摘要:

AbstractThe incremental harmonic balance method has been successful for harmonic excitation. It is extended to determine the steady‐state solutions of a non‐linear oscillator subject to periodic (two‐harmonic) excitation. Higher‐order subharmonic solutions result from bifurcations. As the bifurcation process continues in an accelerated rate, chaotic solutions are obtained when no simple subharmonic solution coexists. When periodic solutions do coexist, the final steady‐state solution depends on the initial conditions. The evolution of the amplitude against the system parameters can be recorded on a bifurcation graph. An initial bifurcation graph is constructed when one of the system parameters varies. Neighbouring bifurcation graphs when other system parameters are changing are obtained in an incremental manner. If only the boundaries dividing the qualitatively different solutions are constructed, a parametric diagram is obtained. The characteristic of the solutions can be read directly from the diagram. For an oscillator subject to two‐harmonic excitation, the parametric diagram is found to be qualitatively different from those with one‐harmonic excitation. The parametric diagram is highly foliated when many stable and unstable higher‐order subharmonic solutions coexist at the same time under some combination of conditions. It is possible that the periodic solutions disappear suddenly and give way to chaotic solutions due to a small change in the system parameters without undergoing

ISSN:0748-8025    

DOI:10.1002/cnm.1630060802

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractA straightforward extension of the return mapping algorithm forJ2‐plasticity at finite strains to a non‐associative Drucker‐Prager yield criterion, assuming elastic volumetric response, is presented. It is shown that the concept of plastic incompressibility, assumed at the outset, does not hold for a certain range of str

ISSN:0748-8025    

DOI:10.1002/cnm.1630060803

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractA multi region boundary‐element method is employed to study the scattering of time‐harmonic waves by cracks in a three‐dimensional elastic solid. Special shape functions are employed to model the near‐crack singularity. The multi region formulation enables removal of singularities from all boundary integral equations. The matter of fictitious eigenfrequencies is discussed and resolved. Values of dynamic stress intensity factors for three problems involving penny‐shaped cracks are compared with results of other inve

ISSN:0748-8025    

DOI:10.1002/cnm.1630060804

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractTurbulent flows around aerofoils and wings are simulated by solving the two‐and three‐dimensional Navier‐Stokes equations in quadrilaterals and hexahedrons, respectively. Turbulent flow is described by an algebraic eddy viscosity model. Boundary‐conforming O‐and O‐Otype meshes are generated by the transfinite interpolation method. The finite‐volume technique is employed for spatial discretization using two cells in each computational co‐ordinate direction more than the conventional approach to evaluate the viscous fluxes. An explicit three‐stage Runge–Kutta scheme is used for time integration. The method is applied to compute turbulent transonic flow over the NACA 0012 aerofoil and the ONERA M6 wing. The results are compared with experimental and

ISSN:0748-8025    

DOI:10.1002/cnm.1630060805

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThis paper is concerned with the numerical solution of kinematically non‐linear shell problems using approximate techniques. The interest is focused on shells of revolution, for which a technique proposed by Nagy and König has been implemented and assessed by means of numerical studies. The non‐linear path is approximated using a reduced basis of buckling modes. The results illustrate that reasonable estimates of moderately non‐linear paths can only be expected for cases in which the fundamental path is governed by membrane

ISSN:0748-8025    

DOI:10.1002/cnm.1630060806

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractA numerical technique is proposed for solving two‐dimensional transient wave propagation problems. The technique involves the use of the combination of a transform (such as Fourier, sine, cosine) for one space variable and the method of characteristics. Because of its inclusion of the latter method in the analysis, the proposed technique is capable of describing the sharp variations of the disturbances which may occur in the neighbourhood of wave fronts. In the study, an example problem is presented which involves transient waves in an elastic layer generated by out‐ofplane shear stresses acting on its top surface. The formulation of the example problem is kept general in the sense that the variations of the applied shear tractions in the horizontal direction of the layer and in time are kept arbitrary. In the analysis, the Fourier transform is used for the horizontal co‐ordinate. The numerical results are obtained and presented for the uniform strip loading case. The assessment of the proposed technique is made by obtaining the results for the case in which the width of the strip load is very large compared to the height of the layer, and by comparing them with exact ones. It is found that the proposed technique yields the results which compare very well with the exact ones and that it is capable of describing the sharp variations at the wave f

ISSN:0748-8025    

DOI:10.1002/cnm.1630060807

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractIn modal analysis of damping systems, the criteria matrix of damping ratios is of importance for both experiments in identification of structure parameters and theoretical analysis of assessing dynamical response. In a single degree of freedom system, the damping ratio can be defined easily and obtained by some simple calculations. So the vibration response envelope can be predicted, which is important for passive isolation and active control of vibration in dynamical design. Likewise, in a multiple degree of freedom system, the concept can be defined similarly to the single degree of freedom,1while it involves complicated manipulations and calculations to obtain the damping ratio matrix in terms of mass, damping and stiffness matrices. Some available stimulating references have discussed the damping ratio matrix and presented some alternative criteria matrices.1–4However, the final formula to evaluate the damping ratios is quite complex and it needs several eigensolutions. If the mass matrix is formed by uniform interpolation to the stiffness, the calculations are even greater than that in the state space calculating eigensolutions directly. Regarding these, a new approach is presented in this paper in terms of modal parameters to calculate the damping ratio matrix. Therefore, the damping ratio matrix takes the parallel form to the single degree of freedom system, and the calculations are greatly reduced. Further, the paper also discusses the case of incomplete sets of eigenpairs, which is of practical importance since for most large structures the complete eigensolution is either unnecessary or computer‐timeconsuming and inaccurate for higher modes; in finite‐element modelling only lower‐order Ritz vectors or even static deformation modes in normal cases are e

ISSN:0748-8025    

DOI:10.1002/cnm.1630060808

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

ISSN:0748-8025    

DOI:10.1002/cnm.1630060809

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

ISSN:0748-8025    

DOI:10.1002/cnm.1630060801

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY