Heat propagation due to torsional vibration of shafts

Torsional vibration of rotating shafts can yield substantial temperatures in the shaft due to heat generated from material damping. It has been recently observed that such a situation in electric generators can lead to insulation failures and machine outages. In the study reported here forced torsional vibration is assumed, and both lumped mass and continuous systems are considered. The hysteretic model for material damping is used to yield the heat generation in the elastic deformation range and an elastoplastic material is assumed in the plastic range. The heat conduction equation is solved for a cylindrical shaft with surface cooling. Closed form solutions and expressions for the maximum temperatures and the maximum surface temperatures are obtained and tabulated for design purposes. It is shown that substantial temperatures can develop in shafts undergoing torsional vibration.     

Exact transient vibration of stepped bars, shafts and strings carrying lumped masses

A new analytical method is developed for transient vibration analysis of stepped systems composed of distributed components like elastic bars, flexible shafts and taut strings, and lumped masses. The method, with a distributed transfer function formulation and a residue formula for inverse Laplace transform, gives the exact transient response of a stepped system with any number of components and subject to arbitrary external, boundary and initial excitations. The proposed method does not depend on system eigenfunctions, is able to accurately predict jumps in stress and strain distributions, and is numerically efficient as its utility only requires simple operations of two-by-two matrices.     

Normal vibration frequencies of two- and three-dimensional arrays of alternating point masses

Normal vibration frequencies are calculated for alternating point-masses of mass M and m in two-dimensional rectangular and a three-dimensional parallelepiped arrays. The method of intermediate co-ordinate transformation is used in the analysis. In applying this method, the vibrating systems consisting of alternating masses are treated as the basic systems of linear chains of identical point-masses of mass m (the zero-order system) that are coupled together to form the two- and three-dimensional systems and then further modified by inclusion of an additional mass ?m at alternating sites, where M = (1 + ?)m. The zero-order solution for the linear array of identical particles of mass m is well known. The present calculation shows the advantage of the process of intermediate co-ordinate transformation in simplifying problems which are otherwise complicated and also illustrates how such a process can be applied in more than one successive step.     

Critical velocity of flexible shafts with concentrated masses and intermediate supports

The present paper deals with the analysis of whirling of flexible shafts, taking into account the presence of a concentrated mass and intermediate supports. It is shown that the Rayleigh-Schmidt approach is an extremely useful tool for this type of problem also, in view of its inherent simplicity and good engineering accuracy.     

Bounds for frequencies of rib reinforced plates

Rigorous upper and lower bounds are presented for the frequencies of vibration of a thin elastic plate reinforced by an elastically attached rib. This study has two purposes: the first is to indicate how a method for lower bounds can be applied to simple built-up structures and the second is to demonstrate the effectiveness of the method in a relatively easy but useful application.     

Bounds on particle masses in the Weinberg-Salam model

Various conditions necessary for the self-consistency of the Weinberg-Salam model are used to place constraints on fermion and Higgs Boson masses. We find that spontaneous symmetry breakdown cannot generate fermion masses in excess of about 300 GeV.     

Influence of the torsional vibration of the periodically attached perpendicular beam resonator on the flexural band of a Euler-Bernoulli beam

The bending and torsional vibration of the periodic perpendicular cantilever beam-mass resonators (PCBMR) is idealized as translational and rotational oscillators attached to the main beam. In this paper, the effect of that torsional vibration of the PCBMR on the dynamics of an infinitely long Euler-Bernoulli beam is evaluated. The band-structure is explored by implementing the transfer matrix method in conjunction with Bloch-Floquet's theorem. The combination of the translational and rotational oscillator modifies the relative position of the coupling coefficient in the transfer matrix, which plays a pivotal role in the band-gap formation. The flexural band-structure is highly sensitive to the torsional vibration while the radius of gyration of the tip mass is considerably higher than the length of the PCBMR. Ill-tuning leads to split and reduction of attenuation band to 50%; whereas, around 38% elongation of the attenuation band in the low frequency regime can be achieved by proper tuning.     

Bounds on the number and masses of quarks and leptons

We assume weak, electromagnetic and strong interactions to be asymptotically divergent, and to become strong at very large energies, of the order of the Plank mass. In this picture, the “low-energy” couplings (i.e. in the 10² GeV region) must be near the infrared stable point, and this allows us to put bounds on the number of elementary fermions (quarks and leptons). Similar assumptions on the Higgs couplings give bound on the fermion and on the Higgs boson masses. We consider the cases where weak and electromagnetic interactions are described by the gauge groups SU(2) ? U(1) or SU(2)_R ? U(1). The weak neutral current mixing angle is computed in both cases.     

A precision optoelectronic system for monitoring torsional vibrations of turbine drive shafts

A precision optoelectronic system for monitoring torsional vibrations of the drive shaft of a powerful turbine unit and a technique for carrying out measurements by a single detector are described. The results of operation of the monitoring system on a 350 MW-power turbine unit over a year of observations are considered.     

