Different Types ◽  
Generalized Matrix ◽  
T Matrix

In this paper, the scattering of flexural waves on a thin Kirchhoff plate by an ensemble of through-thickness circular scatterers is formulated by using the concept of the T-matrix in a generalized matrix notation, with a focus on deterministic numerical computations. T-matrices for common types of scatterers, including the void (hole), rigid, and elastic scatterers, are obtained. Wave field properties in the multiple-scattering setting, such as the scattering amplitude, and scattering cross section, as well as properties of the T-matrix due to the energy conservation are discussed. After an extensive validation, numerical examples are used to explore the band gap formation due to different types of scatterers. One of the interesting observations is that a type of inclusion commonly referred to as the “rigid inclusion” in fact represents a clamped boundary that is closer to a riveted confinement than a rigid scatterer; and an array of such scatterers can block the wave transmission at virtually all frequencies.

Piezoelectric T-Matrix Development and Multiple Scattering Analysis of Electroacoustic Wave Propagation in Thin Plates

2017 ◽  
Author(s):  
Amir Darabi ◽  
Michael Leamy
Keyword(s):  
Multiple Scattering ◽  
Wave Energy ◽  
Research Direction ◽  
Thin Plates ◽  
Matrix Formulation ◽  
Reflected Waves ◽  
Piezoelectric Patch ◽  
Electroacoustic Wave ◽  
T Matrix ◽  
New Research

Harvesting of acoustoelastic wave energy in thin plates and other structures is a promising new research direction for scavenging energy to power small sensors and devices. In particular, metamaterial-inspired harvesting concepts have shown strong potential for enhancing harvesting of acoustoelastic wave energy. In support of continued development of these metamaterial-based concepts, this paper presents a fully-coupled T-matrix formulation for assessing scattering of incident wave energy from a piezoelectric patch attached to a thin plate. The T-matrix serves as an input-output relationship between incident and reflected waves, and is developed herein for a piezoelectric patch connected to an external circuit. The utility of the T-matrix is evident in problems with multiple piezoelectric harvesters, where it can be used with other T-matrices (such as those previously formulated for rigid, void, and elastic inclusions) in a multiple scattering context. This has the potential for many uses in predicting the dynamic response of smart and active structures, but may be particularly useful in accurately assessing metamaterial-based energy harvesting enhancement strategies. Following development of the requisite T-matrix, harvesting in an example Gradient-Index (GRIN) metamaterial structure is predicted using the multiple scattering approach.

scholarly journals Second-order neutrosophic boundary-value problem

2021 ◽  
Author(s):  
Sandip Moi ◽  
Suvankar Biswas ◽  
Smita Pal(Sarkar)
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Differential Calculus ◽  
Boundary Value ◽  
Second Order ◽  
Numerical Examples ◽  
Different Types ◽  
First Time

AbstractIn this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed. This is the first time where a second-order neutrosophic boundary-value problem has been introduced with different types of first- and second-order derivatives. Some numerical examples have been examined to explain different systems of neutrosophic differential equation.

scholarly journals Supply Chain Coordination Contracts under Double Sided Disruptions Simultaneously

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Huan Zhang ◽  
Yang Liu ◽  
Jingsi Huang
Keyword(s):  
Supply Chain ◽  
Supply Chain Coordination ◽  
Optimal Price ◽  
Supply Chain System ◽  
Pricing Policy ◽  
Product Cost ◽  
Numerical Examples ◽  
Supply Chain Contracts ◽  
Different Types ◽  
Key Factor

Supply chain coordination models are developed in a two-echelon supply chain with double sided disruptions. In a supply chain system, the supplier may suffer from the product cost disruption and the retailer suffers from the demand disruption simultaneously. The purpose of this study is to design proper supply chain contracts, under which the supply chain with double sided disruption can be coordinated. Firstly, the centralized decision-making models are applied to find the optimal price and quantity under three cases as the baseline. The different cases are divided by the different relationship between the product cost disruption and the demand disruption. Secondly, two different types of contracts are introduced to coordinate the whole supply chain. One is all-unit wholesale quantity discount policy (AQDP) contract, and the other one is capacitated linear pricing policy (CLPP) contract. And it is found out that the gap between the demand disruption and the product cost disruption is the key factor to influence the supply chain coordination. Some numerical examples and sensitivity analysis are given to illustrate the models. The AQDP contracts are listed out under different cases to show how to use it under double sided disruptions.

The study of neutron capture processes in AlN nanoparticles

2021 ◽  
pp. 2150127
Author(s):  
T. G. Naghiyev
Keyword(s):  
Computer Modeling ◽  
Cross Section ◽  
Neutron Capture ◽  
Absorption Cross Section ◽  
Effective Cross Section ◽  
Absorption Cross ◽  
Effective Absorption ◽  
Different Types ◽  
N Isotopes

The neutron capture processes in the AlN nanoparticles were investigated by computer modeling. Neutrons absorption were separately investigated for aluminum (Al) and nitrogen (N) atoms in the AlN nanoparticles. The modeling was performed separately for each stable Al and N isotopes, because the effective absorption cross-section of different types of isotopes of Al and N atoms is different. Moreover, effective cross-section spectra of neutron capture for aluminum and nitrogen atoms were comparatively investigated.

scholarly journals Numerical Assessment of the Performance of Elastic Cloaks for Transient Flexural Waves

2020 ◽  
Vol 7 ◽  
Author(s):  
Marco Rossi ◽  
Daniele Veber ◽  
Massimiliano Gei
Keyword(s):  
Finite Element ◽  
Thin Plates ◽  
Winkler Foundation ◽  
Finite Element Code ◽  
Flexural Waves ◽  
Transient Waves ◽  
Mathematical Transformation ◽  
Plane Body ◽  
Numerical Assessment ◽  
Subgrade Modulus

A relevant application of transformation elastodynamics has shown that flexural waves in a Kirchhoff-Love plate can be diverted and channeled to cloak a region of the ambient space. To achieve the goal, an orthotropic meta-structural plate should be employed. However, the corresponding mathematical transformation leads to the presence of an unwanted strong compressive prestress, likely beyond the buckling threshold of the structure, with a set of in-plane body forces to warrant equilibrium. In addition, the plate must possess, at the same time, high bending stiffnesses, but a null twisting rigidity. With the aim of estimating the performance of cloaks modelled with approximate parameters, an in-house finite element code, based on a subparametric technique, is implemented to deal with the cloaking of transient waves in orthotropic thin plates. The tool allows us to explore the sensitivity of specific stiffness parameters that may be difficult to match in a real cloak design. In addition, the finite element code is extended to investigate a meta-plate interacting with a Winkler foundation, to confirm how the subgrade modulus should transform in the cloak region.

Convolutional Neural Network Representation of the Total Multiple Scattering Cross Section

2021 ◽  
Author(s):  
Thang Tran ◽  
Peter Lai ◽  
Wei-Ching Wang ◽  
Amaris Rosa ◽  
Feruza Amirkulova ◽  
...  
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Multiple Scattering ◽  
Cross Section ◽  
Scattering Cross Section ◽  
Scattering Cross ◽  
Network Representation
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