Nonlocal nonlinear mechanics of imperfect carbon nanotubes

In this article, for the first time, a coupled nonlinear model incorporating scale influences is presented to simultaneously investigate the influences of viscoelasticity and geometrical imperfections on the nonlocal coupled mechanics of carbon nanotubes; large deformations, stress nonlocality and strain gradients are captured in the model. The Kelvin-Voigt model is also applied in order to ascertain the viscoelasticity effects on the mechanics of the initially imperfect nanoscale system. The modified coupled equations of motion are then derived via the Hamilton principle. A solution approach for the derived coupled equations is finally developed applying a decomposition-based procedure in conjunction with a continuation-based scheme. The significance of many parameters such as size parameters, initial imperfections, excitation parameters and linear and nonlinear damping effects in the nonlinear mechanical response of the initially imperfect viscoelastic carbon nanotube is assessed. The present results can be useful for nanoscale devices using carbon nanotubes since the viscoelasticity and geometrical imperfection are simultaneously included in the proposed model

Motion limiting nonlinear dynamics of initially curved beams

An initially curved beam is considered and its motion is constrained using two elastic constraints; the corresponding non-smooth nonlinear transverse dynamics is investigated for the first time. A clamped-clamped beam with one axially movable end is modelled via Bernoulli-Euler beam theory together with the inextensibility condition, giving rise to nonlinear inertial terms along with nonlinear geometric terms. Furthermore, the damping is modelled via Kelvin-Voigt internal damping model. The proposed model is verified for linear and nonlinear behaviours via comparison to a finite element model. The impact between beam and constraints is incorporated via calculating its work contribution. The nonlinear equation of motion is derived while incorporating geometric, damping, inertial, and constraints nonlinearities. A series of spatial basis functions together with corresponding vibration modes are used as the proposed solution of the transverse displacement. A modal discretisation is performed via the weighted-residual method of Galerkin and the corresponding non-smooth terms are kept intact while conducting numerical integration. A numerical continuation technique is utilised to solve the resultant equations. The non-smooth response is obtained for various cases and the effects of several parameters are studied thoroughly

Extremely large dynamics of axially excited cantilevers

The nonlinear parametric resonance of a cantilever under axial base excitation is examined while capturing extremely large oscillation amplitudes for the first time. A geometrically exact model is developed for the cantilever based on the Euler-Bernoulli beam theory and inextensibility condition. In order to be able to capture extremely large oscillation amplitudes accurately, the equation of motion is derived for centreline rotation while keeping trigonometric terms intact. The developed model is verified for the static case through comparison to a three-dimensional nonlinear finite element model. The internal energy dissipation model of Kelvin-Voigt is used to model the system damping in large amplitudes more accurately. The Galerkin modal decomposition scheme is utilised for discretisation procedure while keeping the trigonometric terms intact. It is shown that in parametric resonance region, the oscillation amplitudes grow extremely large even for smallest possible amplitudes of the base excitation, which highlights the significant importance of employing a geometrically exact model to examine the parametric resonance response of a cantilever

Extremely large-amplitude dynamics of cantilevers under coupled base excitation

Extremely large-amplitude nonlinear dynamics of a cantilever with a mass at the tip under coupled base excitations is examined for the first time. An exact model of the centreline rotation of the cantilever is developed capable of accurately predicting the cantilever dynamic response even at extremely large amplitudes; a nonlinear static finite element analysis is conducted to verify the accuracy of the proposed model at very large deflection amplitudes. The proposed model is based on the theory of Euler-Bernoulli and the internal damping model of Kelvin-Voigt; the centreline of the cantilever is assumed to remain inextensible. The proposed model for the cantilever centreline rotation is discretised via the Galerkin modal decomposition method while keeping all terms exact. Extensive numerical simulations are conducted to examine the primary and parametric resonance of the cantilever due to transverse and axial base excitations, respectively. It is shown that under the same axial and transverse amplitudes of excitation, the parametric resonance is much stronger than the primary resonance

Nonlinear broadband performance of energy harvesters

Broadband nonlinear energy harvesting capabilities of a parametrically excited bimorph piezoelectric energy harvester is investigated for the first time. The performance of the energy harvester is significantly enhanced via use of stoppers and an added tip mass in conjunction with parametric excitation. A fully nonlinear electromechanical model of the energy harvester was developed using beam theory of Euler-Bernoulli and the coupled constitutive equations for piezoelectric materials, with the motion constraints modelled as nonlinear springs. A multi-modal discretisation was conducted utilising the Galerkin scheme; the resultant set of equations was examined numerically through use of continuation technique. It is shown that a resonance bandwidth of 46% (normalised with respect to parametric resonance frequency) is achieved which is almost 10 times the resonance bandwidth of the system without any constraints

Experimentally validated geometrically exact model for extreme nonlinear motions of cantilevers

