Vol. 2, No. 4 (2018): Regular Issue

Targeted energy transfer, presented in two-dimensional wing coupled with two Nonlinear Energy Sinks (NESs) under freestream, is studied numerically, it is feasible to partially or even completely suppress aeroelastic instability by passively transferring vibration energy from the wing to the NES in a one-way irreversible fashion, and the relationship between the vibration suppression and Targeted Energy Transfer (TET) of the system is analyzed in detail. First, the model of the coupling system, which includes heave and pitch motions, is presented, and the NESs are located at the leading edge and trailing edge (NES1 and NES2) separately. Then, the vibrations suppressed by NESs are also investigated from the viewpoint of energy transfer etc., and the Resonance Captures (RCs) in the nonlinear coupling system are studied using spectrum analysis. Furthermore, the ensuing TET through the modes of wing (Heave and Pitch) and the NESs are discussed in detail. The results show that the NESs could absorb and dissipate a significant portion of energy fed from the flow to the wing, and the NESs could absorb the energy from every single motion of the wing, and the TET and RCs between modes can be more available in the coupling system. Therefore, the TET is more efficient between the wing and NESs, and it leads to the increase of the critical velocity of freestream under which the nonlinear vibration of the wing can be suppressed by NESs effectively.

The power density theory is an alternate description of fatigue failure. It is derived from the concept of power density, which is physically equivalent to the amount of power deposited into a unit volume of the material experiencing dynamic loading. Power density results from changes in stress magnitude over time. All the stress alterna- tions that occur across a broad bandwidth of frequencies contribute to the accumulation of power density. Higher frequencies coupledwith faster changes in stress contribute more power density. Once this accumulation reaches a threshold – a fundamental property of the material – it is expected to fail by fatigue. The power density based methodology is applied to properly interpret the multiaxial vi- bration fatigue test results reported by Mršnik, Slavič and Boltežar [15] using computer simulations. This serves as a feasibility study for the approach, as well as an example of how to apply it. The power density response of the system is analyzed, and the failure locations are predicted for each of the ten load cases that are considered. The predicted failure locations are in excellent agreement with the exper- imental results. Further examination of the approach would result in a better understanding of fatigue failure, thus improving engineering work across many industries.

In this article, the dynamics of a spinning shaft during spin-up/down operation, is examined analytically, around the equilibrium points. The system of equations of motion of a spinning shaft with non- constant rotating speed has no linear part therefore the equilibri- um points are rather essential. In the first instance, the equilibrium points of the original system are determined. A restricted system is obtained by neglecting the rigid body angular position of the shaft, and the equilibrium manifold with its’ bifurcations is defined. It is shown that this manifold, is formed by the backbone curve of the nonlinear normal modes which are associated with the rigid body angular motions of the spinning shaft. It is shown that all the equilibrium points of the original and the restricted system are degenerate. The original and restricted systems have been linearized around the equilibrium points, and examination of their stability through the eigenvalues of the Jacobian matrix showed that there are centres and unstable regions. Then, the frequencies and initial conditions of the normal modes of the linearized system around the equilibrium points are determined with the associated analytical solutions. The comparison of analytical with numerical results shows very good agreement, noting that the linearization around equilibrium is valid only for very small perturbations. This work is essential for understanding critical situations in the dynamics of the spinning shaft during spin-up/down operation, based on the associated normal modes. The stability analysis of the spinning shaft can be used further to identify regions with chaotic attractors, which should be considered for normal operation. Finally, considering other rotating structures with non-constant rotating speed, the equations of motion are similar to those of a spinning shaft. Therefore, the approach that is followed in this article can be considered as more general, and could be applied in all rotating structures during spin-up/down, and expecting similar results.

In this paper, the analytical solutions of independent period-m evolutions (m=3;5;7;9) of chemical concentrations in a periodically forced Brusselator are obtained through the generalized harmonic balance method. Stability and bifurcation of independent periodic evolutions are determined through eigenvalue analysis. The nonlinear frequency-amplitude characteristics of independent periodic evolutions are discussed. To illustrate the analytical solutions, numerical simulations of stable and unstable period-m evolutions (m = 3;5;7;9) are presented herein. The harmonic amplitude spectrums give an approximate estimation of harmonic effects on analytical solutions of periodic motions.

In this study, a simple, effective damage detection approach is proposed for truss structures to locate damage onto exact member(s) using vibration responses. First, a parameter that reflects the axial strain in truss members and is sensitive to local damage is proposed. This parameter is called the member axial-strain mode shape and can be extracted from the translational mode shapes. Each component in an member axial-strain mode shape is associated with a member, reflecting the axial strain in that member. Because damage to a member directly affects the axial strain in that member, the proposed member axial-strain mode shape is an effective parameter for evaluating the condition of truss members. Second, a damage indicator constructed by both member axial- strain mode shapes and natural frequencies are proposed. Experimental tests are conducted on a full-scale sign support truss to demonstrate the effectiveness of the proposed approach. The results illustrate that the proposed approach can be applied to truss structures instrumented with a few accelerometers and using only response data.