PSI - Issue 77

Structural Integrity Procedia Structural Integrity Procedia Structural Integrity Procedia Structural Integrity Structural Integrity Procedia Structural Integrity Procedia

Structural Integrity Procedia 00 (2025) 1–7

Available online at www.sciencedirect.com

ScienceDirect Structural Integrity Procedia 00 (2025) 1–7 International Conference on Structural Integrity Structural Integrity Procedia 00 (2025) 1–7 Structural Integrity Procedia 00 (2025) 1–7 Structural Integrity Procedia 00 (2025) 1–7

Procedia Structural Integrity 77 (2026) 64–70 International Conference on Structural Integrity International Conference on Structural Integrity About airborne fatigue life predictions by means of full-field receptances. Part A: retrieving structural forces from pressure fields. International Conference on Structural Integrity About airborne fatigue life predictions by means of full-field receptances. Part A: retrieving structural forces from pressure fields. International Conference on Structural Integrity About airborne fatigue life predictions by means of full-field receptances. Part A: retrieving structural forces from pressure fields. Structural Integrity Procedia 00 (2025) 1–7 International Conference on Structural Integrity About airborne fatigue life predictions by means of full-field receptances. Part A: retrieving structural forces from pressure fields. About airborne fatigue life predictions by means of full-field receptances. Part A: retrieving structural forces from pressure fields. About airborne fatigue life predictions by means of full-field receptances. Part A: retrieving structural forces from pressure fields. Alessandro Zanarini ∗ DIN, Industrial Engineering Dept., University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy Alessandro Zanarini ∗ DIN, Industrial Engineering Dept., University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy Alessandro Zanarini ∗ DIN, Industrial Engineering Dept., University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy Alessandro Zanarini ∗ DIN, Industrial Engineering Dept., University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy Alessandro Zanarini ∗ DIN, Industrial Engineering Dept., University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ICSI organizers Abstract By means of a simplified inverse vibro-acoustic relation – based on the Rayleigh integral approximation of the sound propagated by a vibrating surface, modelled by the testing-based full-field receptances – in Part A the spectrum of the induced force by the airborne pressure fields can be retrieved, taking into account all the hardly modellable conditions of the set-up realisation. This part starts therefore from the modelling of the acoustic pressure field, in its spatial and broad frequency band contents. By means of the simplified receptances-aided inverse vibro-acoustics, the complete spectrum of the induced force is retrieved in the location of the impedance head of the direct characterisation testing of the surface. Details and considerations on the airborne force retrieval method, together with examples coming from a real thin plate tested, are provided in this Part A of the work. Keywords: airborne pressure fields; Rayleigh integral approximation; inverse vibro-acoustics; airborne force identification; full-field receptance FRFs; full-field dynamic testing. 1. Introduction Airborne pressure fields, with their variable spectral content in the acoustic and frequency domains, can become a threatening dynamic distributed loading for many surfaces in industrial applications, thus leading to airborne fatigue. The latter can be dangerous especially for lightweight parts with tight structural dynamics in the frequency range of interest, typical of aerospace and automotive engineering. The working life of these components can be severely short ened – also with catastrophic failures – due to unexpectedly high dynamic responses to the airborne pressure fields. The latter may indeed excite excessively the modal base or may shorten the life of the actual realisation. Advanced de sign and manufacturing methodologies need therefore to consider carefully any generalised damping distribution and specific boundary condition in the structural dynamics of the actual realisation of the mounted component, especially for mission critical ones. When simplified numerical models can not cope with real-life complex structural dynamics, experiment-based full-field optical techniques can substitute – by means of full-field receptances - the former in hybrid modelling of the vibro-acoustic coupling, at the base of airborne fatigue. Furthermore, experiment-based full-field op tical techniques can provide advanced benchmarks for the improvement of the more traditional modelling tools, such as FEM / BEM (see Wyckaert et al. (1996); Kirkup and Thompson (2007)), for the accurate design and manufacturing Abstract By means of a simplified inverse vibro-acoustic relation – based on the Rayleigh integral approximation of the sound propagated by a vibrating surface, modelled by the testing-based full-field receptances – in Part A the spectrum of the induced force by the airborne pressure fields can be retrieved, taking into account all the hardly modellable conditions of the set-up realisation. This part starts therefore from the modelling of the acoustic pressure field, in its spatial and broad frequency band contents. By means of the simplified receptances-aided inverse vibro-acoustics, the complete spectrum of the induced force is retrieved in the location of the impedance head of the direct characterisation testing of the surface. Details and considerations on the airborne force retrieval method, together with examples coming from a real thin plate tested, are provided in this Part A of the work. Keywords: airborne pressure fields; Rayleigh integral approximation; inverse vibro-acoustics; airborne force identification; full-field receptance FRFs; full-field dynamic testing. 