Curved multi-layer beams, such as leaf springs, are widely used in vehicle suspension systems for both road and rail vehicles in automotive industry due to their capacity for high loads and their vibrational damping properties. To design suspension systems that experience a large number of load types and complexities of friction, we must first understand the nonlinear dynamic behavior of curved beams. In this paper, the governing equations for the nonlinear vibrations of curved two-layer beams in the presence of interlayer slip are first derived. Then, the characteristic equation, the longitudinal and transverse mode shapes of the beam, are determined independently using eigenvalue problem solutions. Subsequently, using the calculated mode shapes, different phases of the dynamics of these structures are investigated, taking into account interlayer friction. The results of numerical simulations are compared and validated with finite element analysis using ANSYS software. The results show that the dynamic behavior of curved two-layer beams experiences chaotic regimes after initial slip. Different regimes of periodic, quasi-periodic and chaotic motions are found in the dynamics of the system.

The effectiveness of single-axis solar tracking in enhancing the performance of flat-plate solar collectors (FPSCs) has been widely acknowledged, particularly under clear-sky conditions. However, the precision of solar tracking systems—governed by the electro-mechanical transmission's discrete rotation step size—has a critical impact on energy yield. In this study, the influence of varying rotation step sizes on the incident solar irradiance received by flat-plate collectors with single-axis tracking (SAT) has been numerically investigated using the EnergyPlus simulation environment. Eight discrete step sizes—1°, 2°, 5°, 10°, 15°, 30°, 45°, and 90°—were examined under clear-sky conditions on July 26, using meteorological data specific to Kragujevac, Serbia. The tracking system was configured to follow the solar trajectory along the east–west (E–W) direction, rotating around a north–south (N–S) inclined axis. Results demonstrated that incident solar irradiance was significantly enhanced—by over 35%—when rotation step sizes ranged between 1° and 15°, compared to fixed (non-tracking) collectors. Slight reductions in performance were observed for step sizes of 30° (34.26% improvement) and 45° (32.95%), with the lowest gain (23.04%) associated with the coarsest resolution of 90°. Although dual-axis tracking (DAT) systems provide superior irradiance capture, single-axis systems offer substantial advantages in residential and small-scale applications due to their lower capital investment, simpler design, reduced maintenance requirements, and greater architectural integration potential. These findings underscore the importance of optimizing rotation step size in the design and deployment of cost-effective, energy-efficient solar tracking systems. In light of increasingly stringent energy performance directives within the European Union, the deployment of optimally configured SAT systems is expected to expand across the residential sector.