Abstract

A novel strong-form meshless method based on Lagrange interpolation is proposed for vibro-acoustic coupling analysis. The governing equations of acoustic and structural domains, together with the coupling interface conditions, are discretized directly in differential form without relying on predefined meshes, thereby improving geometric flexibility. The computational domain is partitioned into local subdomains, within which Lagrange interpolation is employed to construct approximation functions from nodal distributions. In this manner, the proposed framework combines the flexibility of meshless formulations with a zonal parameterization strategy similar to that used in isogeometric analysis. Moreover, spatial derivatives and system matrices are directly evaluated and assembled at nodal points, avoiding numerical integration and simplifying the implementation procedure. Owing to the Kronecker delta property of Lagrange polynomials, boundary conditions can be imposed accurately and conveniently. For transient analysis, the Newmark-β scheme is adopted to integrate both first- and second-order temporal terms, ensuring stable and accurate time integration. Finally, numerical examples, including comparisons with commercial software, demonstrate the accuracy and effectiveness of the proposed method for complex vibro-acoustic problems.

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