Embedding negative structures to model holes and cut-outs

It has now been established that geometric boundary conditions and continuity conditions can be modelled by using either positive or negative stiffness or inertia type penalty term [1-5]. The experience of working with negative stiffness and inertial parameters has led to the question: what if both stiffness and mass were to be taken as negative? Changing the sign of all stiffness and inertial terms of a structure is simply equivalent to multiplying both sides of an eigenvalue equation by minus one, which does not change its frequencies or modes. Basically, a negative structure in such a sense has the same vibratory properties as that of its positive counterpart, although the structure itself may not have a physical meaning

An intelligent hammer: a novel concept for automating nail and pile driving

Some interesting novel ideas on how the compliance needs of manipulators may be met by changing the stiffness of a structure have been presented in a paper by Ang and Andeen [1]. The purpose of the present note is to outline a novel concept for another variable-stiffness mechanism that may be useful in automating the process of driving nails or piles

The use of pseudo-inertia in asymptotic modelling of constraints in boundary value problems

In recent publications, the validity of using positive and negative inertial penalty parameters and the advantage of this approach over the conventional positive penalty function approach have been established for linear eigenvalue problems. This paper shows how this method may be applied to solve a boundary value problem. A steady-state 2-D heat transfer problem is used to demonstrate the method. First, the governing partial differential equation is modified by adding a pseudo-inertial term that results in an equation, which is mathematically identical to the equation governing the free vibration of a membrane. The essential boundary conditions of zero temperature along a specified line are imposed using inertial penalty parameters. The characteristic vibration modes found in this way are used to generate the complementary function to the heat transfer problem. This solution satisfies all natural boundary conditions (adiabatic) and zero temperature conditions using the inertial penalty parameter. To satisfy any additional temperature distribution imposed on the system, two sets of corrector terms are superimposed resulting in the final solution. The results are compared with constrained solutions obtained using the Lagrangian multiplier method and the ordinary penalty method

Transient vibration analysis of a completely free plate using modes obtained by Gorman's superposition method

This paper shows that the transient response of a plate undergoing flexural vibration can be calculated accurately and efficiently using the natural frequencies and modes obtained from the superposition method. The response of a completely free plate is used to demonstrate this. The case considered is one where all supports of a simply supported thin rectangular plate under self weight are suddenly removed. The resulting motion consists of a combination of the natural modes of a completely free plate. The modal superposition method is used for determining the transient response, and the natural frequencies and mode shapes of the plates used are obtained by Gorman's superposition method. These are compared with corresponding results based on the modes using the Rayleigh–Ritz method using the ordinary and degenerated free–free beam functions. There is an excellent agreement between the results from both approaches but the superposition method has shown faster convergence and the results may serve as benchmarks for the transient response of completely free plates

Vibration Behaviour Of In-plane Loaded Thin Rectangular Plates With Initial Geometrical Imperfections

The effect of in-plane loading on the natural frequencies of simply supported thin rectangular plates with initial geometrical imperfection is investigated theoretically and experimentally. It is shown that the natural frequencies depend on applied in-plane load, initial geometrical imperfection and the in-plane boundary conditions.;In the theoretical analysis, the natural frequencies, out-of-plane static displacements and in-plane stress distribution are calculated using the Rayleigh-Ritz minimization technique. A concept of \u27connection coefficients\u27 has been used to reduce the computational work. In this concept, the relationship between the out-of-plane and in-plane displacement coefficients are first determined by solving the equations resulting from the minimization of the total potential energy with respect to the in-plane displacement coefficients. This relationship is then substituted into the equations obtained by minimizing the total potential energy with respect to the out-of-plane displacement coefficients.;In the experimental side of the work, tests were carried out on several thin (thickness ranging from 0.56 mm to 1.15 mm) mild steel plates (300 mm x 250 mm). Uniaxial in-plane loading was applied through two \u27V\u27 grooved edge beams. The other two edges were supported between two rows of ball bearings placed in \u27V\u27 grooves, carefully adjusted to minimize the friction along these edges.;The agreement between the measured and calculated values of natural frequencies, out-of-plane central displacements and static strain distribution is very good. An interesting observation from the result is that a simple approximate linear relationship between a load-frequency parameter (involving the fundamental natural frequency and the state of in-plane stress) and the square of the central deflection is obtained. Further experimental and theoretical work in this field is strongly recommended