A unique feature of flexible cantilevered beams, which is used in a range of applications from energy harvesting to bio-inspired actuation, is their capability to undergo motions of extremely large amplitudes. The well-known third-order nonlinear cantilever model is not capable of capturing such a behaviour, hence requiring the application of geometrically exact models. This study, for the first time, presents a thorough experimental investigation on nonlinear dynamics of a cantilever under base excitation in order to capture extremely large oscillations to validate a geometrically exact model based on the centreline rotation. To this end, a state-of-the-art in vacuo base excitation experimental set-up is utilised to excite the cantilever in the primary resonance region and drive it to extremely large amplitudes, and a high-speed camera is used to capture the motion. A robust image processing code is developed to extract the deformed state of the cantilever at each frame as well as the tip displacements and rotation. For the theoretical part, a geometrically exact model is developed based on the Euler–Bernoulli beam theory and inextensibility condition, while using Kelvin–Voigt material damping. To ensure accurate predictions, the equation of motion is derived for the centreline rotation and all terms are kept geometrically exact throughout the derivation and discretisation procedures. Thorough comparisons are conducted between experimental and theoretical results in the form of frequency response diagrams, time histories, motion snapshots, and motion videos. It is shown that the predictions of the geometrically exact model are in excellent agreement with the experimental results at both relatively large and extremely large oscillation amplitudes

Aeromechanical Analysis of a Complete Wind Turbine Using Nonlinear Frequency Domain Solution Method

The high-fidelity computational fluid dynamics (CFD) simulations of a complete wind turbine model usually require significant computational resources. It will require much more resources if the fluid-structure interactions between the blade and the flow are considered, and it has been the major challenge in the industry. The aeromechanical analysis of a complete wind turbine model using a high-fidelity CFD method is discussed in this paper. The distinctiveness of this paper is the application of the nonlinear frequency domain solution method to analyse the forced response and flutter instability of the blade as well as to investigate the unsteady flow field across the wind turbine rotor and the tower. This method also enables the aeromechanical simulations of wind turbines for various inter blade phase angles in a combination with a phase shift solution method. Extensive validations of the nonlinear frequency domain solution method against the conventional time domain solution method reveal that the proposed frequency domain solution method can reduce the computational cost by one to two orders of magnitude

Numerical Investigation of the Effect of Flutter Instability of the Blade on the Unsteady Flow in a Modern Low-Pressure Turbine

Modern aeronautical Low-Pressure Turbines (LPTs) are prone to aeroelastic instability problems such as flutter. The aerodynamic performance of a modern LPT is often influenced by the interaction between the transient flow and the dynamic behaviour of the blade. Therefore, the investigation and understanding of the physics behind the interaction between the unsteady flow and the flutter phenomenon of the blade in an LPT, which is normally left out by existing studies, is an important aspect of the research to improve the aerodynamic performance of the turbine as well as to ensure the blade mechanical integrity. In this paper, a novel analysis is conducted to explore the flutter instability in a modern LPT, T106A turbine, using two inter blade phase angles (IBPAs), and their effects on the unsteady flow field are investigated. The zero degree and 180 degrees IBPAs are considered in this paper. A high-fidelity direct numerical simulation method is used for the flow simulations. Another distinctive feature of this paper is the use of the 3D model to analyse the effects associated with the 3D blade structure and the 3D vibration mode. The investigation and identification of adequate working ranges of the harmonic balance method, which has been widely used for the aeromechanical analysis of turbomachines, are also presented in this work. This paper will bridge a key gap in the knowledge of aeroelasticity modelling and analysis of modern LPTs

Viscoelastically coupled mechanics of fluid-conveying microtubes

In this paper, the complex viscoelastically coupled global mechanics of fluid-conveying microtubes is examined for the first time. The externally excited microtube is assumed to be embedded in a nonlinear elastic medium. A scale-dependent theoretical model is presented with consideration of curvature nonlinearity within the context of the modified version of the couple stress theory (CST). According to Hamilton's energy/work principle, the coupled nonlinear equations of fluid-conveying microscale tubes are presented. Both the transverse and longitudinal displacements and inertia are taken into account in the continuum-based model and numerical calculations. In order to discretise the governing nonlinear differential equations, Galerkin's weighted-residual procedure is employed. The bifurcation characteristics of the fluid-conveying microsystem with clamped-clamped boundary conditions are obtained within the framework of a direct time-integration procedure. It is found that the complex global dynamics of the fluid-conveying microsystem is very sensitive to the speed of the flowing fluid

Efficient Broadband Vibration Energy Harvesting Using Multiple Piezoelectric Bimorphs

This paper presents complete nonlinear electromechanical models for energy harvesting devices consisting of multiple piezoelectric bimorphs (PBs) connected in parallel and series, for the first time. The proposed model is verified against available experimental results for a specific case. The piezoelectric and beam constitutive equations and different circuit equations are utilized to derive the complete nonlinear models for series and parallel connections of the PBs as well as those of piezoelectric layers in each bimorph, i.e., four nonlinear models in total. A multi-modal Galerkin approach is used to discretize these nonlinear electromechanical models. The resultant high-dimensional set of equations is solved utilizing a highly optimized and efficient numerical continuation code. Examining the system behavior shows that the optimum load resistance for an energy harvester array of 4 PBs connected in parallel is almost 4% of that for the case with PBs connected in series. It is shown an energy harvesting array of 8 PBs could reach a bandwidth of 14 Hz in low frequency range, i.e., 20–34 Hz. Compared with an energy harvester with 1 PB, it is shown that the bandwidth can be increased by more than 300% using 4 PBs and by more than 500% using 8 PBs. Additionally, the drawbacks of a multi-PB energy harvesting device are identified and design enhancements are proposed to improve the efficiency of the device