Table 1 List of notations and symbols
No. | Notations or symbols | Description | Locations |
|---|---|---|---|
1. | \(\times\) | The cross product of two vectors in R\(^3\).For two vectors in R\(^2\), the result of this product is a scalar as follows: give \(\mathbf{a }= \left[ {a}_\mathrm{1} \;\; {a}_\mathrm{2} \right] ^\text {T}\), \(\mathbf{b }= \left[ {b}_{1} \;\; {b}_{2} \right] ^{\rm T}\); then: \(\mathbf{a }\times \mathbf{b }= \left| \begin{array}{cc} {a}_{1} & {a}_{2}\\ {b}_{1}& {b}_{2} \end{array} \right| ={a}_{1}{b}_{2}-{a}_{2}{b}_{1}\) | |
2. | \({n}\) | Number of global motion DoFs of the top plate | |
3. | Subscripts: | ||
\(_{Ld}\) | Denote component belongs to DAM | ||
\(_{Lv}\) | Denote component belongs to VCM | ||
\(_{{N}_{D}}\) | Number of DAM with VCM | ||
\(_{{N}_{V}}\) | Number of DAM without VCM | ||
\({k}\) | Ordering number of DAM without VCM contains in DAM with VCM | ||
4. | \({\mathbf{W}}_{{Gi}}\) | Matrix of global motion from DAM without VCM | Eq. (23) |
5. | \({\mathbf{W}}_{{GV}_{m}}\) | Matrix of global motion from DAM with VCM | Eq. (23) |
6. | \({\mathbf{S}}_{{AC}}\), \({\mathbf{S}}_{{PC}}\) | Active and passive constraint space | Eq. (26) |
7. | \(\varvec{\alpha }\) | Coefficient matrix | |
8. | \({\mathbf{C}}\) | Constraint matrix | |
9. | \({\mathbf{C}}_{P}\) | Producible global velocity matrix | |
10. | \({\mathbf{W}}_{{CVC}}\) | Matrix of resultant force on the top plate in the constraint space |