Abstracts of Journal Articles - Accepted for Publication


Frictional Effects on the Nonlinear Dynamics of an Overhung Rotor

Authors
E Chipato, AD Shaw & MI Friswell (Swansea University)
Journal
Communications in Nonlinear Science and Numerical Simulation
accepted for publication
Abstract
An overhung rotor model is explored to determine the effect of friction during contact between the rotor and stator. The model has two degrees of freedom with rotor stator contact and the equations of motion are non-dimensionalised. A parametric study of the friction coefficient and eccentricity is conducted and the results displayed on three dimensional bifurcation plots, orbit plots, Poincare maps and spectral intensity plots to classify the solutions. It is shown for the first time that in the presence of friction there are two fundamentally different forms of asynchronous bouncing motion, that can coexist in the same system. Furthermore, the analysis shows that the synchronisation of rotor spin speed, backward whirl (BW) and forward whirl (FW) persists in presence of friction. Also, additionally it was observed from the bifurcation diagram that besides the primary resonance there is a region with high radial displacement; the dominant frequency component was the backward whirling frequency of the stiffened system in this region. The region with backward whirling solutions is seen to expand as the friction coefficient is increased.

Time-Domain Response of Damped Stochastic Multiple-Degree-of-Freedom Systems

Authors
E Jacquelin, D Brizard (Universite Claude Bernard Lyon, France), S Adhikari & MI Friswell (Swansea University)
Journal
Journal of Engineering Mechanics
accepted for publication
Abstract
Characterizing the time-domain response of a random multiple-degree-of-freedom dynamical system is challenging and often requires Monte Carlo simulation (MCS). Differential equations must therefore be solved for each sample, which is time consuming. This is why polynomial chaos expansion (PCE) has been proposed as an alternative to MCS. However, it turns out that PCE is not adapted to simulate a random dynamical system for long-time integration. Recent studies have shown similar issues for the steady-state response of a random linear dynamical system around the deterministic eigenfrequencies. A Pade approximant approach has been successfully applied; similar interesting results were also observed with a random mode approach. Therefore the latter two methods were applied to a random linear dynamical system excited by a dynamic load to estimate the first two statistical moments and the probability density function at a given instant of time. Whereas the random modes method has been very efficient and accurate to evaluate the statistics of the response, the Pade approximant approach has given very poor results when the coefficients were determined in time domain. However, if the differential equations were solved in the frequency domain, the Pade approximants, which were also calculated in the frequency domain, provided results in excellent agreement with the MCS results.

Bidirectional Spiral Pulley Negative Stiffness Mechanism for Passive Energy Balancing

Authors
J Zhang, AD Shaw, MR Amoozgar, MI Friswell (Swansea University) & BKS Woods (University of Bristol)
Journal
Journal of Mechanisms and Robotics
accepted for publication
Abstract
The energy balancing concept seeks to reduce actuation requirements for a morphing structure by strategically locating negative stiffness devices to tailor the required deployment forces and moments. One such device is the spiral pulley negative stiffness mechanism. This uses a cable connected with a pre-tension spring to convert decreasing spring force into increasing balanced torque. The kinematics of the spiral pulley are first developed for bidirectional actuation developed and its geometry is then optimized by employing an energy conversion efficiency function. The performance of the optimized bidirectional spiral pulley is then evaluated through the net torque, the total required energy and energy conversion efficiency. Then, an additional test rig tests the bidirectional negative stiffness property and compares the characteristics with the corresponding analytical result. Exploiting the negative stiffness mechanism is of significant interest not only the field of morphing aircraft, but also in many other energy and power reduction applications.

