A new paper from Hamburg University of Applied Sciences proposes an elegantly simple field method — add mass, watch the resonance shift — to quantify how structurally integrated a battery pack is in a vehicle. The modal mass estimate at its core draws on a pair of Vibrationdata tutorials.
It is always a pleasure to see the Vibrationdata tutorials put to work in new research. Plaumann, Hein, Chodvadiya, and Knorr of HAW Hamburg presented “A key indicator for integral vs differential design of battery packs in battery electric vehicles under structural dynamic loads” at the DESIGN 2026 conference, published open-access in the Proceedings of the Design Society. Their modal mass participation estimate cites my beam bending frequencies tutorial and my Modal Participation Factor paper — the same material behind the recent effective modal mass post on this blog. This post summarizes what they did and why it matters for anyone concerned with battery pack vibration testing.
The Design Question: Integral or Differential?
The battery pack is typically the heaviest and most expensive single component of a battery electric vehicle, and its reliability under road-induced vibration and shock is central to safety and resale value. Vibration-related mechanisms — loosened connections at every level from cell to pack, structural fatigue, rattling, deflection-driven contact changes, and seal deterioration that invites corrosion — contribute to a large share of battery faults, which the authors note are dominated by internal and external short circuits.
Pack architecture faces a fundamental fork in the road. A differential design groups cells into mechanical modules within the pack: heavier and bulkier, but repairable module-by-module, with the module structure partially decoupling the cells from road loads. An integral design integrates cells directly into the pack structure — or, in the limiting case, glues them into the vehicle body itself: lighter, cheaper, more volume for active cell material, and better efficiency, but often unrepairable and scrapped whole after a serious fault, with the cells more directly exposed to structural loads. The market currently spans this spectrum. The authors compare three packs of similar energy: a Tesla Model 3 Performance with 4416 small cylindrical cells loosely grouped in four clusters, a VW ID.Buzz with 288 pouch cells rigidly bonded inside twelve very stiff module housings, and a BYD design with 120–160 large blade cells needing no module structure at all. Counting cells, modules, or interfaces gives conflicting answers about which is “more integrated” — which is precisely the problem.
The test standard ISO 19453-6 recognizes the dynamic consequence: its categories run from small packs mounted at discrete points, where the vehicle body stiffness barely matters, up to large-area-mounted packs where body deformations transfer directly into the battery and the pack may itself be part of the load-carrying structure. For that highest category, the pack’s dynamic behavior cannot be separated from the vehicle it sits in — and a laboratory shaker test must somehow represent that coupling.
The Method: Add Mass, Watch the Resonance Move
HAW Hamburg has instrumented nine different BEVs and collected hundreds of road load measurements. The difficulty is that OEMs share little design information, so the researchers needed a way to assess pack-to-vehicle coupling purely from post-production measurements — without fifty accelerometers and a full transfer path analysis campaign.
Their solution rests on the most familiar relation in our field. For a resonant mode,
$$ f_n \propto \sqrt{k/m} $$
If mass is added to a vibrating system, its resonance frequency drops; if the added mass is not coupled to the mode, nothing happens. So the team measures the pack’s first global bending mode on the road, then repeats the runs with roughly 200 kg of sandbags spread on the vehicle floor above the pack. A strongly integrated pack — one whose bending mode engages the floor structure carrying the sandbags — shows a clear frequency drop. A loosely coupled pack shrugs the sandbags off.
Quantifying the drop requires knowing how much mass participates in the bending mode in the first place. Not all of the pack vibrates in a bending shape — the supported edges barely move while the center moves most. This is the modal mass participation concept, and the authors estimate a participation factor of about \( p = 80\% \) for the first bending mode of an edge-supported pack, citing the Vibrationdata beam frequency and modal participation factor references:
$$ m_{vibrating} = p \, m_{pack} $$
A 500 kg pack thus carries roughly 400 kg of effective vibrating mass in the mode. The coupling factor \( c \) — the fraction of the added mass that actually joins the vibrating system — then follows from the measured frequency change factor, with stiffness assumed unchanged:
$$ c = \left( \frac{m_{vibrating}}{f_{change}^{\,2}} – m_{vibrating} \right) \Big/ \, m_{added} $$
The sensitivity is illustrative: with 400 kg vibrating and 200 kg added, a mere 1% frequency drop corresponds to about 8 kg of the sandbags coupling in (c ≈ 4%), while a 5% drop corresponds to about 41 kg (c ≈ 20%). Small, easily measurable frequency shifts resolve meaningful differences in structural coupling. Where peak-matching between the loaded and unloaded spectra is ambiguous, the Modal Assurance Criterion sorts out which mode is which — though for the few-hertz shifts observed here, nearest-frequency matching sufficed.
