Theoretical and experimental free vibration analysis of a beam-tendon system with an eccentrically placed tendon

Abstract

Theoretical and experimental free vibration analysis of a beam-tendon system is presented in this paper. The system consists of a thin-walled cantilever beam with an open cross-section and a tip mass which is loaded by an eccentrically placed tendon. The novel beam-tendon system is modelled using a set of partial differential equations and numerical free vibration analysis is conducted using a boundary problem solver. The results are thoroughly validated using a bench-top experiment and a high-fidelity finite element model. The effect of the tendon location on the frequency-loading diagrams is systematically investigated for the first time. The results demonstrate that the location of the tendon significantly influences natural frequency shifts caused by the applied axial load and it is observed that some natural frequencies can even increase with the increasing compressive axial loading for certain locations of the tendon. In addition, veering between the beam-dominated and tendon-dominated modes is studied and the structural stability of the system is discussed. The paper concludes with suggestions of practical applications of a beam-tendon system with an eccentrically placed tendon.

Damping augmentation of a rotating beam-tendon system via internally placed spring-damper elements

“…Although developing models of the beam/blade based on Timoshenko theory may bring about difficulty in the modelling, the agreement with the experiment seems to be better than the previous studies [3,4,7,43]. For the thin-walled rotorcraft or other blades where the shear deformation and rotary inertia effect cannot be neglected, modelling the blade based on the Timoshenko theory can be beneficial when compared to both the alternative simpler as well as more advanced beam theories owing to its balanced relationship between the model fidelity and modelling complexity.…”

Simulation and Experimental Substantiation of Beam Deflection under Guided End Conditions

“…Analytical results are compared with the experimental results and also with the existing literature. Free vibration analysis of a thin-walled cantilever beam is studied using a boundary problem solver [18]. Tip of the cantilever beam is loaded with an eccentrically positioned tendon.…”

Modal analysis of a rotating pre-twisted beam axially loaded by an internally guided tendon

“…This work advances the previous research presented in [10] and [11] by introducing a new model and corresponding analysis of the realistically configured rotating helicopter blade with an internally guided tendon. Previous studies considered the modal properties of a non-rotating beam-tendon system without or with bending-bending-torsion coupling of the beam [8,27], a rotating beam with bending-bending-torsion coupling and pre-twist axially loaded by a free tendon [9], and a non-rotating beam-tendon system with attachments but without bending-bending-torsion coupling [10,11]. To the best of the authors' knowledge, no studies of the modal properties of a rotating, pre-twisted beam with bending-bending-torsion coupling axially loaded by a tendon that is fixed at several spanwise locations are available in the open academic literature.…”

“…The deflections of the beam and tendon are expressed as the summation of the multiplication of the orthogonal polynomials which satisfy the geometric boundary conditions and the generalised coordinates whilst the artificial springs are introduced for the desired beam-tendon coupling and load transfer. Therefore, in contrast with previous research [8,9,27], this formulation leads to an explicit set of ordinary differential equations which constitute the full model of the proposed problem and permit the standard linear-algebra-based modal analysis. The modal analysis based on this method can detect two modes with very close natural frequencies, which is usually difficult for boundary value problem solver [8,9,27].…”

“…Therefore, in contrast with previous research [8,9,27], this formulation leads to an explicit set of ordinary differential equations which constitute the full model of the proposed problem and permit the standard linear-algebra-based modal analysis. The modal analysis based on this method can detect two modes with very close natural frequencies, which is usually difficult for boundary value problem solver [8,9,27]. In addition, this method is also applicable to systems with damping and systems with stability questions arising from the presence of the nonconservative forces.…”