Conceptual-level Evaluation of a Variable Stiffness Skin for a Morphing Wing Leading Edge

Authors
C Wang, H Haddad Khodaparast, MI Friswell (Swansea University), A Magrini, R Ponza, E Benini (HIT09, Italy), V Landersheim, D Laveuve & C Contell Asins (Fraunhofer Institute for Structural Durability and System Reliability LBF, Germany)
Journal
Journal of Aerospace Engineering
accepted for publication
Abstract
A morphing leading edge produces a continuous aerodynamic surface that has no gaps between the moving and fixed parts. The continuous seamless shape has the potential to reduce drag, compared to conventional devices, such as slats, that produce a discrete aerofoil shape change. However, the morphing leading edge has to achieve the required target shape by deforming from the baseline shape under the aerodynamic loads. In this paper, a conceptual-level method is proposed to evaluate the morphing leading edge structure. The feasibility of the skin design is validated by checking the failure index of the composite when the morphing leading edge undergoes the shape change. The stiffness of the morphing leading edge skin is spatially varied using variable lamina angles, and comparisons to the skin with constant stiffness are made to highlight its potential to reduce the actuation forces. The structural analysis is performed using a two-level structural optimisation scheme. The first level optimisation is applied to find the optimised structural properties of the leading edge skin and the associated actuation forces. The structural properties of the skin are given as a stiffness distribution, which is controlled by a B spline interpolation function. In the second level, the design solution of the skin is investigated. The skin is assumed to be made of variable stiffness composite. The stack sequence of the composite is optimised element-by-element to match the target stiffness. A failure criterion is employed to obtain the failure index when the leading edge is actuated from the baseline shape to the target shape. Test cases are given to demonstrate that the optimisation scheme is able to provide the stiffness distribution of the leading edge skin and the actuation forces can be reduced by using a spatially variable stiffness skin.

Identification of Weak Nonlinearities in MDOF Systems Based on Reconstructed Constant Response Tests

Authors
GB Zhang, CP Zang (Nanjing University of Aeronautics and Astronautics, China) & MI Friswell (Swansea University)
Journal
Archive of Applied Mechanics
accepted for publication
Abstract
A novel strategy to characterize and identify structural nonlinearities in MDOF systems based on reconstructing constant response tests from constant excitation tests is developed in this paper. Constant displacement frequency response functions (FRFs) can be measured by a stepped sine test where the displacement is controlled at every frequency of interest. In these FRFs the nonlinear restoring force is effectively linearized and natural frequencies can be estimated by linear modal analysis. Using a series of constant displacement tests, the relationship of equivalent stiffness versus displacement can be established by curve fitting and hence the nonlinear stiffness characterized. This paper proposes a method to reconstruct the constant displacement FRFs from stepped sine tests with constant excitation; this avoids the requirement to control either the response or force amplitude, leads to a faster and more stable testing programme. Similarly, damping nonlinearities in structures can be characterized and identified by constant velocity tests reconstructed in a similar way. This approach of FRF reconstruction is mathematically simple and suitable for structures with weak nonlinearities. The method is demonstrated on a framed structure with unknown weak nonlinearities, and the nonlinear stiffness and damping parameters of the structure are identified and validated. The results demonstrate the feasibility and effectiveness of the approach, and also show the potential for practical applications in engineering.

A Finite Element Model for the Thermo-Elastic Analysis of Imperfect Functionally Graded Porous Nanobeams

Authors
AI Aria (Tabriz University, Iran), T Rabczuk (Bauhaus University Weimar, Germany) & MI Friswell (Swansea University)
Journal
European Journal of Mechanics / A Solids
accepted for publication
Abstract
In this study, for the first time, a nonlocal finite element model is proposed to analyse thermo-elastic behaviour of imperfect functionally graded porous nanobeams (P-FG) on the basis of nonlocal elasticity theory and employing a double-parameter elastic foundation. Temperature-dependent material properties are considered for the P-FG nanobeam, which are assumed to change continuously through the thickness based on the power-law form. The size effects are incorporated in the framework of the nonlocal elasticity theory of Eringen. The equations of motion are achieved based on first-order shear deformation beam theory through Hamilton's principle. Based on the obtained numerical results, it is observed that the proposed beam element can provide accurate buckling and frequency results for the P-FG nanobeams as compared with some benchmark results in the literature. The detailed variational and finite element procedure are presented and numerical examinations are performed. A parametric study is performed to investigate the influence of several parameters such as porosity volume fraction, porosity distribution, thermal loading, material graduation, nonlocal parameter, slenderness ratio and elastic foundation stiffness on the critical buckling temperature and the nondimensional fundamental frequencies of the P-FG nanobeams. Based on the results of this study, a porous FG nanobeam has higher thermal buckling resistance and natural frequencies compared to a perfect FG nanobeam. Also, the format of the porosity distribution is important, that uniform distributions of porosity result in greater critical buckling temperatures and vibration frequencies, in comparison with functional distributions of porosities.