Minimum weight design of beams in torsional vibration with several frequency constraints

The design of beams of cantilever form carrying and end inertia so as to minimize the total mass subject to the constraint that one, two or three of its torsional natural frequencies are fixed at specified values is considered. The problem is stated in variational form with the constraints introduced through Lagrange multipliers. The problem is taken analytically as far as possible and reduces to a set of first order non-linear differential equations. These are integrated numerically. The known solutions for less constrained problems are used as a basis from which to iterate to the required solutions. Optimum profiles and tables of numerical data computed for various examples are given.     

Bounds on fourth-generation fermion masses in the standard model

In the standard model, if the ratios of Yukawa couplings to gauge couplings are bounded functions of the renormalization point, then the fourth-generation fermion massesm _U , m _D , andm _L (in GeV) are constrained to lie within a domain approximately given by (m _U /213)^4.8+(m _D /209)^4.8+(m _L /161)^2.4<1.     

The high frequency, transient response of a panel with attached masses

The general, high-frequency response of a panel with attached masses is approximated using a transient form of asymptotic modal analysis (AMA). This method is derived by applying asymptotic simplifications to classical solutions in both the time and frequency domains. These relations are applied to a panel with one or more attached masses that is excited by impulsive loads. Predictions are made of the mean-squared, transverse displacement histories as well as localized responses near the added masses. It is shown that the latter compare well with experimental data when the masses are separated by more than the mean wavelength of the frequency band. The approximate solutions are shown to require relatively little computational time and memory and are applicable to general forms of excitation.     

Optimization of orthotropic distributed-mode loudspeaker using attached masses and multi-exciters

Based on the orthotropic model of the plate, the method to optimize the sound response of the distributed-mode loudspeaker (DML) using the attached masses and the multi-exciters has been investigated. The attached masses method will rebuild the modes distribution of the plate, based on which multi-exciter method will smooth the sound response. The results indicate that the method can be used to optimize the sound response of the DML.     

Coupled bending and torsional vibration of a beam with in-span and tip attachments

In this paper, the coupled flexural-torsional free and forced vibrations of a beam with tip and/or in-span attachments are studied. First, a mathematical model is established, which consists of a beam with several tip attachments, i.e, a tip mass of non-negligible dimensions, a linear spring grounding the tip mass, and a torsional spring connected at the end of the beam. The modal functions of this model and the orthogonality condition among them are derived. For the purpose of verification the properties of the tip attachments are changed, and the numerical results obtained are compared with those given in the relevant literature. Effects of tip mass and distributed mass in-span on natural frequencies and modes are investigated for two cantilever beams with different cross sections. An application of the orthogonality condition in the case of a beam with tip mass is also presented for a forced vibration example.     

Free vibration of two elastically coupled rectangular plates with uniform elastic boundary restraints

An analytical method is derived for determining the vibrations of two plates which are generally supported along the boundary edges, and elastically coupled together at an arbitrary angle. The interactions of all four wave groups (bending waves, out-of-plane shearing waves, in-plane longitudinal waves, and in-plane shearing waves) have been taken into account at the junction via four types of coupling springs of arbitrary stiffnesses. Each of the transverse and in-plane displacement functions is expressed as the superposition of a two-dimensional (2-D) Fourier cosine series and several supplementary functions which are introduced to ensure and improve the convergence of the series representation by removing the discontinuities that the original displacement and its derivatives will potentially exhibit at the edges when they are periodically expanded onto the entire x-y plane as mathematically implied by a 2-D Fourier series. The unknown expansions coefficients are calculated using the Rayleigh-Ritz procedure which is actually equivalent to solving the governing equation and the boundary and coupling conditions directly when the assumed solutions are sufficiently smooth over the solution domains. Numerical examples are presented for several different coupling configurations. A good comparison is observed between the current results and the FEA models. Although this study is specifically focused on the coupling of two plates, the proposed method can be directly extended to structures consisting of any number of plates.     

A shape memory alloy-based tunable phononic crystal beam attached with concentrated masses

Shape memory alloys (SMAs) in phononic crystals (PCs) or metamaterials mostly serve as smart inserts or local resonators to generate tunable bandgaps for other structures. In this letter, we address the method for creating tunable bandgaps in structures made of SMA. Specifically, we consider concentrated masses, realized by steel balls, as attachments on a SMA. To provide a design guideline, we derived the closed-form bandgap formula of the proposed SMA PC beam. As the bandgap order increases, the coefficient of the nth Bragg bandgap width decreases. In addition, the practical final beam enlarges bandgap edges than ideally infinite PCs or metamaterials. Our experimental results on the PC beam with different sizes of the steel ball arrays agree with the analytical predictions of the bandgap behaviors. With the bandgaps formed by the steel balls and the shape memory effect, wide tunability of the bandgaps are achieved on the SMA beam.     

Bounds on the masses of neutral generation-changing gauge bosons

The existence of several generations of quarks and leptons suggests the possibility of a gauge symmetry connecting the different generations. The neutral gauge bosons of such a scheme would mediate rare processes such as K_L⁰→μ^±, K⁺→π⁺e^?π⁺, μN→eN and would contribute to ΔM(K_S⁰?K_L⁰). We study these and other processes within a simple theoretical framework and derive bounds involving the masses and coupling constants of the generation-changing gauge bosons and various generation-mixing angles. The lower bounds for the relevant masses lie in the 10–100 TeV region. Various remarks concerning the relevance of these bounds to currently popular theoretical ideas and to future experiments are presented.