Rotating composite beams and blades have a wide range of applications in various engineering structures such as wind turbines, industrial fans, and steam turbines. Therefore, proper understanding of such structures is of a great importance. As a result, the behavior of rotating composite beam structures has received a lot of attention. This paper presents a comprehensive review of scholarly articles about rotating composite beams as published in the past decades. The review addresses analytical, semi-analytical and numerical studies dealing with dynamical problems involving adaptive/smart/intelligent materials (e.g. piezoelectric materials, electrorheological fluids, shape memory alloys, etc.), damping and vibration control, advanced composite materials (e.g. functionally graded materials and nanocomposites), complicating effects and loadings (e.g. added mass, tapered beams, initial curve and twist, etc.), and experimental methods. Moreover, the influence of Vlasov or restrained warping, out-of-plane warping, transverse shear, arbitrary cross-sectional geometry, trapeze phenomena, swept tip, size-dependent effect, as well as other areas that have been considered in research, are reviewed in depth. The review concludes with a presentation of the remaining challenges and future research needs.

Dynamics, vibration and control of rotating composite beams and blades: A critical review

Graphene nanostrips with single or few layers can be used as bending resonators with extremely high sensitivity to environmental changes. In this paper we report molecular dynamics (MD) simulation results on the fundamental and secondary resonant frequencies f of cantilever graphene nanostrips with different layer number n and different nanostrip length L . The results deviate significantly from the prediction of not only the Euler–Bernoulli beam theory ( f ∝ nL −2 ), but also the Timoshenko's model. Since graphene nanostrips have extremely high intralayer Young's modulus and ultralow interlayer shear modulus, we propose a multibeam shear model (MBSM) that neglects the intralayer stretch but accounts for the interlayer shear. The MBSM prediction of the fundamental and secondary resonant frequencies f can be well expressed in the form f − f mo n o ∝[( n –1)/ n ] b L −2(1− b ) , where f mono denotes the corresponding resonant frequency as the layer number is 1, with b =0.61 and 0.77 for the fundamental and secondary resonant modes. Without any additional parameters fitting, the prediction from MBSM agrees excellently with the MD simulation results. The model is thus of importance for designing multilayer graphene nanostrips based applications, such as resonators, sensors and actuators, where interlayer shear has apparent impacts on the mechanical deformation, vibration and energy dissipation processes therein.

The interlayer shear effect on graphene multilayer resonators

Piezoelectric bimorph cantilevered beams are often used as energy harvesting devices. These devices are desired for, among other applications, remote sensing and animal tracking due to their potential for eliminating the need for battery replacement. Existing models of piezoelectric bimorph cantilevered beams have proved to describe the dynamics of slender beams at high frequencies accurately. In this paper, a Timoshenko model of transverse piezoelectric beam vibration is developed to address these limitations. Exact expressions for the voltage, current, power, and tip deflection of the piezoelectric beam are derived. Subsequently, several case studies are presented that examine the frequency response of vibration-based energy harvesters using this model. It is shown that the predicted responses converge towards previously derived Euler–Bernoulli beam models under certain limiting conditions. The Timoshenko model shows that the Euler–Bernoulli model severely over-predicts the tip displacement and consequently the power transduction of a cantilevered piezoelectric bimorph at low length-to-width aspect ratios.

/pdf/a-timoshenko-beam-model-for-cantilevered-piezoelectric-3l6zlok2pj.pdf

A Timoshenko beam model for cantilevered piezoelectric energy harvesters

Analytical predictions of natural frequencies of cracked simply supported beams with a stationary roving mass

Piezoelectric materials are excellent candidates for use in energy harvesting applications due to their high electromechanical coupling properties that enable them to convert input mechanical energy into useful electric power. The electromechanical coupling coefficient of the piezoelectric material is one of the most significant parameters affecting energy conversion and is dependent on the piezoelectric mode of operation. In most piezoceramics, the d15 piezoelectric shear coefficient is the highest coefficient compared to the commonly used axial and transverse modes that utilize the d33 and the d31 piezoelectric strain coefficients. However, complicated electroding methods and challenges in evaluating the performance of energy harvesting devices operating in the shear mode have slowed research in this area. The shear deformation of a piezoelectric layer can be induced in a vibrating sandwich beam with a piezoelectric core. Here, a model based on Timoshenko beam theory is developed to predict the electric power output from a cantilever piezoelectric sandwich beam under base excitations. It is shown that the energy harvester operating in the shear mode is able to generate ~50% more power compared to the transverse mode for a numerical case study. Reduced models of both shear and transverse energy harvesters are obtained to determine the optimal load resistance in the system and perform an efficiency comparison between two models with fixed and adaptive resistances.

