Shear Horizontal Waves in Orthotropic Layer/Piezoelectric Cylinder Structures

2014 ◽  
Vol 905 ◽  
pp. 105-108 ◽  
Author(s):  
Xing Zhao ◽  
Hong Jun Wang
Keyword(s):  
Boundary Conditions ◽  
Bessel Function ◽  
Piezoelectric Materials ◽  
Interface Conditions ◽  
Dispersion Characteristics ◽  
Orthotropic Layer ◽  
Sh Waves ◽  
Numerical Examples ◽  
Piezoelectric Cylinder ◽  
Shear Horizontal

This paper investigates the dispersion characteristics of shear horizontal waves propagating in a piezoelectric cylinder covered by orthotropic layer. The surface of the orthotropic layer is assumed to be mechanically free; The stress and displacement at the interface is continuous. The solution of the equation is expressed by Bessel function, and the dispersion equation is derived by using the boundary conditions and the interface conditions, the numerical examples are provided to show the influences of the orthotropic degree and the properties of piezoelectric materials on the dispersion characteristics of SH waves.

Propagation Behaviors of SH Waves in Piezoelectric Layer/Elastic Cylinder with an Imperfect Interface

2012 ◽  
Vol 151 ◽  
pp. 130-134 ◽  
Author(s):  
Yan Hong Wang ◽  
Mei Li Wang ◽  
Jin Xi Liu
Keyword(s):  
Dispersion Equation ◽  
Layered Structure ◽  
Material Properties ◽  
Piezoelectric Layer ◽  
Elastic Cylinder ◽  
Imperfect Interface ◽  
Interface Conditions ◽  
Sh Waves ◽  
Numerical Examples ◽  
Basic Equations

The dispersion behaviors of SH waves are investigated propagating in a layered structure consisting of a piezoelectric layer and an elastic cylinder. The interface between the piezoelectric layer and the elastic cylinder is assumed to be imperfect bonding. The surface of the piezoelectric layer is assumed to be mechanically free and electrically shorted. The dispersion equation is derived by the basic equations, the boundary and the interface conditions. The numerical examples are provided to show the influences of the imperfect interface, the thickness ratios and the material properties of the piezoelectric on the dispersive characteristics.

scholarly journals On a nonlinear system of Riemann-Liouville fractional differential equations with semi-coupled integro-multipoint boundary conditions

2021 ◽  
Vol 19 (1) ◽  
pp. 760-772
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Badrah Alghamdi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Numerical Examples ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

Abstract We study a nonlinear system of Riemann-Liouville fractional differential equations equipped with nonseparated semi-coupled integro-multipoint boundary conditions. We make use of the tools of the fixed-point theory to obtain the desired results, which are well-supported with numerical examples.

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

Scattering of SH Wave on Periodic Cracks in an Infinite Plane of Piezoelectric/Piezomagnic Composite Materials

2012 ◽  
Vol 166-169 ◽  
pp. 3364-3368
Author(s):  
Wei Shi ◽  
Li Xia Ma
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Composite Materials ◽  
Piezoelectric Materials ◽  
Infinite Plane ◽  
Sh Wave ◽  
Scattering Problems ◽  
Sh Waves ◽  
Periodic Cracks ◽  
The Fourier Transform

In this paper, the scattering problems of SH waves on periodic cracks in an infinite of piezoelectric/piezomagnic composite materials bonded to an infinite of homogeneous piezoelectric materials is investigated, the Fourier transform techniques are used to reduce the problem to the solution of Hilbert singular integral equation, the latter is solved by Lobotto-Chebyshev and Gauss integral equation, at last, numerical results showed the effect of the frequency of wave, sizes and so on upon the normalized stress intensity factor.

Shear horizontal (SH) waves propagating in piezoelectric–piezomagnetic bilayer system with an imperfect interface

2012 ◽  
Vol 223 (9) ◽  
pp. 1999-2009 ◽  
Author(s):  
Guoquan Nie ◽  
Jinxi Liu ◽  
Xueqian Fang ◽  
Zijun An
Keyword(s):  
Imperfect Interface ◽  
Sh Waves ◽  
Bilayer System ◽  
Shear Horizontal

scholarly journals Extension of the Chebyshev Method of Quassi-Linear Parabolic P.D.E.S With Mixed Boundary Conditions

