Wave Propagation in Smart Materials: Linear Elasticity

Michael Pedersen

Wave Propagation in Smart Materials: Linear Elasticity

Michael Pedersen

Research output: Contribution to journal › Journal article › Research

Abstract

In this paper we deal with the behavior of solutions to hyperbolicequations such as the wave equation:\begin{equation}\label{waveeq1}\frac{\partial^2}{\partial t^2}u-\Delta u=f,\end{equation}or the equations of linear elasticity for an isotropic medium:\begin{equation}\label{elasteq1}\frac{\partial^2}{\partial t^2}u -(\lambda+\mu){\text{\rm grad div}} u -\mu\Deltau=0,\end{equation}where $u=u(t,x)$ denotes a 3-vector field on $\Bbb R\times\Bbb R^3$,and $\lambda$ and $\mu$ are the Lame-constants.

Original language	English
Book series	Mat Report
Issue number	23
Publication status	Published - 1999

OpenUrl availability

Full text

Cite this

@article{9938d565916a4e26abba9c01f97137f4,

title = "Wave Propagation in Smart Materials: Linear Elasticity",

abstract = "In this paper we deal with the behavior of solutions to hyperbolicequations such as the wave equation:\textbackslash{}begin\{equation\}\textbackslash{}label\{waveeq1\}\textbackslash{}frac\{\textbackslash{}partial\textasciicircum{}2\}\{\textbackslash{}partial t\textasciicircum{}2\}u-\textbackslash{}Delta u=f,\textbackslash{}end\{equation\}or the equations of linear elasticity for an isotropic medium:\textbackslash{}begin\{equation\}\textbackslash{}label\{elasteq1\}\textbackslash{}frac\{\textbackslash{}partial\textasciicircum{}2\}\{\textbackslash{}partial t\textasciicircum{}2\}u -(\textbackslash{}lambda+\textbackslash{}mu)\{\textbackslash{}text\{\textbackslash{}rm grad div\}\} u -\textbackslash{}mu\textbackslash{}Deltau=0,\textbackslash{}end\{equation\}where \$u=u(t,x)\$ denotes a 3-vector field on \$\textbackslash{}Bbb R\textbackslash{}times\textbackslash{}Bbb R\textasciicircum{}3\$,and \$\textbackslash{}lambda\$ and \$\textbackslash{}mu\$ are the Lame-constants.",

author = "Michael Pedersen",

year = "1999",

language = "English",

journal = "Mat Report",

number = "23",

}

TY - JOUR

T1 - Wave Propagation in Smart Materials

T2 - Linear Elasticity

AU - Pedersen, Michael

PY - 1999

Y1 - 1999

N2 - In this paper we deal with the behavior of solutions to hyperbolicequations such as the wave equation:\begin{equation}\label{waveeq1}\frac{\partial^2}{\partial t^2}u-\Delta u=f,\end{equation}or the equations of linear elasticity for an isotropic medium:\begin{equation}\label{elasteq1}\frac{\partial^2}{\partial t^2}u -(\lambda+\mu){\text{\rm grad div}} u -\mu\Deltau=0,\end{equation}where $u=u(t,x)$ denotes a 3-vector field on $\Bbb R\times\Bbb R^3$,and $\lambda$ and $\mu$ are the Lame-constants.

AB - In this paper we deal with the behavior of solutions to hyperbolicequations such as the wave equation:\begin{equation}\label{waveeq1}\frac{\partial^2}{\partial t^2}u-\Delta u=f,\end{equation}or the equations of linear elasticity for an isotropic medium:\begin{equation}\label{elasteq1}\frac{\partial^2}{\partial t^2}u -(\lambda+\mu){\text{\rm grad div}} u -\mu\Deltau=0,\end{equation}where $u=u(t,x)$ denotes a 3-vector field on $\Bbb R\times\Bbb R^3$,and $\lambda$ and $\mu$ are the Lame-constants.