Remarks on Nodal Method

 

a) The terms of an element connected to a node 'χ' and stationary surface (reference) is,

Fig1(a)

 b) The term of an element between the two nodes 'χ ₁' and 'χ ₂' i.e. between two moving surfaces is,

Fig1(b)

       No mass can be between the two nodes as due to mass there cannot be change in force as mass cannot  store potential energy.

c) All elements which are under the influence of same displacement get connected in parallel under that node indicating the corresponding displacement .

      e.g. consider the part of the system, shown in the Fig2(a).

     Here M, B and K all are under the influence of χ(t). Hence in equivalent system all of them will get  connected in parallel under the node 'χ'. Consider another example of the system shown in the Fig.3. In this system M₁, B₁ and K₁ all are under the influence of displacement χ1. This is because all are connected to rigid support

Fig.3

      While there is  change from χ ₁ to χ ₂ due to simultaneous effect of B₂ and K₂. So B₂ and K₂ are under the influence of (χ ₁- χ ₂). But mass M2 is under the influence of χ ₂ alone. Mass cannot under be the influence of difference between displacement s. So in equivalent system the elements B₁, k₁ and M₁, all in parallel under χ ₁ while B₂ and K2 in parallel between χ ₁ and χ ₂ and element M2 is under node χ ₂ as shown in the Fig.3(a).

Fig.3(a)