Yes, you need to independently measure the force to be able to construct the FRF

It might be possible to try the following (open to corrections)

1. Obtain the acceleration vs time from computed response

 of a model of the beam ..(hopefully a linear response..).else number

of outputs ..

2. Use FFT to obtain frequency response of above viz 1. and plot Force

 vs Freq .

3. Compare with measured result...

4. For improved results perhaps Kalman filter applied to m/s error and

  statistical  result for perturbed input around estimated operating point may be

useful..

 Cheers

When the system you are dealing with is known, the FRF can be directly calculated from mass, stiffness and damping matrices, according to the classical formulation of the dynamic problem. Whereas if the system is unknown, the FRF can be computed from vibration measurements, but this implies not only the measurement of the response, but also the measurement of the excitation force. I hope it to be useful.  

In case modeling is not possible ..it is still interesting to figure a method

of finding the force function from the response measured by the accelerometer.

It might be possible to attach a known simple system to the end of the

cantilever (perhaps a spring-mass system ) and with responses from both systems

it is probable that the force function can be worked out..

Cheers

 One application of a vibrator motor is to generate a sinusoidally varying

force ( a vibrator motor has symmetrical  eccentric weights attached to the shaft )

which generates a good sinusoidal Force with known amplitude.Frequency can be varied with an inverter. So with known applied force and measured output

response .. we obtain the frequency response of the system as we vary

the frequency. This should work whether the system is known or unknown.

Cheers

Since you are using only a 3-channel accelerometer, I suppose the cantilever beam is not that big. In this case, making use of an impact hammer is the best and simplest solution. Instead, if you need to generate a force in a certain frequency-bandwidth in order to capture only determined modes of your system, then you can a vibrator motor.