Материал из Department of Theoretical and Applied Mechanics
|
|
| Строка 1: |
Строка 1: |
| − | [[Department of TM]] > [[Project "Termokristall"]] > [[Fluctuations in energy in the one-dimensional crystal with a substrate]] <HR>
| |
| − | [[Virtual Laboratory]] > [[Fluctuations in energy in the one-dimensional crystal with a substrate]] <HR>
| |
| − | <math>
| |
| − | \def\be#1{\begin{equation}\label{#1}}
| |
| − | \def\ee{\end{equation}}
| |
| − | \def\({\left(}
| |
| − | \def\){\right)}
| |
| − | \let\eps=\varepsilon
| |
| − | \let\w=\omega
| |
| − | \let\al=\alpha
| |
| − | \renewcommand {\=}{\mathrel{\stackrel{\rm def}=}}
| |
| − | </math>
| |
| − | Examines the chain consisting of identical masses <math>m</math>, connected by springs stiffness <math>C_0</math>. The chain is on an elastic foundation stiffness <math>C_1</math>. Then the equation of the dynamics of the chain of particles is of the form:
| |
| − | ::<math>
| |
| − | \be{1Delta}
| |
| − | \ddot{u}_n
| |
| − | =\(\w^2_0 \Delta^2_n-\w^2_1\) u_n
| |
| − | ,\qquad
| |
| − | \w_0\=\sqrt{C_0/m}
| |
| − | ,\qquad
| |
| − | \w_1\=\sqrt{C_1/m}
| |
| − | ,\ee
| |
| − | </math>
| |
| − | where <math>u_n</math> — moving the <math>n</math>-th particle;
| |
| − | <math>\Delta^2_n</math> — difference operator of second order:
| |
| − | ::<math>
| |
| − | \be{delta2}
| |
| − | \Delta^2_n u_n \= u_{n-1}-2u_{n}+u_{n+1},
| |
| − | \ee
| |
| − | </math>
| |
| − | <math>n</math> — an index that takes arbitrary integer.
| |
| | | | |
| − | {{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Equations/Equation_substrate_5.1%20release_stand/Equations.html |width=840 |height=800 |border=0 }}
| |
| − |
| |
| − | Developers: [[Tsvetkov Denis]], [[Krivtsov Anton]]
| |
| − |
| |
| − |
| |
| − |
| |
| − | [[Category: Virtual Laboratory]]
| |
| − | [[Category: Programming]]
| |
| − | [[Category: Project "Termokristall"]]
| |
Текущая версия на 20:54, 3 июня 2016
