## 1 Introduction
This feature is particularly important in the case of adhesive joints as it can trigger cracks and premature failures [25]. Indeed, the scientific and technical interest in detecting, quantifying, and assessing stress-singularities in adhesive joints is demonstrated by several remarkable studies, such as [26; 27], two of the oldest studies concerning bi-material wedges [28; 29], which concern bi-material coupons; and [30] where stress singularities were analyzed in the frame of a failure initiation. In [31], singularity analyses were performed on joint configurations not explored before; [32; 33; 34] offered stress evaluations based on stress-singular terms, whereas [35] produced a profound literature review regarding the presence of stress singularities in components and their effects on the structural integrity. Additionally, mixed adhesive joints have been investigated [36], as well as the magnitude of the singular field with respect to the variation in the elastic modulus [37]. More recently, detailed analyses exploiting cohesive zone modelling studied the effects of stress singularity for failure assessments [38]. However, in recent years, research and investigation have concentrated on the development of safer components by removing the stress singularity. This goal is achievable through the analysis of mechanical and geometrical conditions that prevent this issue [39; 40]; additionally, innovative testing methods for better material characterization have become accessible [41; 42]. Furthermore, a significant increase in fatigue performance has been exhibited when a stress singularity is removed from a specimen under investigation [43]. Moreover, due to the increased lifetime of components, experimental investigations of fatigue responses should focus also on the very high cycle fatigue (VHCF, \(N>10^{7}\)) life range with low-amplitude loads [44; 45] applied for a long time or with a high frequency, e.g., those due to vibrations. For example, in recent years, VHCF tests have been carried out to investigate a wide set of materials such as stainless steel [46], steels produced with different processes [47], steels with large risk volume [48], and adhesively bonded joints [49; 50], confirming the industrial and academic interest towards this research field. Particular attention has also been paid to the quantification of the influence of stress singularities on the joint life [43], size effects [51], and, in general, the fatigue responses of adhesives under the VHCF regime. The research presented in this paper aimed to investigate loading frequency-related effects on the fatigue response of a structural adhesive. Ultrasonic fatigue tests at a loading frequency of 20 kHz and conventional frequencies of 5, 25, and 50 Hz were performed with a servo-hydraulic testing machine. Adhesively bonded butt joints, with a geometry limiting the adhesive singularity (epoxy resin SikaPower(r)-1277--aluminium 7075 T6) were subjected to symmetrical tension-compression loading (R = \(-\)1) tests. The non-singular specimen was accurately designed through analytical relationships based on the inverse Bogy formulation [40], numerically verified with finite element (FE) procedures, and thus tested under fatigue conditions. The experimental outcomes showed a relevant difference between ultrasonic and conventional fatigue tests, thus confirming a significant loading frequency effect for the investigated adhesive. Indeed, the estimated S-N curves demonstrated an increased fatigue response as the applied frequency increased. The fatigue strength at 2 \(\times\) 10\({}^{6}\) cycles was found to follow a linear trend in a bi-logarithmic chart. Data scattering is present among the test conditions, but this effect had a minor impact on experimental outcomes. The paper is organized as follows: Section 2 describes the material, analytical, and numerical methods followed to design the specimens and the experimental activity. Section 3 focuses on the fatigue results and the related analysis. Section 4 discusses the experimental outcomes.