N. Popplewell

Performance of the bean bag impact damper for a sinusoidal external force

Abstract The performance of a resilient bean bag and a conventional rigid impact damper are compared for sinusoidal external forces. The bean bag damper is not only a better attenuator of the resonant displacement of a lightly damped oscillator but the contact forces and the noise generated by collisions are also reduced. Two semi-empirical approaches are detailed to predict the dynamic behaviour of this new damper. They both produce quite accurate forecasts of the steady displacement of the oscillator. The deformation of the bean bag itself, however, is less predictable due to its sensitivity to the contact forces.

Stable periodic motions of an impact-pair

Abstract The asymptotically stable motion of two rigid masses separated by a clearance is formulated most generally when the masses collide periodically. Predictions are shown to agree satisfactorily with comprehensive experimental results. Difficulties encountered in the practical application of this and similar stability theories are discussed with the help of empirical data. A technique is proposed for determining a clearances dimensions in situ which could provide a basis for detecting progressive wear in mechanisms like gear trains.

Finite element modelling of transmission line galloping

A computationally efficient, finite element idealization is presented to analyse galloping, which is characterized by large amplitude vibrations of iced, multi-span, electrical transmission lines. A three-node, isoparametric cable element having three translational and a torsional degree-of-freedom at each node is developed to model a conductor. Support insulator strings and remote conductor spans are represented by linear static springs. A transmission lines interactions with a support tower are modelled through the towers equivalent stiffness at the conductors suspension point. An expedient time marching scheme is developed to obtain the envelope of galloping. The scheme can be utilized to integrate dynamic equilibrium equations involving not only geometric and material nonlinearities but also nonlinear damping. Time integration is performed in the sub-space to minimize computational effort. The finite element model has been employed to successfully simulate field galloping records. It is shown that it is necessary to consider a multi rather than a single span for a conservative estimate of the galloping amplitudes to enable sufficient clearances to be designed between adjacent conductors.

Stable periodic vibroimpacts of an oscillator

Abstract The asymptotically stable vibrations of a loaded oscillator colliding periodically with a rigid mass are described. Comparison of the numerical results with the few existing examples is encouraging but inconclusive. Better overall agreement is demonstrated with fairly comprehensive measurements from a specially built experimental rig. Impact motions are shown to be very sensitive to small fluctuations in the clearance between masses and the stiffness and loading of the oscillator near its linear, or collisionless, resonant frequency. The rigid mass is quite an effective damper at or just above this frequency condition.

GEOMETRIC NONLINEAR STATIC ANALYSIS OF CABLE SUPPORTED STRUCTURES

Abstract A numerically efficient procedure is presented for generating the stiffness of a parabolic, three-node finite element for the static, nonlinear analysis of three-dimensional cable-supported structures. Numerical computations are minimized by explicitly evaluating the large deformation stiffness matrix with respect to global coordinates while avoiding incompatibilities with existing, displacement-based elements. Representative improvements are illustrated by using three typical geometrically nonlinear, cable supported structures. Also, an efficient method is presented to evaluate the self weight profile of a pretensioned inclined cable.

Repeated impacts on a sinusoidally vibrating table reappraised

The traditional simplification for one commonly used example of repeated collisions is shown to be frequently erroneous for a wide range of coefficients of restitution. Bounded errors arise from an artificial speed constraint whose circumvention is largely but not exclusively unpredictable. Therefore exact equations, whose periodic solutions are detailed, should be generally used.

A critical appraisal of the elimination technique

For large dynamic structural problems, condensation techniques used in conjunction with appropriately sophisticated finite elements should best balance the often conflicting requirements of accuracy, problem size and computer economy. This balance is investigated for Irons Elimination Technique, a particular type of condensation which appears attractive for linear and especially non-linear transient problems requiring direct step-by-step integration. Information is generated to improve, geneialize and possibly automate inadequate criteria presently forming the basis for elimination. It is demonstrated that the often implicitly assumed success of the Elimination Technique relative to original idealizations generally cannot be guaranteed and even eliminations successful in free vibrations may not reflect the advantages in transient problems. The main advantage could be in very complex problems where elimination may retain a systems characteristics better than the skilled lumping of components often necessary with coarse grids.

Three-dimensional steady state Green function for a layered isotropic plate

The elastodynamic response of a layered isotropic plate to a source point load having an arbitrary direction is studied in this paper. A decomposition technique is developed within each homogeneous isotropic lamina to simplify the general three-dimensional plane-wave propagation problem as a separate plane-strain problem and an anti-plane-wave propagation problem. The accuracy of computation is assured by cross-checking the numerical results by different methods. Results are checked numerically for a vertical point load acting on a homogeneous and a layered plate by using a hybrid method. On the other hand, results are checked for a horizontal point load by using dynamic reciprocal identities. Results are presented for both a homogeneous as well as a layered plate.

Combined effects of early reflections and background noise on speech intelligibility

Abstract An experiment, similar to the one devised by Lochner and Burger to find the integration characteristics of the ear, was performed in an anechoic chamber. The experiment was conducted in the absence of any disturbing background noise at a speech level approaching the threshold of hearing (22 dB(A) re 20 μPa). It is concluded that, under these conditions, the ear integrates reflections fully as described by Lochner and Burger. An experiment is presented which demonstrates the differences in speech intelligibility scores that occur when different speakers are employed. Further experiments were performed to investigate the combined effects of a single early reflection and the background noise level on speech intelligibility. The tests were conducted at speech levels of 35 dB(A), 45 dB(A) and 55 dB(A) for signal to noise ratios of −5, 0 and +5 dB. It was found that under these more realistic speech and noise levels a single reflection is no longer integrated fully. It appears that a reflection becomes more useful as its delay time is reduced to 0 ms. Also, the usefulness of a reflection is directly dependent on the background noise level. A further experiment revealed that, as for a single reflection, the ear does not fully integrate multiple reflections in the presence of background noise. Some of the implications of these findings are considered.

The vibration of a box-type structure I. Natural frequencies and normal modes☆

Abstract The free vibrations of a box-type structure have been investigated using rectangular finite elements. It was found that, for the same number of elements, the element with four unknown displacements per nodal point gave far more accurate results than the element with three unknowns. Then the natural frequencies of several boxes with openings were computed in order to demonstrate the flexibility of the finite element method.