Results and Why They Matter
Applying the indicator across their fleet, the authors found the larger, heavier packs — the Tesla Model 3 Performance and the VW ID.Buzz with their largest battery variants — showed the higher coupling factors, marking them as representative of more highly integrated designs. This ran against initial intuition (a larger vibrating span might be expected to move more freely) but is consistent with those designs’ numerous stiff fixation points connecting rigid module structures to the floor. A smaller pack like the Opel Corsa E’s, fixed mainly at its outer frame, showed weaker coupling of its vibrating center.
The payoff is in test method development. Industry trends point toward ever more integral packs, but you cannot buy a future vehicle to measure today. With a quantitative coupling indicator, the existing measurement database can be clustered by integration level, the highly integrated vehicles weighted more heavily, and trends extrapolated — so that tomorrow’s vibration test specifications reflect tomorrow’s architectures rather than the average of yesterday’s. The authors are candid about the limitations: integration is more than rigid connection, a product can be integral at one architectural level and differential at another, and the indicator is deliberately a coarse, global measure for use when design-phase details are unavailable.
KEY POINT: The added-mass resonance shift is a wonderfully economical diagnostic: one extra test condition (sandbags on the floor) converts an ordinary road load measurement into a quantitative measure of pack-to-vehicle structural coupling. The physics is nothing more than \( f \propto \sqrt{k/m} \) plus a modal mass participation estimate — a reminder that the fundamentals, applied cleverly, still solve modern problems.
Related Vibrationdata Posts
Lithium Battery Vibration Hazard — on lithium battery vibration sensitivities, transportation vibration test requirements, and the UPS Flight 6 cargo fire investigation: https://blog.vibrationdata.com/2013/08/08/lithium-battery-vibration-hazard/
Surface Ship Shock, SRS, DDAM, MIL-DTL-901, UNDEX — including underwater explosion shock effects on submerged components such as batteries: https://blog.vibrationdata.com/2026/07/07/surface-ship-shock-srs-ddam-mil-dtl-901-undex/
MV Tacoma Ferry Vibration — vibration measurements aboard a Jumbo Mark II diesel-electric ferry, a vessel class relevant to hybrid-electric battery conversion: https://blog.vibrationdata.com/2021/09/07/mv-tacoma-ferry-vibration/
Effective Modal Mass & Modal Participation Factors (Revision K) — the unified formulation for base-excited and force-excited systems that underlies the participation factor estimate used in this paper: https://www.researchgate.net/publication/400560090_EFFECTIVE_MODAL_MASS_MODAL_PARTICIPATION_FACTORS_Revision_K
References
B. Plaumann, E. Hein, A. Chodvadiya, and M. Knorr, “A key indicator for integral vs differential design of battery packs in battery electric vehicles under structural dynamic loads,” Proceedings of the Design Society, Vol. 6 (DESIGN 2026), pp. 757–766. DOI: 10.1017/pds.2026.10434 (open access): Cambridge Core article page
T. Irvine, “Bending Frequencies of Beams, Rods and Pipes,” Revision S, vibrationdata.com, 2012.
T. Irvine, “Effective Modal Mass and Modal Participation Factors,” Revision K: ResearchGate link (originally published at vibrationdata.com, 2012, as cited by Plaumann et al.).
ISO 19453-6, Road Vehicles — Environmental Conditions and Testing for Electrical and Electronic Equipment — Part 6: Traction Battery Packs and Systems, 2020.
J. M. Hooper and J. Marco, “Characterising the in-vehicle vibration inputs to the high voltage battery of an electric vehicle,” Journal of Power Sources, Vol. 245, pp. 510–519, 2014.
T. Heinzen, B. Plaumann, and M. Kaatz, “Influences on Vibration Load Testing Levels for BEV Automotive Battery Packs,” Vehicles, Vol. 5(2), pp. 446–463, 2023.
R. J. Allemang, “The Modal Assurance Criterion — Twenty Years of Use and Abuse,” Sound and Vibration, 2003.
T. Irvine, Vibrationdata publications & free ebooks: https://blog.vibrationdata.com/2025/11/27/toms-ebooks/