1. Introduction Airborne pressure fields, with their variable spectral content in the acoustic and frequency domains, can become a threatening dynamic distributed loading for many surfaces in industrial applications, thus leading to airborne fatigue. The latter can be dangerous especially for lightweight parts with tight structural dynamics in the frequency range of interest, typical of aerospace and automotive engineering. The working life of these components can be severely short ened – also with catastrophic failures – due to unexpectedly high dynamic responses to the airborne pressure fields. The latter may indeed excite excessively the modal base or may shorten the life of the actual realisation. Advanced de sign and manufacturing methodologies need therefore to consider carefully any generalised damping distribution and specific boundary condition in the structural dynamics of the actual realisation of the mounted component, especially for mission critical ones. When simplified numerical models can not cope with real-life complex structural dynamics, experiment-based full-field optical techniques can substitute – by means of full-field receptances - the former in hybrid modelling of the vibro-acoustic coupling, at the base of airborne fatigue. Furthermore, experiment-based full-field op tical techniques can provide advanced benchmarks for the improvement of the more traditional modelling tools, such as FEM / BEM (see Wyckaert et al. (1996); Kirkup and Thompson (2007)), for the accurate design and manufacturing Abstract By means of a simplified inverse vibro-acoustic relation – based on the Rayleigh integral approximation of the sound propagated by a vibrating surface, modelled by the testing-based full-field receptances – in Part A the spectrum of the induced force by the airborne pressure fields can be retrieved, taking into account all the hardly modellable conditions of the set-up realisation. This part starts therefore from the modelling of the acoustic pressure field, in its spatial and broad frequency band contents. By means of the simplified receptances-aided inverse vibro-acoustics, the complete spectrum of the induced force is retrieved in the location of the impedance head of the direct characterisation testing of the surface. Details and considerations on the airborne force retrieval method, together with examples coming from a real thin plate tested, are provided in this Part A of the work. Keywords: airborne pressure fields; Rayleigh integral approximation; inverse vibro-acoustics; airborne force identification; full-field receptance FRFs; full-field dynamic testing. 1. Introduction Airborne pressure fields, with their variable spectral content in the acoustic and frequency domains, can become a threatening dynamic distributed loading for many surfaces in industrial applications, thus leading to airborne fatigue. The latter can be dangerous especially for lightweight parts with tight structural dynamics in the frequency range of interest, typical of aerospace and automotive engineering. The working life of these components can be severely short ened – also with catastrophic failures – due to unexpectedly high dynamic responses to the airborne pressure fields. The latter may indeed excite excessively the modal base or may shorten the life of the actual realisation. Advanced de sign and manufacturing methodologies need therefore to consider carefully any generalised damping distribution and specific boundary condition in the structural dynamics of the actual realisation of the mounted component, especially for mission critical ones. When simplified numerical models can not cope with real-life complex structural dynamics, experiment-based full-field optical techniques can substitute – by means of full-field receptances - the former in hybrid modelling of the vibro-acoustic coupling, at the base of airborne fatigue. Furthermore, experiment-based full-field op tical techniques can provide advanced benchmarks for the improvement of the more traditional modelling tools, such as FEM / BEM (see Wyckaert et al. (1996); Kirkup and Thompson (2007)), for the accurate design and manufacturing ∗ Corresponding author. Tel + 39 051 209 3442. Email address: a.zanarini@unibo.it (Alessandro Zanarini) 1 Abstract By means of a simplified inverse vibro-acoustic relation – based on the Rayleigh integral approximation of the sound propagated by a vibrating surface, modelled by the testing-based full-field receptances – in Part A the spectrum of the induced force by the airborne pressure fields can be retrieved, taking into account all the hardly modellable conditions of the set-up realisation. This part starts therefore from the modelling of the acoustic pressure field, in its spatial and broad frequency band contents. By means of the simplified receptances-aided inverse vibro-acoustics, the complete spectrum of the induced force is retrieved in the location of the impedance head of the direct characterisation testing of the surface. Details and considerations on the airborne force retrieval method, together with examples coming from a real thin plate tested, are provided in this Part A of the work. Keywords: airborne pressure fields; Rayleigh integral approximation; inverse vibro-acoustics; airborne force identification; full-field receptance FRFs; full-field dynamic testing. 1. Introduction Airborne pressure fields, with their variable spectral content in the acoustic and frequency domains, can become a threatening dynamic distributed loading for many surfaces in industrial applications, thus leading to airborne fatigue. The latter can be dangerous especially for lightweight parts with tight structural dynamics in the frequency range of interest, typical of aerospace and automotive engineering. The working life of these components can be severely short ened – also with catastrophic failures – due to unexpectedly high dynamic responses to the airborne pressure fields. The latter may indeed excite excessively the modal base or may shorten the life of the actual realisation. Advanced de sign and manufacturing methodologies need therefore to consider carefully any generalised damping distribution and specific boundary condition in the structural dynamics of the actual realisation of the mounted component, especially for mission critical ones. When simplified numerical models can not cope with real-life complex structural dynamics, experiment-based full-field optical techniques can substitute – by means of full-field receptances - the former in hybrid modelling of the vibro-acoustic coupling, at the base of