Multirotors are gaining great importance in the layout of innovative and more agile mobility. In this framework, a possible solution to developing an aircraft complying with the stringent size requirements characterizing this type of application may be a coaxial rotor configuration. To exploit several possibilities linked to coaxial rotors, a scaled experimental model is designed to evaluate the performances of the counter-rotating propeller system, specifically regarding the distance between the two propellers. Both thrust and noise are considered as parameters of interest. Two brushless motors are deployed, whereas the propellers’ angular velocity, in terms of rounds per minute (rpm), is controlled by an external control system. Tests are conducted on both single isolated propellers as well as on the counter-rotating system: the two propellers and their respective motors are characterized regarding the thrust. Furthermore, a comparison with a numerical model is performed. Noise evaluation on the single propeller shows a motor contribution prevalence at a low rpm range (1140–1500 rpm) and a propeller prevalence for angular velocities higher than 1860 rpm. By varying the distances between the propellers, a sensitivity analysis is performed with the aim of identifying the optimum configuration, taking into account both noise and thrust performances.

Gradient-based optimization techniques need precise and efficient sensitivities. Numerical sensitivity methods such as finite differences are easy to implement but imprecise and computationally inefficient. In contrast, analytical sensitivity methods, such as the discrete and continuum ones are highly accurate and efficient. Continuum Sensitivity Analysis (CSA) is an analytical method used to calculate derivatives of shape or value parameters. While CSA has been successfully applied in static analysis and dynamic problems in the time domain, this work presents an extension of the approach to eigenvalue sensitivities for the first time. However, CSA revealed limitations, prompting the exploration of an alternative approach based on discrete analytical differentiation. This method is employed for the first time in shape sensitivities. The derivatives of the stiffness and mass matrices required by the method are calculated analytically, resulting in high accuracy and computational efficiency. In addition, an element agnostic approach has been developed leveraging primary analysis matrices to calculate their derivative. This characteristic, along with the nonintrusivity, makes the method employable with standard commercial software. Both approaches have been applied and validated in a wide range of scenarios, involving vibration and buckling problems.

Sensitivity analysis is essential for understanding how changes in design variables affect system performance. Numerical methods for calculating sensitivities, such as finite difference methods, are often easy to implement but can suffer from high computational costs and limited accuracy. Continuum Sensitivity Analysis (CSA) is an alternative approach for calculating analytical derivatives with respect to shape or value parameters. It is easy to implement and can be as accurate as conventional analytical sensitivity methods. By employing Spatial Gradient Reconstruction (SGR), continuous sensitivity equations can be solved in a nonintrusive manner. This method has been applied and validated on a wide range of problems. This work aims to extend the range of applicability of CSA to composite laminates. Composite materials may be characterized by several cross-coupling between loads and deformations, which leads to complex stress fields. A general formulation is introduced that applies to any plate-discretized Finite Element (FE) problem. The developed methodology utilizes the plate elements’ resultant forces and moments instead of the stresses to reconstruct spatial gradients and apply boundary conditions. Because of that, the method does not depend on the material type or lamination sequence and is also computationally inexpensive. It can be used indifferently for isotropic or composite materials, with any lamination sequence. This feature makes CSA attractive for classical FE models used in design optimization problems. This novelty extends the range applicability of CSA to any possible plate-based structural problem.