2009 ◽  
Vol 6 (3) ◽  
pp. 603-611
Author(s):  
Baghdad Science Journal
Keyword(s):  
Error Analysis ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Linear Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Numerical Examples ◽  
Chebyshev Method

The researcher [1-10] proposed a method for computing the numerical solution to quasi-linear parabolic p.d.e.s using a Chebyshev method. The purpose of this paper is to extend the method to problems with mixed boundary conditions. An error analysis for the linear problem is given and a global element Chebyshev method is described. A comparison of various chebyshev methods is made by applying them to two-point eigenproblems. It is shown by analysis and numerical examples that the approach used to derive the generalized Chebyshev method is comparable, in terms of the accuracy obtained, with existing Chebyshev methods.

Parameter Estimation for an Imperfectly Clamped Plate: Numerical Examples

1995 ◽  
Author(s):  
H. T. Banks ◽  
R. C. Smith ◽  
Yun Wang
Keyword(s):  
Parameter Estimation ◽  
Boundary Conditions ◽  
Circular Plate ◽  
Simple Zero ◽  
Numerical Examples ◽  
Vibrating Structures ◽  
Physical Experiments ◽  
Slight Rotation ◽  
Physical Manifestation ◽  
Clamped Edges

Abstract The problems associated with maintaining truly fixed (zero displacement and slope) or simple (zero displacement and moment) boundary conditions in applications involving vibrating structures have led to the development of models which admit slight rotation and displacement at the boundaries. In this paper, numerical examples demonstrating the dynamics of a model for a circular plate with imperfectly clamped boundary conditions are presented. The latitude gained when using the model for estimating parameters through fit-to-data techniques is also demonstrated. Through these examples, the manner in which the model accounts for the physical manifestation of imperfectly clamped edges is illustrated, and issues regarding the use of the model in physical experiments are defined.

Immunity of the second harmonic shear horizontal waves to adhesive nonlinearity for breathing crack detection

2021 ◽  
pp. 147592172110571
Author(s):  
Fuzhen Wen ◽  
Shengbo Shan ◽  
Li Cheng
Keyword(s):  
Crack Detection ◽  
Guided Waves ◽  
Lamb Waves ◽  
Second Harmonic ◽  
Sh Waves ◽  
High Order Harmonic ◽  
Thin Walled Structures ◽  
Harmonic Shear ◽  
Contact Acoustic Nonlinearity ◽  
Shear Horizontal

High-order harmonic guided waves are sensitive to micro-scale damage in thin-walled structures, thus, conducive to its early detection. In typical autonomous structural health monitoring (SHM) systems activated by surface-bonded piezoelectric wafer transducers, adhesive nonlinearity (AN) is a non-negligible adverse nonlinear source that can overwhelm the damage-induced nonlinear signals and jeopardize the diagnosis if not adequately mitigated. This paper first establishes that the second harmonic shear horizontal (second SH) waves are immune to AN while exhibiting strong sensitivity to cracks in a plate. Capitalizing on this feature, the feasibility of using second SH waves for crack detection is investigated. Finite element (FE) simulations are conducted to shed light on the physical mechanism governing the second SH wave generation and their interaction with the contact acoustic nonlinearity (CAN). Theoretical and numerical results are validated by experiments in which the level of the AN is tactically adjusted. Results show that the commonly used second harmonic S0 (second S0) mode Lamb waves are prone to AN variation. By contrast, the second SH0 waves show high robustness to the same degree of AN changes while preserving a reasonable sensitivity to breathing cracks, demonstrating their superiority for SHM applications.

Interface Conditions for Coupled Atomistic and Continuum Models of Solids for Dynamics Problems at Finite Temperature

2006 ◽  
Vol 978 ◽  
Author(s):  
Xiantao Li ◽  
Weinan E
Keyword(s):  
Molecular Dynamics ◽  
Boundary Conditions ◽  
Finite Temperature ◽  
Langevin Equations ◽  
Continuum Models ◽  
Interface Conditions ◽  
System Temperature ◽  
Dynamics Simulations ◽  
Dynamics Problems ◽  
Generalized Langevin Equations

AbstractWe will present a general formalism for deriving boundary conditions for molecular dynamics simulations of crystalline solids in the context of atomistic/continuum coupling. These boundary conditions are modeled by generalized Langevin equations, derived from Mori-Zwanzig's formalism. Such boundary conditions are useful in suppressing phonon reflections, and maintaining the system temperature.

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