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• A system consisting of the Euler-Bernoulli beam subjected to tendon-induced axial loading is studied. • The system is modelled using a set of partial differential equations derived by Hamilton's principle. • The model is thoroughly experimentally validated for a wide range of loadings and configurations. • The effect of the tendon tension and its mass on the modal properties and frequency loci veering are studied. • Further numerical studies show the effect of the tendon on the torsional modes and structural stability. Theoretical and experimental modal analysis of the system consisting of the Euler-Bernoulli beam axially loaded by a tendon is studied in the paper. The beam-tendon system is modelled using a set of partial differential equations derived by Hamilton's principle and the coupling between the beam and the tendon is ensured by the boundary conditions. Theoretical modal analysis is conducted using a boundary value problem solver and the results are thoroughly experimentally validated using a bench-top experiment. In particular, the effect of the tendon tension on the modal properties of the system is studied. It is found that by increasing the tension, the natural frequencies of the beam decrease while the natural frequencies of the tendon increase. It is also shown that these two sets of modes interact with each other through frequency loci veering. The effect of the tendon mass is also experimentally and numerically studied and it is shown that lighter tendon produces fewer vibration modes in the studied frequency region. Two further numerical studies are conducted to demonstrate the effect of the tendon on the torsional modes of the beam, and to study the structural stability. Overall, an excellent agreement between the numerical and experimental results is obtained, giving the confidence in the derived theoretical model. [ABSTRACT FROM AUTHOR]

A method for non-parametric identification of systems with asymmetric non-linear restoring forces is proposed in this paper. The method, named the zero-crossing method for systems with asymmetric restoring forces (ZCA), is an extension of zero-crossing methods and allows identification of backbones, damping curves and restoring elastic and dissipative forces from a resonant decay response. The validity of the proposed method is firstly demonstrated on three simulated resonant decay responses of the systems with off-centre clearance, bilinear and quadratic stiffness. Then, the method is applied to experimental data from a micro-electro-mechanical resonator in order to quantify its non-linear damping and stiffness effects. Throughout the paper the proposed method is also compared with the Hilbert vibration decomposition to demonstrate that the ZCA yields more accurate results with much less effort. [ABSTRACT FROM AUTHOR]

This paper presents a method for detection and characterisation of structural non-linearities from a single frequency response function using the Hilbert transform in the frequency domain and artificial neural networks. A frequency response function is described based on its Hilbert transform using several common and newly introduced scalar parameters, termed non-linearity indexes, to create training data of the artificial neural network. This network is subsequently used to detect the existence of non-linearity and classify its type. The theoretical background of the method is given and its usage is demonstrated on different numerical test cases created by single degree of freedom non-linear systems and a lumped parameter multi degree of freedom system with a geometric non-linearity. The method is also applied to several experimentally measured frequency response functions obtained from a cantilever beam with a clearance non-linearity and an under-platform damper experimental rig with a complex friction contact interface. It is shown that the method is a fast and noise-robust means of detecting and characterising non-linear behaviour from a single frequency response function. [ABSTRACT FROM AUTHOR]

[Display omitted] • A system consisting of the Euler-Bernoulli beam subjected to tendon loading is studied. • The tendon is attached to the beam at the tip and in several locations • Computational free vibration analysis is conducted and validated. • The effect of the number and location of the attachment points is evaluated. • Structural stability of the beam-tendon system is investigated. Free vibration and stability analysis of the system consisting of the Euler–Bernoulli beam axially loaded by a tendon is studied in the paper. The tendon is attached to the cantilever beam at the tip as well as in several spanwise locations using mechanical attachment points. This novel beam-tendon system is modelled using a set of partial differential equations and the coupling between the beam and the tendon is ensured by the boundary and continuity conditions. Computational free vibration analysis is conducted using a boundary value problem solver and the results are thoroughly experimentally validated using a bench-top experiment. In particular, the effect of the number of the attachment points and their location on the frequency-loading diagram of the beam-tendon system is investigated for the first time. It is found that the applied axial load causes a frequency shift of beam-dominated natural frequencies, and frequency loci veering between beam-dominated and tendon-dominated modes. Both of these features are shown to be dependent on a number and location of the attachment points. In addition, the effect of the attachment points on the structural stability of the system is numerically studied and it is observed that the critical force of the system with the intermittently attached tendon is always higher than for the system with no attachment points. [ABSTRACT FROM AUTHOR]

