## 1 Introduction  
In many engineering fields, complex mechanical structures are required to withstand fluctuating loads over a broad frequency spectrum during nominal working conditions. Such loads are typically non-stationary, and detailed investigations based on response spectra [1] are performed during the development of components to assess their performance [2, 3]. For example, mechanical systems in the aerospace industry are designed to sustain launch loads that are ascribable to quasi-statics events (i.e., \(\approx\)0 Hz), sinusoidal excitations (i.e., 5-100 Hz), mechanical random vibrations (i.e., 20-2000 Hz), acoustic pressure loads (i.e., 20-8000 Hz), and shocks (i.e., 100-10,000 Hz) [4]. Dedicated structural analyses are thus performed in advance during the design, qualification, and acceptance campaign to assess and confirm that the system can comply with the frequency spectrum of interest. In the meanwhile, structures are required to demonstrate their safe-life or fail-safe performances to avoid jeopardizing the structural integrity [5, 6]. In this context, the design phase is usually approached using numerical tools, such as finite element (FE) analyses, where the analyst in charge of executing simulations translates the physical model into a numerical description. In this context, to simplify calculations or due to a lack of experimental data, designers tend to assume constant and load/frequency-independent material properties within the simulation environment. While this hypothesis could be considered valid for some metals [7] or non-critical equipment, to consider material properties in this way could be dangerous for high-performance structures. These types of structures are usually produced with engineered materials, such as composites or adhesives, that can be sensitive to the nature of loads, such as thermal loads [8; 9], impact loads [10], and strain rate-dependent loads [11; 12], the load direction [13], and the applied loading frequency [14; 15]. With a particular emphasis on adhesives, such materials have become even more popular in current engineering products for joining different materials (e.g., metal-composites, metal-glass, ceramic-composites,...) [16]. Indeed, adhesives allow a smoother stress distribution along the bonding area compared to conventional joining technologies [17] and, at the same time, are efficient for mass-saving purposes and repair applications. The specific nature of adhesives has been recognized as being particularly responsive to dynamic excitations in terms of damages and reductions in material properties, and such effects were mainly attributable to the applied loading frequency and mode shapes [18]. Recently, research has highlighted that, under vibration loads, both the absorbed energy and the ultimate load sustained by the adhesive layer decrease as the applied number of cycles increases [19]. Under multiple frequencies of excitation fatigue loads, a relevant degradation of modal properties as the fatigue cycles increase [20] has been observed depending on the adhesive type. Mechanical strengths were found to be highly subjected to vibration loads, and experimental results demonstrated a complex interaction between the adhesive layer and the substrate [21]. Specifically, certain load magnitudes lead to an increase in the strength compared to others. The stress distribution was also investigated through analytical and numerical models and results demonstrated the existence of specific patterns and intensities for different magnitudes, with variations in the frequency content [22]. The substantial interest in loading frequency effects and the dynamic behaviors of adhesive joints has accelerated research on up-to-date calculation models and applicable numerical techniques [23], as well as the exploitation of frequency-related effects for improving the performance of this joining technique [24]. Another peculiarity that is typically exhibited by adhesive joints refers to the presence of stress-singularities.