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The term Sv(x, f) represents the virtual displacement, which can be written in terms of the generalized coordinates and mode shapes as

;=i where <5£,(f) is an arbitrary increment in the ,'th generalized coordinate. Thus, the virtual work becomes

Identifying the generalized force as

S/(f) = / F(x, t )4>i(x) dx J o one finds that the virtual work reduces to oo

The loading F(x, f ) in the above development is a distributed load with units of force per unit length. If instead this loading is concentrated at one or more points, say as Fc(t) with units of force acting at x — xc as shown in Fig. 2.8, then its functional representation must include the Dirac delta function, <)(x — xr), which is similar to the impulse function in the time domain. In this case the distributed load can be written as

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