Hi

There are straightforward ways of determining the data you want if you are able to manufacture a beam with simple cross section, e.g circular or rectangular, and have good control over the test object dimensions.

You can use impiulse measurement (force intrumented hammer + accelerometer) and measure so called Frequency Response Functions (acceleration/force, FRFs).

If you are on a tight budget, you can use just the accelerometer and impact the beam and take a FFT of the output signals.

The above will tell you the resonance frequencies of your specimen.

You can use hand calculation or FE models with good accuracy when you suspend the test object with free-free conditions (you should use steel wires and short mechanical springs to do so and ascertain that all 6 rigid body modes have a natural frequency 1/10 or lower than you first flexible mode).

The trick in getting accurate material data lies in making your test boundary conditions well and in controlling the geometry of the test object.

Poisson's ratio will matter if you make your test object thick. Resonance frequencies and simulation models can then help you work out the Poisson's ratio. 

Direct measurement of Poisson's ratio can otherwise be determined using strain gauges. Measure FRFs for strain in two perpendicular directions for a straight beam.

Sincerely

Claes