For example, the generalized force generated by an ffs shaker at the fundamental structural frequency for a simply supported beam is given by 1.65 P r/l where P is the high frequency out of balance force, r is the throw amplitude and l is the beam length.
A total of 100 samples of the time histories of the generalized force are generated using spectral representation method [9].
This method uses the molecular dynamics method of a generalized force model as a generation scheme to produce a microstructure with a pattern combining a variable aspect ratio and a variable microstructure orientation.
Lagrange-Euler formulation is used to derive the system dynamic model using the following n-coordinates dynamic equations: frac{text{d}}{{{text{d}}t}}left( {frac{partial L}{{partial dot{q}_{i} }}} right) - frac{partial L}{{partial q_{i} }} = Q_{i},quad i = 1,2, ldots,n (1 where ( Q_{i} ) is generalized force vector and q i is generalized coordinate vector.
If ri is a generalized coordinate (say, an angular displacement of a rigid body), then Fi is the generalized force such that Fi dri is the work done (for an angular displacement, Fi is a component of torque).
To express the principle, label the generalized coordinates r1, r2,..., ri,.... Then if Fi is the net component of generalized force acting along the coordinate ri, Here, Fi dri is the work done when the generalized coordinate is changed by the infinitesimal amount dri.
Generalized force vector.
On the basis of spectrum analysis of the time-history of the generalized force, the dominant frequency of the generalized force and its magnitude can be obtained.
The generalized mass matrix M s and the generalized force vector h s are given as.
F ct is the generalized force applied on the contact point of the rail surface.
where M s is a generalized mass matrix and h s is a generalized force vector.