• Identification of complex non-linear modes using the Hilbert-Huang transform (HHT) is presented. • The ability of the HHT to identify the complex non-linear modes is numerically investigated. • The findings highlight that the HHT can detect and characterise, but not quantify, non-linear behaviour. • The estimation of complex non-linear modes is also demonstrated experimentally. Modal analysis is a well-established method for analysis of linear systems, but its extension to non-linear structures has proven to be much more problematic. Several competitive definitions of non-linear modes and a variety of experimental methods have been introduced. In this paper, the definition of complex non-linear modes (CNMs) of mechanical systems is adopted and the possibility of their identification from experimental free decay responses using the Hilbert-Huang transform (HHT) is explored. It is firstly discussed that since there are similarities in the definition of intrinsic mode functions obtained using the HHT and reduced order model of slow-flow dynamics based on the CNMs, there is a reason to believe that the HHT can indeed extract the CNMs. This paper, however, presents a new insight into the use of the Hilbert-Huang transform by showing that the amplitude-dependent frequency and damping extracted from a free decay response are only suitable for detection and characterisation of non-linearities, but they cannot be used to quantify the non-linear behaviour by fitting the CNMs even if a model of the system is known. The analytical proof of the HHT cannot be currently formulated due to a limited understanding of its empirical nature. Instead, this unconventional conclusion is supported by a series of numerical studies of conservative and non-conservative non-linear systems with a wide range of parameters. In all cases, a special care is taken to apply the basic HHT only on such signals for which mode separation is possible (no mode-mixing occurs). This eliminates the need for more sophisticated HHT versions and clearly demonstrates the inability of the HHT to extract CNMs even for the simplest cases. In addition to numerical studies, the identification of several non-linear modes is demonstrated experimentally using the free decay responses obtained from the ECL benchmark. It is shown that the HHT is able to successfully extract several non-linear modes whose character correspond to the numerical reference, but which cannot be used to quantify the system parameters due to conclusions made in this paper. The findings highlight that the ability of the HHT to quantify non-linear behaviour using non-linear modes extracted from free decay responses is severely limited, while detection and characterisation of non-linear behaviour in a non-parametric manner is feasible. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to investigate free vibration of a rotating pre-twisted beam with bending-bending-torsion coupling that is axially loaded by a tendon. The tendon is connected to the tip of the beam, passes through its body, and is fixed and loaded at the axis of rotation. Due to their connection, the motion of the beam influences the motion of the tendon and vice versa. The equations of motion of the beam-tendon system are introduced and solved numerically by a combination of a boundary value problem solver and differential quadrature method to obtain the natural frequencies and mode shapes of the system. The numerical implementation is firstly validated against literature for a non-rotating beam-tendon system and a rotating pre-twisted blade. Then, the effect of the tendon on the free vibration of the system is studied for a wide range of loading cases and rotation speeds. From the computed modal characteristics, it is found that the presence of a tendon leads to the frequency shift of beam's natural frequencies as well as frequency loci veering between the beam-dominated and tendon-dominated modes. Both of these effects strongly depend on the beam-tendon rotation speed. • A rotating pre-twisted beam subjected to tendon-induced axial loading is studied. • The coupled beam-tendon system is modelled using partial differential equations. • Free vibration analysis is numerically conducted. • The effect of the tendon on the modal properties is studied for a range of configurations. • The presence of the tendon results in frequency shifts and frequency loci veering. [ABSTRACT FROM AUTHOR]

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. • A beam axially loaded by an eccentrically placed tendon is studied. • A theoretical model of the beam-tendon system is validated using an FE model and experimentally. • The effect of tendon location is shown to have significant effect on modal properties. • Frequency loci veering between beam-dominated and tendon-dominated modes is observed. • The impact of the tendon location on the structural stability is discussed. [ABSTRACT FROM AUTHOR]