186 lines
2.7 KiB
Markdown
186 lines
2.7 KiB
Markdown
---
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title: "Damping matrix"
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chunk: 1/1
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source: "https://en.wikipedia.org/wiki/Damping_matrix"
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category: "reference"
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tags: "science, encyclopedia"
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date_saved: "2026-05-05T11:46:56.497350+00:00"
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instance: "kb-cron"
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---
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In applied mathematics, a damping matrix is a matrix corresponding to any of certain systems of linear ordinary differential equations. A damping matrix is defined as follows. If the system has n degrees of freedom un and is under application of m damping forces. Each force can be expressed as follows:
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f
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D
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c
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1
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u
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1
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+
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c
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⋯
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c
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u
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∑
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j
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=
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c
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,
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j
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u
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{\displaystyle f_{Di}=c_{i1}{\dot {u_{1}}}+c_{i2}{\dot {u_{2}}}+\cdots +c_{in}{\dot {u_{n}}}=\sum _{j=1}^{n}c_{i,j}{\dot {u_{j}}}}
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It yields in matrix form;
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F
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D
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C
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U
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{\displaystyle F_{D}=C{\dot {U}}}
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where C is the damping matrix composed by the damping coefficients:
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C
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=
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(
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c
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i
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,
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j
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)
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1
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≤
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i
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≤
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n
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,
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1
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≤
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j
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≤
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m
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{\displaystyle C=(c_{i,j})_{1\leq i\leq n,1\leq j\leq m}} |