Steady-state coupling vibration analysis of shaft–disk–blade system with blade crack

Nonlinear Dynamics - Rotating shaft–disk–blade (RSDB) system is one of the most important parts of turbomachinery, such as aero-engine, gas turbine and power plant. The coupling...     

Nonlinear flexural–torsional dynamic analysis of beams of variable doubly symmetric cross section—application to wind turbine towers

In this paper, a boundary element solution is developed for the nonlinear flexural–torsional dynamic analysis of beams of arbitrary doubly symmetric variable cross section, undergoing moderate large displacements, and twisting rotations under general boundary conditions, taking into account the effect of rotary and warping inertia. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading in both directions and to twisting and/or axial loading. Four boundary-value problems are formulated with respect to the transverse displacements, to the axial displacement, and to the angle of twist and solved using the Analog Equation Method, a Boundary Element Method (BEM) based technique. Application of the boundary element technique yields a system of nonlinear coupled Differential–Algebraic Equations (DAE) of motion, which is solved iteratively using the Petzold–Gear Backward Differentiation Formula (BDF), a linear multistep method for differential equations coupled with algebraic equations. Numerical examples of great practical interest including wind turbine towers are worked out, while the influence of the nonlinear effects to the response of beams of variable cross section is investigated.     

Principal resonance bifurcation of bending–torsion coupling of aero-engine compressor blade with assembled clearance under lateral displacement excitation of rotor shaft

The principal resonance of bending–torsion coupling of a compressor blade with an assembled clearance and a cubic structural nonlinearity, subjected to the lateral displacement excitation of rotor shaft and aerodynamic loads, is analyzed to explore the topology transformation of amplitude–frequency response along with the changes of the physical parameters. The bifurcation equation of the first-order principal resonance response is derived from using the averaging method. The transition set and the bifurcation figures of the response solution are obtained by the singularity theory. The effects of the main physical parameters of the system on the topology transformation of amplitude–frequency response are discussed.     

Nonlinear dynamic stability analysis of Euler–Bernoulli beam–columns with damping effects under thermal environment

In this study, a unified nonlinear dynamic buckling analysis for Euler–Bernoulli beam–columns subjected to constant loading rates is proposed with the incorporation of mercurial damping effects under thermal environment. Two generalized methods are developed which are competent to incorporate various beam geometries, material properties, boundary conditions, compression rates, and especially, the damping and thermal effects. The Galerkin–Force method is developed by implementing Galerkin method into force equilibrium equations. Then for solving differential equations, different buckled shape functions were introduced into force equilibrium equations in nonlinear dynamic buckling analysis. On the other hand, regarding the developed energy method, the governing partial differential equation for dynamic buckling of beams is also derived by meticulously implementing Hamilton’s principles into Lagrange’s equations. Consequently, the dynamic buckling analysis with damping effects under thermal environment can be adequately formulated as ordinary differential equations. The validity and accuracy of the results obtained by the two proposed methods are rigorously verified by the finite element method. Furthermore, comprehensive investigations on the structural dynamic buckling behavior in the presence of damping effects under thermal environment are conducted.     

Nonlinear characteristics of a multi-degree-of-freedom wind turbine’s gear transmission system involving friction

Nonlinear Dynamics - In this study, a 42-degree-of-freedom (42-DOF) translation–torsion coupling dynamic model of the wind turbine’s compound gear transmission system considering...     

Finite element analysis of functionally graded plates for coupling effect of extension and bending

In this paper, the coupling effect of extension and bending in functionally graded plate subjected to transverse loading for Kirchhoff-Love plate theory equations is studied. The material properties of the FG plates are assumed to vary continuously throughout the thickness direction of the layer according to sigmoid distribution of the volume fractions of constituents. The two plate functionals are used which are developed by Gateaux differential and potential operator concept. A layer wise, isoparametric, mixed finite element approach was used and results of two different quadrilateral elements, one considering the membrane forces and the other one not, were compared by an analytical study. Finally, for different composition profiles the effect of variations of the Young’s moduli and of variations volume fraction index to dimensionless displacement, strain and stress values are studied.     

Nonlinear stability analysis of the Bénard problem for fluids with a convex nonincreasing temperature depending viscosity

A nonlinear energy stability analysis of the onset of convection for fluids with viscosity convex nonincreasing function of temperature, is performed. It is shown that condition assuring linear stability, assures nonlinear (conditional) asymptotic stability too.     