http://iopscience.iop.org/article/10.1088/0964-1726/24/5/055005/pdf

Piezoelectric energy harvesting through shear mode operation

Free vibration of Timoshenko beam with finite mass rigid tip load and flexural–torsional coupling

/pdf/nonlinear-dynamic-response-of-an-accelerating-composite-2j7k3i1qdj.pdf

Nonlinear dynamic response of an accelerating composite rotor blade using perturbations

In this paper, a theoretical investigation of nonlinear vibrations of a 2 degrees of freedom system when subjected to saturation is studied. The method has been especially applied to a system that consists of a DC motor with a nonlinear controller and a harmonic forcing voltage. Approximate solutions are sought using the method of multiple scales. It is shown that the closed-loop system exhibits different response regimes. The nature and stability of these regimes are studied and the stability boundaries are obtained. The effects of the initial conditions on the response of the system have also been investigated. Furthermore, the second-order solution is presented and the corresponding results are compared with those of the first-order solution. It is shown that by increasing the amplitude of the excitation voltage, the higher-order term in the solution becomes significant and causes a drift in the response. In order to verify the obtained theoretical results, they are compared with the corresponding numerical results. Good agreement between the two sets of results is observed.

Control of a Nonlinear System Using the Saturation Phenomenon

Application of saturation to provide active nonlinear vibration control was introduced not long ago. Saturation occurs when two natural frequencies of a system with quadratic nonlinearities are in a ratio of around 2:1 and the system is excited at a frequency near its higher natural frequency. Under these conditions, there is a small upper limit for the high-frequency response and the rest of the input energy is channeled to the low-frequency mode. In this way, the vibration of one of the degrees of freedom of a coupled 2 degrees of freedom system is attenuated. In the present paper, the effect of dry friction on the response of a system that implements this vibration absorber is discussed. The system is basically a plant with a permanent magnet DC (PMDC) motor excited by a harmonic forcing term and coupled with a quadratic nonlinear controller. The absorber is built in electric circuitry and takes advantage of the saturation phenomenon. The method of multiple scales is used to find approximate solutions. Various response regimes of the closed-loop system as well as the stability of these regimes are studied and the stability boundaries are obtained. Especial attention is paid on the effect of dry friction on the stability boundaries. It is shown that while dry friction tends to shrink the stable region in some parts, it enlarges other parts of the stable region. To verify the theoretical results, they have been compared with numerical solution and good agreement between the two is observed.

Nonlinear Vibration Control of a System with Dry Friction and Viscous Damping Using the Saturation Phenomenon

Noise and vibration is a major issue in helicopters. Active and passive control systems have been used in attempts to reduce these effects. This paper presents a system for the active control of a rotor blade anhedral tip flap with the intention of reducing noise due to Blade Vortex Interaction (BVI). In the experiments, the flap hinge is represented by a shaft and actuated by Shape Memory Alloy (SMA) wires. Closed-loop control of the angular position of the shaft is accomplished first with a single SMA wire, and next with two antagonistic SMA wires. The results of these experiments are presented and discussed. To get a rough approximation of the number of SMA wires that are required, the aerodynamic loads imposed at the anhedral tip flap are estimated by a one dimensional analysis. The setup is then modeled using the SMA constitutive and transformation equations as well as the equations of equilibrium of the whole system. The resulting system of nonlinear equations is solved using a fixed point solution method. The close agreement between the output of the simulations and the corresponding experimental results demonstrates the validity of the model.

Mehrdaad Ghorashi

Papers

Free vibration of Timoshenko beam with finite mass rigid tip load and flexural–torsional coupling

Nonlinear dynamic response of an accelerating composite rotor blade using perturbations

Control of a Nonlinear System Using the Saturation Phenomenon

Nonlinear Vibration Control of a System with Dry Friction and Viscous Damping Using the Saturation Phenomenon

On the use of shape memory alloy wires for anhedral angle control in helicopter rotor blades