Research theme one of five
Structural and ensemble dynamics
What happens to the dynamics of a structure when its properties are known only as a distribution, and what an average over many nominally identical structures actually measures.
The problem
A population of nominally identical structures shows higher apparent damping than any individual unit. This is observed routinely in aerospace and automotive testing and is usually absorbed into an empirical damping factor. The energy stays in the system. It is the mean of an ensemble losing amplitude because the realisations drift out of phase.
Made precise, the effect has a closed form. For an undamped oscillator whose natural frequency is Gaussian with standard deviation sigma, the envelope of the mean response is Gaussian in time, so the equivalent viscous damping ratio grows linearly with time, and the characteristic phase decoherence time is tau = sqrt(2)/sigma. Calling the effect damping describes the consequence and hides the mechanism.
Why it matters
Certification is granted to a fleet, and testing is done on one article. A damping value measured on a single prototype transfers to the fleet only once the excess seen across a population is attributed to the right mechanism. Attribute it to dissipation and the model is tuned to a mechanism borrowed from elsewhere, so it holds for that build and drifts as soon as the design changes. Attribute it to loss of coherence and the excess follows from the parameter dispersion the process already reports, which makes it predictable at the design stage. That is the difference between an empirical damping factor carried forward by habit and a number an engineer can defend.
Current frontier
- ensemble dynamics and ensemble damping
- phase decoherence and its characteristic timescale
- stochastic modal dynamics and random eigenproblems
- damped localisation in disordered chains
- stochastic Green functions
- random spectra and level repulsion
- mode veering and mode mixing under uncertainty
- nonlinear ensemble behaviour
Signature concepts
- coherence
- decoherence
- ensemble attenuation
- localisation
- emergent temporal nonlocality
Open problems
- At what parameter dispersion does an ensemble stop being usefully described by its mean?
- How do decoherence and physical dissipation combine when both are present?
- What is the correct ensemble for a manufactured population: independent perturbations, or a correlated random field set by the process?
Selected papers
- Impulse response of stochastic oscillators: ensemble damping and phase decoherence
S. Adhikari · Journal of Sound and Vibration 643, 119982 · 2026 - Mode veering via inertial coupling
A. Jacques, S. Adhikari · Journal of Sound and Vibration 617, 119292 · 2025 - Identification of damping: part 1, viscous damping
S. Adhikari, J. Woodhouse · Journal of Sound and Vibration 243(1), 43-61 · 2001 - Identification of damping: part 2, non-viscous damping
S. Adhikari, J. Woodhouse · Journal of Sound and Vibration 243(1) · 2001 - Damping modelling using generalized proportional damping
S. Adhikari · Journal of Sound and Vibration · 2006 - Structural dynamic analysis with generalized damping models
S. Adhikari · Wiley-ISTE · 2014
Foundations
Generalised and non-proportional damping, non-viscous damping models, eigenvalue and eigenvector derivatives, continuous-system vibration and the dynamic stiffness method. This material remains in active use and underpins everything above.