Experimental and Numerical Dynamic Behavior of Bending-Torsion Coupled Box-Beam

Abstract

Purpose Structural configurations related to new green aircraft design require high efficiency and low weight. As a consequence, moderate-to-large deformation under operating loads arise and aeroelastic instabilities different with respect to rigid counterpart are possible. Coupled structural configurations can provide the right mean to overcome such a critical situations selecting the right coupling parameters and structural performance. In this work, the dynamic behaviour of stiffened box-beam architecture with selected optimal stiffener orientation to emphasize the bending-torsion coupling characteristics has been investigated. Methods An extensive experimental activity has been performed for a validation and confirmation of the numerical results. Two cantilever beams produced with different technologies and materials have been tested. Modal performance has been determined by means of a laser Doppler vibrometer (LDV), while Finite-Element Method (FEM) numerical simulation based on solid elements and equivalent single layer approach have been applied and compared. Experimental/numerical comparison have been presented pointing out the specific coupling performance of this architecture with respect to natural frequencies and modal shapes. Results The activity demonstrates a good correlation in natural frequencies that remains mostly under 4$$\%$$ % . Modal assurance criterion (MAC) has been considered in comparing experimental and numerical modal shapes. Conclusion The proposed innovative configuration demonstrates its capability to be used in aeroelastic critical problem as a mean to reduce their influence in aircraft design. The numerical procedure used for equivalencing the stiffened parts of the box-beam has also been validated in dynamical response confirming the possibility to be used in design phase.

Optimization of Curvilinear Stiffener Beam Structures Simulated by Beam Finite Elements with Coupled Bending–Torsion Formulation

“…The thickness of the C-shaped spars and of the mid-layer of the stiffened panels was s = 2 mm. The geometry followed the dimensions of the beam used in [28,29], where the structure was widely analyzed, and many numerical and experimental data are available for model verification; moreover, it can be manufactured and tested with the procedures and methods used in previous works. The material considered for the structural analysis was an Al6060 aluminum alloy, with its properties listed in Table 1.…”

“…The allowable orientations ranged from ϑ lb to ϑ ub , which represented the lower and upper boundaries of the problem. The stiffness coefficients C 11 , C 12 , C 22 , and C 33 were computed with Equation (2); the CLT matrices were obtained by considering the stiffeners as equivalent orthotropic materials, according to [28,29,44], and with properties computed with Equation ( 12) and listed in Table 2. For each element, the stiffener orientations were considered equal to the mean angle between the angles at the element nodes.…”

“…In the present work, a beam finite element with bending-torsion coupling formulation (Figure 1), developed and validated with numerical and experimental results by Patuelli et al [28,29], was adopted to find the optimal configuration of curvilinear stiffener panels of a box-beam structure. The bending-torsion coupling beam finite element (BTCE) was used in a topological optimization to find the optimal stiffener orientation that guaranteed prescribed levels of deflection and torsion for three different load cases (LC1, LC2, and LC3) located on the beam axis; these design cases were identified as LC1_C, LC2_C, and LC3_C.…”

A Nonlinear Beam Finite Element with Bending–Torsion Coupling Formulation for Dynamic Analysis with Geometric Nonlinearities

“…The linear finite element was derived with Galerkin's method, while the bending-torsion coupling was obtained with specific shape functions and the hypothesis of constant torsional moment along the beam element. The resulting model was validated with experimental and numerical results [34,35], showing good accuracy for static and dynamic analysis. The scope of the present research work is to develop a procedure to perform dynamic analysis in the presence of geometric nonlinearities.…”