Dynamical stability in a delayed neural network with reaction–diffusion and coupling

Nonlinear Dynamics - In this paper, a delayed neural network with reaction–diffusion and coupling is considered. The network consists of two sub-networks each with two neurons. In the first...     

Stochastic response of an axially loaded composite Timoshenko beam exhibiting bending–torsion coupling

A spectral finite element method is proposed to investigate the stochastic response of an axially loaded composite Timoshenko beam with solid or thin-walled closed section exhibiting bending–torsion materially coupling under the stochastic excitations with stationary and ergodic properties. The effects of axial force, shear deformation (SD) and rotary inertia (RI) as well as bending–torsion coupling are considered in the present study. First, the damped general governing differential equations of motion of an axially loaded composite Timoshenko beam are derived. Then, the spectral finite element formulation is developed in the frequency domain using the dynamic shape functions based on the exact solutions of the governing equations in undamped free vibration, which is used to compute the mean square displacement response of axially loaded composite Timoshenko beams. Finally, the proposed method is illustrated by its application to a specific example to investigate the effects of bending–torsion coupling, axial force, SD and RI on the stochastic response of the composite beam.     

Flutter analysis of a viscoelastic tapered wing under bending–torsion loading

The dynamic stability of a tapered viscoelastic wing subjected to unsteady aerodynamic forces is investigated. The wing is considered as a cantilever tapered Euler–Bernoulli beam. The beam is made of a linear viscoelastic material where Kelvin–Voigt model is assumed to represent the viscoelastic behavior of the material. The governing equations of motion are derived through the extended Hamilton’s principle. The resulting partial differential equations are solved via Galerkin’s method along with the classical flutter investigation approach. The developed model is validated against the well-known Goland wing and HALE wing and good agreement is obtained. Different solution methods, namely; the k method, the p-k method, and the flutter determinant method are compared for the case of elastic wing. However, when the viscoelastic damping is introduced, the k and p-k methods become less effective. The flutter determinant method is modified and employed to carry out non-dimensional parametric study on the Goland wing. The study includes the effects of parameters such as the taper ratio, the density ratio, the viscoelastic damping of wing structure and many other parameters on the flutter speed and flutter frequency. The study reveals that a tapered wing would be more dynamically stable than a uniform wing. It is also observed that the viscoelastic damping provides wider stability region for the wing. The investigation shows that the density ratio, bending-to-torsion frequency ratio, and the radius of gyration have significant effects on the dynamic stability of the wing. Based on the obtained results, a wing with an elastic center and inertial center that are located closer to the mid-chord would be more dynamically stable.     

Energy expressions and free vibration analysis of a rotating Timoshenko beam featuring bending�Cbending-torsion coupling

In this study, free vibration analysis of a uniform, rotating, cantilever Timoshenko beam featuring bending?Cbending-torsion coupling is performed. To the best of the authors?? knowledge, there is no explicit formulation in open literature for rotating Timoshenko beams featuring bending?Cbending-torsion coupling. Therefore, in this study, derivation of the kinetic and the potential energy expressions for the mentioned beam model is carried out in a detailed way by using several explanatory tables and figures. The parameters for the hub radius, rotational speed, rotary inertia, shear deformation and bending?Cbending-torsion coupling are incorporated into the energy expressions. The governing differential equations of motion are obtained by applying the Hamilton??s principle to the derived energy expressions and solved using an efficient mathematical technique, called the differential transform method. The natural frequencies are calculated, and comparisons are made with the results in open literature. Consequently, it is observed that there is a good agreement between the results, which validates the accuracy of the derived formulation and the built beam model.     

Stroh-like formalism for the coupled stretching–bending analysis of composite laminates

Due to the two-dimensional nature of thin plates, the lamination theory considering the composite laminates with in-plane and plate bending problems coupling each other is treated in this paper by using complex variable formulation. By following the steps of Stroh formalism for two-dimensional linear anisotropic elasticity, a displacement complex variable formalism developed by the other researchers was introduced and re-derived in a different but more Stroh-like way. In addition, a brand-new mixed formalism (mixed use of displacements and stresses as basic functions) is established to compensate the displacement formalism. In order to transfer all the related formulae and mathematical techniques of the Stroh formalism to these two formalisms, the general solutions for the basic equations of lamination theory and their associated eigenrelations have been purposely arranged in the form of Stroh formalism. Moreover, by using the presently developed mixed formalism, the explicit expressions for the fundamental matrix and eigenvectors are obtained first time for the most general composite laminates. Furthermore, letting the coupling stiffness vanish, the formalism has been reduced to the case of symmetric laminates and checked by a recently developed Stroh-like formalism for the plate bending problems. The comparison between Stroh formalism for two-dimensional problem, Stroh-like formalism for plate bending problem, displacement formalism and mixed formalism is then made at the end of this paper, and through their connection some useful relations are obtained.     

