PARALLEL HARMONIC BALANCE METHOD FOR NONLINEAR VIBRATION ANALYSIS OF MECHANICAL STRUCTURES USING QUANSCIENT ALLSOLVE

he accurate prediction of nonlinear vibration phenomena in mechanical structures is a key challenge in modern turbomachinery and aerospace design. As engineering systems become increasingly lightweight and multifunctional, nonlinearities such as large displacements, geometric stiffening, and modal interactions can no longer be neglected. Addressing these behaviours requires robust frequency-domain techniques combined with scalable numerical solvers capable of handling industrial-scale finite
element models.
Thiswork presents a parallel Harmonic Balance (HB) framework for the computation of Nonlinear Frequency Response Curves (NFRCs) and Nonlinear Normal Modes (NNMs) in geometrically nonlinear elastic systems. The methodology is based on the finite element method using the Green–Lagrange strain tensor to represent large deformations. Application of HBM
results in a nonlinear algebraic system which is solved via a Newton–Raphson algorithm embedded within an advanced continuation procedure that permits the computation of unstable branches. The framework is implemented in the Quanscient’s cloud-native multiphysics platform Allsolve, which provides highperformance finite element capabilities and parallel scalability through MUMPS and PETSc linear solvers on distributed cloud infrastructure.
Comprehensive computational studies are conducted on benchmark structures and on a more challenging fan-blade case. Scalability assessments demonstrated strong, efficient scaling up to 64 MPI processes on HPC clusters.
Overall, the results highlight the capability of Quanscient Allsolve coupled to the proposed continuation algorithm to perform large-scale nonlinear vibration simulations in the frequency domain, bridging the gap between academic nonlinear dynamics and industrial high-fidelity modelling.