Whirling of a forced cantilevered beam with static deflection. III: Passage through resonance

Nonstationary excitations of slender, elastic, cantilevered beams with equal principal moments of inertia are considered. The excitation frequency is slowly increased or decreased through a resonance of the first mode at a constant rate. Three resonances are investigated: primary resonance, superharmonic resonance of order two and subharmonic resonance of order two. After application of Galerkin's method with three modes, the nonlinear, nonstationary response of the first mode of the beam is determined by two methods: integration of the modulation equations obtained from the method of multiple scales, and direct numerical integration of the temporal equations of motion. Time histories are presented and the effects of excitation amplitude, rate of acceleration or deceleration through resonance, damping and initial conditions of the disturbance on the maximum response are studied. The effect of a persistent random disturbance is also examined. Although the excitation acts in the vertical plane, whirling occurs if the beam is subjected to out-of-plane disturbances.     

Large oscillations of beams and columns including self-weight

Large-amplitude, in-plane beam vibration is investigated using numerical simulations and a perturbation analysis applied to the dynamic elastica model. The governing non-linear boundary value problem is described in terms of the arclength, and the beam is treated as inextensible. The self-weight of the beam is included in the equations. First, a finite difference numerical method is introduced. The system is discretized along the arclength, and second-order-accurate finite difference formulas are used to generate time series of large-amplitude motion of an upright cantilever. Secondly, a perturbation method (the method of multiple scales) is applied to obtain approximate solutions. An analytical backbone curve is generated, and the results are compared with those in the literature for various boundary conditions where the self-weight of the beam is neglected. The method is also used to characterize large-amplitude first-mode vibration of a cantilever with non-zero self-weight. The perturbation and finite difference results are compared for these cases and are seen to agree for a large range of vibration amplitudes. Finally, large-amplitude motion of a postbuckled, clamped–clamped beam is simulated for varying degrees of buckling and self-weight using the finite difference method, and backbone curves are obtained.     

Development of City Transport System and Two-wheel Vehicles

Based on the study on the city transport systems of some typical cities worldwide, this paper put forward that each city transport system has its own development mode, which is influenced by the city development plan, economic development level, traveling vehicle composition etc.. When some problems occur, such as the congestions caused by contradiction between the road capacity and vehicle composition, the city transport system may come into temporary maturity period. If the improvement for road system is limited meanwhile, optimized structure of vehicle composition should be an effective solution in this case. With the development of economy-internationalization, the development speed of city transport modernization is rapid. When traveling easiness is conflicting with efficiency, the advantages of public transport system become more obvious. Correspondingly, the superiority of two-wheel vehicles will reappear. Though the important function of two-wheel vehicles for alleviating city traffic problems i     

Non-linear oscillations of an inextensible, air-inflated, cylindrical membrane

A long cylindrical membrane, attached to a horizontal base along two generators and inflated with air, is considered. The material is assumed to be inextensible and its weight is neglected, so that the equilibrium shape of the cross section is circular. Two-dimensional non-linear oscillations about this equilibrium configuration are investigated. Galerkin's method is applied, first with one term and then with two terms. The method of multiple scales is utilized to study weakly non-linear motions, and the equation of motion is also integrated numerically. The results of these two methods are compared for various cases. It is seen that the vibration frequencies tend to decrease as the amplitude of the motion increases.     

Restrictions on the cluster decay multiplicity distribution in the independent cluster emission model due to crossing symmetry and isospin invariance

We discuss multiparticle production in high energy proton-proton scattering under the assumption that all produced secondaries are pions. We take into account the pion isospin but neglect the isospin of the protons. In the first part of the paper it is shown that the multiplicity distribution of the independent cluster emission model can be derived from a unitary, crossing symmetric, isospin invariant, impact parameter model. This part is a straight forward generalization of a previous work where similar results were obtained for isospin-zero mesons. In the second part of the paper we shall discuss the restrictions on the cluster decay multiplicity distribution due to crossing symmetry in the meson variables and to isospin invariance. In particular, we shall derive a non-trivial lower bound for the dispersion of the charged particles in the cluster decay multiplicity distribution.     

The effects of various parameters on an aeroelastic optimization problem

The optimal design of a panel flutter problem is investigated in this paper. A semi-infinite flat panel with either a homogeneous or sandwich cross section is considered. The thickness distribution of the panel is allowed to vary while the total weight is held fixed, and the distribution which maximizes the critical flutter parameter for stability is chosen as the optimal design. This design is calculated here by means of a generalized Ritz procedure, with the panel thickness assumed to have a certain form. Variations in the following parameters are then considered: a minimum allowable thickness, aerodynamic damping, in-plane loading, and nonstructural stiffness and mass for the case of a sandwich panel. It is shown that the optimal design may be significantly affected by changes in these parameters.     

A study of QCD scaling violations by direct resolution of Altarelli-Parisi type equations

We present a detailed study of scaling violations for non-singlet, singlet and glue distribution functions in the framework of several approximation schemes of QCD. Our formalism consists of direct resolution of the Altarelli-Parisi type equations and leads to a simple exponential form for the function q(x, Q²). This form is very suitable for the analysis of experimental data and for the exploration of different evolution schemes. In particular, we examine the implications on the QCD scaling parameter Λ and the gluon parameter n_G.     

Graphene growth on h-BN by molecular beam epitaxy

The growth of single layer graphene nanometer size domains by solid carbon source molecular beam epitaxy on hexagonal boron nitride (h-BN) flakes is demonstrated. Formation of single-layer graphene is clearly apparent in Raman spectra which display sharp optical phonon bands. Atomic-force microscope images and Raman maps reveal that the graphene grown depends on the surface morphology of the h-BN substrates. The growth is governed by the high mobility of the carbon atoms on the h-BN surface, in a manner that is consistent with van der Waals epitaxy. The successful growth of graphene layers depends on the substrate temperature, but is independent of the incident flux of carbon atoms.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.