# Historical Church Bell Tower Structural Behavior Induced by [PERSON]'s Acoustic Wave Propagation
## 1 Introduction  
The preservation of historical structures is not only about protecting their architectural design, but also about understanding the principles that shaped construction techniques in relation to their foreseen function throughout history. These principles often include a blend of craftsmanship, materials science and engineering knowledge that evolved over centuries. One intriguing yet less-explored field of study is the interaction between audible sounds. The phenomenon of vibroacoustic coupling occurs when audible sources, between 20 Hz and 20 kHz, induce mechanical vibrations within a structure through its materials, becoming a reverse case with respect to a music instrument, where a vibrating source can produce an audible sound [1, 2, 3]. This interplay underscores the importance of an interdisciplinary methodology that integrates fields such as engineering, acoustics, and materials science to facilitate informed strategies for heritage conservation. In the case of church bells, an acoustic source acts as the initiator of mechanical vibrations across a broader frequency spectrum. The vibrations produced during bell ringing can lead to complex oscillatory behaviors, manifesting as resonant frequencies that amplify selected vibrational modes of the structure [4], that are superimposed to natural and anthropogenic vibration sources [5]. This intrinsic coupling of acoustics and structural responses can produce cumulative damage over time, characterized by phenomena such as microcracking, material fatigue and eventual structural failure [6]. Research into the vibroacoustic interaction of structures has advanced significantly with the development of modeling techniques that integrate analyses of sound and structural responses. Sophisticated finite element modeling (FEM) methods have been employed to characterize the material properties of historical structures while simulating the vibrational influences of nearby sound sources [7]. In assessing how structural behavior adapts to acoustic loading, it is essential to consider not just the material composition, but also the broad spectrum of historical and environmental variables that influence its response [8]. Different materials used in the tower, including local stone and mortar, exhibit varied vibrational properties regarding acoustic wave attenuation. For instance, studies have shown that the acoustic properties of rocks are influenced by factors such as microcracks, porosity and fluid content, leading to variations in their elastic behavior and acoustic attenuation characteristics [9]. Additionally, research on fresh mortar indicates that components like sand size and content significantly affect wave attenuation behavior, with entrapped air bubbles impacting lower frequency ranges [10]. These findings underscore the importance of considering the specific vibrational properties of construction materials when assessing acoustic wave attenuation in structures. This study focuses on the San Michele Arcangelo Cathedral historical bell tower located in Caserta Vecchia (Campania Region, Italy). The investigation examines how the propagation of its bells acoustic waves influences the tower structural behavior. This specific bell tower was chosen because of its historical relevance and since earlier studies analyzed its response to environmental vibrations at lower frequencies but did not account for the effects of acoustic forcing [11]. Additionally, prior research largely focused on seismic behavior and provided only modal analysis of the dynamic model [12; 13; 14]. By combining environmental acoustic measurements with finite element modeling, this study offers new perspectives on the dynamic behavior of historical bell towers subjected to vibroacoustic loads. The San Michele Arcangelo bell tower is an example of medieval architecture. Its design, with a square base transitioning into an octagonal upper section, reflects the architectural features of its time.