airborne fatigue. Furthermore, experiment-based full-field op tical techniques can provide advanced benchmarks for the improvement of the more traditional modelling tools, such as FEM / BEM (see Wyckaert et al. (1996); Kirkup and Thompson (2007)), for the accurate design and manufacturing Abstract By means of a simplified inverse vibro-acoustic relation – based on the Rayleigh integral approximation of the sound propagated by a vibrating surface, modelled by the testing-based full-field receptances – in Part A the spectrum of the induced force by the airborne pressure fields can be retrieved, taking into account all the hardly modellable conditions of the set-up realisation. This part starts therefore from the modelling of the acoustic pressure field, in its spatial and broad frequency band contents. By means of the simplified receptances-aided inverse vibro-acoustics, the complete spectrum of the induced force is retrieved in the location of the impedance head of the direct characterisation testing of the surface. Details and considerations on the airborne force retrieval method, together with examples coming from a real thin plate tested, are provided in this Part A of the work. Keywords: airborne pressure fields; Rayleigh integral approximation; inverse vibro-acoustics; airborne force identification; full-field receptance FRFs; full-field dynamic testing. 1. Introduction Airborne pressure fields, with their variable spectral content in the acoustic and frequency domains, can become a threatening dynamic distributed loading for many surfaces in industrial applications, thus leading to airborne fatigue. The latter can be dangerous especially for lightweight parts with tight structural dynamics in the frequency range of interest, typical of aerospace and automotive engineering. The working life of these components can be severely short ened – also with catastrophic failures – due to unexpectedly high dynamic responses to the airborne pressure fields. The latter may indeed excite excessively the modal base or may shorten the life of the actual realisation. Advanced de sign and manufacturing methodologies need therefore to consider carefully any generalised damping distribution and specific boundary condition in the structural dynamics of the actual realisation of the mounted component, especially for mission critical ones. When simplified numerical models can not cope with real-life complex structural dynamics, experiment-based full-field optical techniques can substitute – by means of full-field receptances - the former in hybrid modelling of the vibro-acoustic coupling, at the base of airborne fatigue. Furthermore, experiment-based full-field op tical techniques can provide advanced benchmarks for the improvement of the more traditional modelling tools, such as FEM / BEM (see Wyckaert et al. (1996); Kirkup and Thompson (2007)), for the accurate design and manufacturing Alessandro Zanarini ∗ DIN, Industrial Engineering Dept., University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy Abstract By means of a simplified inverse vibro-acoustic relation – based on the Rayleigh integral approximation of the sound propagated by a vibrating surface, modelled by the testing-based full-field receptances – in Part A the spectrum of the induced force by the airborne pressure fields can be retrieved, taking into account all the hardly modellable conditions of the set-up realisation. This part starts therefore from the modelling of the acoustic pressure field, in its spatial and broad frequency band contents. By means of the simplified receptances-aided inverse vibro-acoustics, the complete spectrum of the induced force is retrieved in the location of the impedance head of the direct characterisation testing of the surface. Details and considerations on the airborne force retrieval method, together with examples coming from a real thin plate tested, are provided in this Part A of the work. Keywords: airborne pressure fields; Rayleigh integral approximation; inverse vibro-acoustics; airborne force identification; full-field receptance FRFs; full-field dynamic testing. 1. Introduction Airborne pressure fields, with their variable spectral content in the acoustic and frequency domains, can become a threatening dynamic distributed loading for many surfaces in industrial applications, thus leading to airborne fatigue. The latter can be dangerous especially for lightweight parts with tight structural dynamics in the frequency range of interest, typical of aerospace and automotive engineering. The working life of these components can be severely short ened – also with catastrophic failures – due to unexpectedly high dynamic responses to the airborne pressure fields. The latter may indeed excite excessively the modal base or may shorten the life of the actual realisation. Advanced de sign and manufacturing methodologies need therefore to consider carefully any generalised damping distribution and specific boundary condition in the structural dynamics of the actual realisation of the mounted component, especially for mission critical ones. When simplified numerical models can not cope with real-life complex structural dynamics, experiment-based full-field optical techniques can substitute – by means of full-field receptances - the former in hybrid modelling of the vibro-acoustic coupling, at the base of airborne fatigue. Furthermore, experiment-based full-field op tical techniques can provide advanced benchmarks for the improvement of the more traditional modelling tools, such as FEM / BEM (see Wyckaert et al. (1996); Kirkup and Thompson (2007)), for the accurate design and manufacturing 2452-3216 © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ICSI organizers 10.1016/j.prostr.2026.01.010 ∗ Corresponding author. Tel + 39 051 209 3442. Email address: a.zanarini@unibo.it (Alessandro Zanarini) 1 ∗ Corresponding author. Tel + 39 051 209 3442. Email address: a.zanarini@unibo.it (Alessandro Zanarini) 1 ∗ Corresponding author. Tel + 39 051 209 3442. Email address: a.zanarini@unibo.it (Alessandro Zanarini) 1 ∗ Corresponding author. Tel + 39 051 209 3442. Email address: a.zanarini@unibo.it (Alessandro Zanarini) 1 ∗ Corresponding author. Tel + 39 051 209 3442. Email address: a.zanarini@unibo.it (Alessandro Zanarini) 1