First natural frequency of the backplate and launch loads

Flexural rigidity of the 1.6 mm sliding interface, Miles’ equation under GEVS random vibration and the 100 Hz stiffness rule

Author: nadir lab.
Published: 19 October 2026
Reading time: 3 min
Level: Engineering
Tags: Backplate
Structural dynamics
Natural frequency
Random vibration
GEVS
PocketQube

Abstract

Unlike a CubeSat held along four corner rails, a PocketQube is cantilevered in its deployer by a single 1.6 mm thick sliding backplate. We derive the plate's flexural rigidity and fundamental modal frequency across Al 6061-T6, Al 7075-T73, Ti-6Al-4V and FR-4, and evaluate 3σ dynamic deflection under GSFC-STD-7000B (GEVS) random vibration.

Contents

The 1.6 mm sliding backplate constraint#

Issue 1 of the fixes the mechanical interface between spacecraft and deployer as a $58 mm$ wide and $1.6 mm$ thick, overhanging the $50 mm$ body by $4 mm$ along each guide rail[1]. Because thickness $h = 1.6 mm$ is fixed by the slot geometry of and PicoBus deployers, bending stiffness cannot be increased by thickening the flange; it depends solely on the material's Young's modulus $E$ and Poisson ratio $ν$ [2]:

D = \frac{E h ^{3}}{12 ( 1 - ν ^{2} )}

Solid 1P backplate, 58 × 64 × 1.6 mm (5.94 cm³), in candidate materials

Material	Mass (g)	Share of 250 g	Flexural rigidity D (N·m)	D ÷ D of 6061-T6	Stiffness index E^(1/3)/ρ
FR-4, in plane	11.0	4.4%	7.6	0.29	1.51
Mg AZ31B-H24	10.5	4.2%	17.5	0.66	2.01
Al 6061-T6	16.0	6.4%	26.4	1.00	1.52
Al 7075-T73	16.7	6.7%	27.6	1.04	1.48
Ti-6Al-4V, annealed	26.3	10.5%	44.0	1.67	1.09
17-7PH, TH1050	45.4	18.2%	75.6	2.86	0.77

D = E t³ / [12 (1 − ν²)] with ν = 0.12 (FR-4), 0.35 (AZ31B), 0.33 (aluminium), 0.342 (Ti-6Al-4V) and 0.28 (17-7PH). Magnesium falls under the flammability clause PQ-Gen-03.

Fundamental frequency and Miles’ equation#

For a plate of effective span $a \times b$ and effective areal mass density $ρ_{eff}$ (plate mass plus the participating fraction of the internal PCB stack), the fundamental natural frequency $f_{1}$ and the root-mean-square acceleration $G_{rms}$ under a flat power spectral density $W_{PSD}$ (Miles' single-degree-of-freedom approximation, GSFC-STD-7000B qualification level $14.1 G_{rms}$ [3]) are:

f_{1} = \frac{λ _{1}^{2}}{2 π a ^{2}} \frac{D}{ρ _{eff}}, G_{rms} = \frac{π}{2} f_{1} Q W_{PSD}, z_{3 σ} = \frac{3 G _{rms} g _{0}}{( 2 π f _{1} ) ^{2}}

Launch providers require $f_{1} \geq 100 Hz$ (and preferably $> 200 Hz$ at subsystem level) to prevent dynamic coupling with launch-vehicle low-frequency transients and to keep $3 σ$ board deflection below the $4 mm$ internal keep-out margin. Note also that under -Q-ST-70-36C, Al 7075-T6 has low resistance to stress-corrosion cracking () in the short transverse direction; over-aged temper 7075-T73 / T7351 or 6061-T6 is preferred for flight rails and backplates[4].

1P PocketQube structural backplate (50 × 50 mm, 38 g attached board mass): first bending mode f₁ and 14.1 G_rms 3σ deflection

Backplate material	Thickness (mm)	Plate mass (g)	Fundamental mode f₁ (Hz)	3σ peak deflection (mm)	GEVS / Falcon 9 margin
Al 6061-T6	1.6	10.8	2,449	0.002	PASS (> 200 Hz)
Al 7075-T6	1.6	11.2	2,478	0.002	PASS (> 200 Hz)
Al 7075-T6	2.0	14.1	3,297	0.001	PASS (> 200 Hz)
FR-4 / Copper laminate	1.6	7.6	1,410	0.005	PASS (> 200 Hz)
Ti-6Al-4V	1.2	13.3	1,963	0.003	PASS (> 200 Hz)

Explore how form factor ( $1 P$ to $3 P$ ), alloy selection and board mass shift $f_{1}$ and $3 σ$ deflection:

1P PocketQube structural backplate (50 × 50 mm, 38 g attached board mass): first bending mode f₁ and 14.1 G_rms 3σ deflection

Backplate material	Thickness (mm)	Plate mass (g)	Fundamental mode f₁ (Hz)	3σ peak deflection (mm)	GEVS / Falcon 9 margin
Al 6061-T6	1.6	10.8	2,449	0.002	PASS (> 200 Hz)
Al 7075-T6	1.6	11.2	2,478	0.002	PASS (> 200 Hz)
Al 7075-T6	2.0	14.1	3,297	0.001	PASS (> 200 Hz)
FR-4 / Copper laminate	1.6	7.6	1,410	0.005	PASS (> 200 Hz)
Ti-6Al-4V	1.2	13.3	1,963	0.003	PASS (> 200 Hz)

The 1.6 mm sliding backplate constraint#

Fundamental frequency and Miles’ equation#

Interactive backplate modal calculator#