In the calculation of lighting columns, you must take dynamic behaviour
into account. It's done by a factor on the wind loads, that depends on the
period of vibration of the column.
The European EN 40 standard committee says this period must lie
between 0 and 3.5 seconds.

the standard: " ... factor .... takes into account the increase in the load resulting from the dynamic behaviour of the lighting column cause by wind gusts".

Now, when I calculate the period of vibration of a 6 meter pole-with- bracket by means of matrix method (eigenvalue problem with distributed mass matrix) I get LOWEST eigenvalues that result in maximum periods of vibration way higher than 3.5 seconds, and a load factor that is unacceptably high (and not in line with experience).

The questions: Which eigenvalue should I use to determin the period of vibration ? (A column has A LOT of eigenfrequencies...) How should the relation with "wind gusts" be interpreted ?

Here is the array of typical eigenvalues from my calculation: array(24) { [1]=> float(1.81673652086) [2]=> float(1.82377482274) [3]=> float(41.8565929569) [4]=> float(43.8413395721) [5]=> float(138.031662251) [6]=> float(233.428272113) [7]=> float(519.636228268) [8]=> float(710.793797493) [9]=> float(2776.57589519) [10]=> float(4218.21507698) [11]=> float(8078.78449371) [12]=> float(9531.15538271) [13]=> float(11888.6098069) [14]=> float(18685.6311882) [15]=> float(24678.9208868) [16]=> float(25294.8476091) [17]=> float(40684.7831304) [18]=> float(73070.7945844) [19]=> float(83898.8774131) [20]=> float(95870.9738707) [21]=> float(137719.85692) [22]=> float(277530.743338) [23]=> float(368154.480533) [24]=> float(633315.738033) }

(So the eigenfrequencies in rad/s are the sqrt from these values.)

the standard: " ... factor .... takes into account the increase in the load resulting from the dynamic behaviour of the lighting column cause by wind gusts".

Now, when I calculate the period of vibration of a 6 meter pole-with- bracket by means of matrix method (eigenvalue problem with distributed mass matrix) I get LOWEST eigenvalues that result in maximum periods of vibration way higher than 3.5 seconds, and a load factor that is unacceptably high (and not in line with experience).

The questions: Which eigenvalue should I use to determin the period of vibration ? (A column has A LOT of eigenfrequencies...) How should the relation with "wind gusts" be interpreted ?

Here is the array of typical eigenvalues from my calculation: array(24) { [1]=> float(1.81673652086) [2]=> float(1.82377482274) [3]=> float(41.8565929569) [4]=> float(43.8413395721) [5]=> float(138.031662251) [6]=> float(233.428272113) [7]=> float(519.636228268) [8]=> float(710.793797493) [9]=> float(2776.57589519) [10]=> float(4218.21507698) [11]=> float(8078.78449371) [12]=> float(9531.15538271) [13]=> float(11888.6098069) [14]=> float(18685.6311882) [15]=> float(24678.9208868) [16]=> float(25294.8476091) [17]=> float(40684.7831304) [18]=> float(73070.7945844) [19]=> float(83898.8774131) [20]=> float(95870.9738707) [21]=> float(137719.85692) [22]=> float(277530.743338) [23]=> float(368154.480533) [24]=> float(633315.738033) }

(So the eigenfrequencies in rad/s are the sqrt from these values.)