Nonlinear model updating of frictional structures through frequency–energy analysis

Nonlinear Dynamics - Recently, some researchers have suggested using frequency–energy representations of nonlinear normal modes (NNMs) for nonlinear model updating of conservative systems....     

New augmented Lyapunov–Krasovskii functional approach to stability analysis of neural networks with time-varying delays

This paper is concerned with the problem of stability analysis for neural networks with time-varying delays. By constructing a newly augmented Lyapunov functional and some novel techniques, delay-dependent criteria to guarantee the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). The improvement of feasible region of the proposed criteria comparing with the previous works is shown by two numerical examples.     

Nonlinear coupling of transverse modes of a fixed–fixed microbeam under direct and parametric excitation

Tuning of linear frequency and nonlinear frequency response of microelectromechanical systems is important in order to obtain high operating bandwidth. Linear frequency tuning can be achieved through various mechanisms such as heating and softening due to DC voltage. Nonlinear frequency response is influenced by nonlinear stiffness, quality factor and forcing. In this paper, we present the influence of nonlinear coupling in tuning the nonlinear frequency response of two transverse modes of a fixed–fixed microbeam under the influence of direct and parametric forces near and below the coupling regions. To do the analysis, we use nonlinear equation governing the motion along in-plane and out-of-plane directions. For a given DC and AC forcing, we obtain static and dynamic equations using the Galerkin’s method based on first-mode approximation under the two different resonant conditions. First, we consider one-to-one internal resonance condition in which the linear frequencies of two transverse modes show coupling. Second, we consider the case in which the linear frequencies of two transverse modes are uncoupled. To obtain the nonlinear frequency response under both the conditions, we solve the dynamic equation with the method of multiple scale (MMS). After validating the results obtained using MMS with the numerical simulation of modal equation, we discuss the influence of linear and nonlinear coupling on the frequency response of the in-plane and out-of-plane motion of fixed–fixed beam. We also analyzed the influence of quality factor on the frequency response of the beams near the coupling region. We found that the nonlinear response shows single curve near the coupling region with wider width for low value of quality factor, and it shows two different curves when the quality factor is high. Consequently, we can effectively tune the quality factor and forcing to obtain different types of coupled response of two modes of a fixed–fixed microbeam.

     

On the use of bend–twist coupling in full-scale composite marine propellers for improving hydrodynamic performance

Marine propellers are designed to work for a particular operating condition. However, a propeller often requires to operate at different off-design conditions, when its hydrodynamic efficiency drops. In this paper, a comprehensive numerical study is presented on the use of bend–twist coupling of composite propeller blades for improving their hydrodynamic efficiency at off-design conditions. The analysis is carried out on a full-scale propeller of diameter 4.2 m, considering the complete viscous turbulent flow, as the loading and deformation of model propellers that have been typically studied in literature for this purpose cannot be extrapolated to a full-scale prototype propeller. The open water performance is estimated using the finite volume method employing the pressure based RANS equation for the steady, incompressible, turbulent flow. The deformation analysis is done using the finite element method based on the first order shear deformation theory for composite laminates. The fluid–structure interaction is incorporated in an iterative manner. The effect of laminate configurations on the maximum twist achieved in the blade is studied for four different composite materials. The numerical study reveals that, within the limits of material safety, the twist generated in the deformed propeller using commonly used composite materials is inadequate to create any noticeable change in the hydrodynamic efficiency. When the material failure is ignored, however, it is possible to generate sufficient deformation and twist that can cause appreciable improvement in the hydrodynamic performance.     

Identification of physical nonlinearities of a hybrid aeroelastic–pressure balance

Nonlinear Dynamics - This study has presented an improved method for determining physical nonlinearities of weakly nonlinear spring-suspension system and successfully applied to a novel hybrid...     

Nonlinear dynamic analysis of a parametrically excited vehicle–bridge interaction system

Nonlinear Dynamics - In this paper, a nonlinear supported Euler–Bernoulli beam under harmonic excitation coupled to a 2 degree of freedom vehicle model with cubic nonlinear stiffness and...