## 1 Introduction  
Electromagnetic forces appearing between bus bar conductors during normal operation have a static component, but also a vibrational (dynamic) component of a vibration frequency close to twice the frequency of the alternating current or of any other harmonic current of significant magnitude. These electromagnetic forces are of relatively minor consequence in normal operation [1, 2]. However, if the bus bars are installed on supports [3], and if the vibration frequency matches a natural frequency for all bus bars, a resonance phenomenon may occur between every two sets of the supports [1, 2]. In such an uncommon circumstance, the resulting mechanical stresses in the bus bars can be far greater than those caused by the electromagnetic forces due to a peak current [2], and can lead to high vibration amplitudes and possibly to fatigue damage of the bus bars or loosening of connections along them [1]. This problem has been successfully avoided by installing bus bars in line with one of the three standard vibration classes (A, B, or C), according to which vibration amplitudes of up to 3 mm are allowed [4]. Such continuously permissible vibration amplitudes can improve the dissipation of heat by convection from the bus bars and thus affect their ampacities. The questions of how should this be modeled thermally and how should the aforementioned effects be quantified are research gaps that will be addressed by this study. A review of the literature to find possible gaps in the knowledge concerning the effect of vibrations on convection heat transfer from a vertical plate was already carried out by [PERSON], [PERSON], and [PERSON] in 2020 [5]. In the same year, another relevant review on active and passive methods of enhancing heat transfer from a plate fin by means of vibrations was conducted by [PERSON] and [PERSON] in [6]. Based on the content of [5; 6], it is logical that these reviews also cover the case of bus bars installed horizontally with vertical and horizontal major axes. However, these reviews did not include some relevant references, including the older ones used to conduct this study. For instance, in [5; 6] there are no studies on free or forced convection heat transfer from a longitudinally vibrating vertical plate [7], vertical cylinders with vertically oriented plate fins [8], bus bars under short-circuit conditions [9], bus bars used to supply a test bench with high currents [10], and so on. Accordingly, all relevant references that were published in 2020 and later can be regarded as state of the art for this area. The state-of-the-art references directly related to bus bars addressed the following research gaps: finite element method- (FEM-) based electrodynamic modeling of bus bars carrying high currents [11; 12]; FEM-based modeling of bus bars in terms of coupling electromagnetic and thermal phenomena with fluid flow [13]; and vibration response of a bus bar enclosure considering the effect of a strong electric field [14]. In a broader context, these state-of-the-art studies have also closed research gaps, such as the effect of internal plate vibrations on heat transfer in a dryer [15]; visualization of a vibrating plate in a boiling bubble resonator [16]; mixed convection from a vertical plate subjected to periodic oscillations [17]; as well as the effect of vibrations on the phenomena of heat transfer and flow along heat exchange surfaces [18]. Within this broader context, the effects of square and sinusoidal wave-shaped vibrations on forced convection from a heat sink [19] and the modeling of the thermal behavior of different vibrating blades [20] were also addressed. According to this literature review, there is no study dealing with the effect of any vibrations on the ampacity of a bus bar in normal operation.