Experimental Validation of an Impact Off-resonance Energy Harvester

Authors
G Martínez-Ayuso, MI Friswell, H Haddad Khodaparast & S Adhikari (Swansea University)
Journal
European Physical Journal - Special Topics
accepted for publication
Abstract
Most piezoelectric energy harvesting research has focused on developing on-resonance harvesters that work at low frequencies, even though higher frequencies can generate more power. In addition, conventional resonant harvesters have low efficiency when the excitation frequency is away from resonance. Using mechanical impacts has the potential to improve the overall harvested energy since high frequencies are excited during impacts. Also, the presence of impacts reduces the influence of the base excitation frequency and the requirement to exactly match the resonance frequency. To take advantage of the higher frequency response, an impact energy harvester is designed and validated experimentally. The harvester consists of a cantilever beam with a piezoelectric patch attached to its base which impacts with a stiff object. The harvester is modelled using finite element analysis and a Hertzian contact law. The model is tested and validated in the laboratory using an in-house manufactured demonstrator. Good agreement with the experimental data is obtained, setting the basis for future optimisation of the harvester geometry and piezoelectric properties.

Non-conservative Stability Analysis of Columns with Various Loads and Boundary Conditions using Fully Intrinsic Equations

Authors
SA Fazelzadeh, M Tashakorian, E Ghavanloo (Shiraz University, Iran), MI Friswell & MR Amoozgar (Swansea University)
Journal
AIAA Journal
accepted for publication
Abstract
In this paper, the stability analysis of the elastic columns subjected to seven different types of the non-conservative force is investigated on the basis of fully intrinsic beam equations. The generalized differential quadrature method is used for the discretization of the first-order intrinsic equations and corresponding boundary conditions. Altogether, four important boundary conditions, including simply supported, clamped-simply supported, clamped-free and clamped-clamped conditions, are considered. Furthermore, the effect of the combined action of an end- concentrated force and a distributed tangential follower force is investigated. To confirm the validity of the proposed intrinsic formulations, the present results are compared with those obtained from classical formulations. Our results reveal that the fully intrinsic formulation is a suitable framework to model non-conservative problems.

Composite Rotor Blade Twist Modification in Flight by Using a Moving Mass and Stiffness Tailoring

Authors
MR Amoozgar, AD Shaw, J Zhang & MI Friswell (Swansea University)
Journal
AIAA Journal
accepted for publication
Abstract
In this paper, a new concept for morphing composite blades is proposed, and how this concept changes the twist distribution of the blade is explained. A change in the blade twist is obtained by adding a mass to the blade which produces an extra centrifugal force. This centrifugal force then may produce a moment that can change the blade twist via the extension-twist or bend-twist coupling of the composite lamination. These types of couplings are present in anti-symmetrically and symmetrically laminated beams, respectively. The dynamics of the rotating composite blade is modeled by using the geometrically exact fully intrinsic beam equations. The concentrated mass is considered as a non-structural concentrated mass which has offsets with respect to the beam reference line. The nonlinear partial differential equations are discretized by using a time-space scheme, and the converged results are compared with those reported in the literature and very good agreement is observed. It is found that for an antisymmetric lamination, the spanwise location of the concentrated mass affects the twist while in the symmetric case the chordwise position of the concentrated mass is the source of twist change. It is also found that introducing the concentrated mass to a real blade can change the twist dramatically.