A passively adaptive screwdriver: a novel concept for controlling off-diagonal stiffness

A concept for an automated screw driving mechanism is presented. The proposed mechanism has a self-adjusting axial stiffness that depends on the torsional resistance against screwing. It delivers a greater axial thrust when the torsional resistance is greater, for example, towards the final stage of a screwing operation

On the bipenalty method: why is it advantageous to add stiffness and mass

In a recent paper, Askes et al [1] proposed the simultaneous use of stiffness and inertia of large magnitude to model constraints in time domain analysis. From a frequency domain perspective, as stiffness and inertia have opposite effects on the natural frequencies, this seems counter-intuitive. With increasing stiffness, the natural frequencies either increase or remain unchanged, whereas the opposite is true for inertia. However, it can be shown, through very simple illustrative examples, that the natural frequencies and modes of continuous systems can be found in this way, and that there are advantages in using both stiffness and mass simultaneously

Periodicity in Volcanic Gas Plumes: A Review and Analysis

Persistent non-explosive passive degassing is a common characteristic of active volcanoes. Distinct periodic components in measurable parameters of gas release have been widely identified over timescales ranging from seconds to months. The development and implementation of high temporal resolution gas measurement techniques now enables the robust quantification of high frequency processes operating on timescales comparable to those detectable in geophysical datasets. This review presents an overview of the current state of understanding regarding periodic volcanic degassing, and evaluates the methods available for detecting periodicity, e.g., autocorrelation, variations of the Fast Fourier Transform (FFT), and the continuous wavelet transform (CWT). Periodicities in volcanic degassing from published studies were summarised and statistically analysed together with analyses of literature-derived datasets where periodicity had not previously been investigated. Finally, an overview of current knowledge on drivers of periodicity was presented and discussed in the framework of four main generating categories, including: (1) non-volcanic (e.g., atmospheric or tidally generated); (2) gas-driven, shallow conduit processes; (3) magma movement, intermediate to shallow storage zone; and (4) deep magmatic processes

Theoretical Basis of assembling structures in the Rayleigh Ritz Method

The use of negative structures in modelling cavities was discussed in previous symposia [1-3]. A formal proof that the use of negative structures to remove corresponding positive structural components in calculating natural frequencies has been established for discrete systems. This approach introduces extra spurious modes and methods of identifying and eliminating these modes have also been studied for the same. However, a corresponding proof for continuous systems, and its application poses some challenges. The focus of. this paper is on these challenges

Transient degassing events at the lava lake of Erebus volcano, Antarctica: Chemistry and mechanisms

We report here on the chemical signature of degassing at Erebus lava lake associated with intermittent explosions and the return to passive conditions. Explosions caused by bubble bursts were frequent during the 2013 field season, providing the first opportunity to observe such activity since 2005-2006. Several of the explosions were captured by multiple instruments including an open-path Fourier transform infrared spectrometer. Explosive bubble bursts and other transient degassing events are associated with gas compositions that are distinct from the usual range of passive degassing compositions. We set out to compare the chemical signature of explosive degassing during the 2005-06 and 2013 episodes, and to characterise the chemistry of gases emitted during the period of lake refilling after explosions. We found little change in the explosive gas chemistry between 2005-06 and 2013, suggesting reactivation of a common mechanism of gas segregation. Bubbles can be distinguished by their size and composition, the ranges of which are likely modified during ascent by gas-melt interaction and adiabatic expansion. The proportions of water, SO2, and HCl in the emitted gas plume increase during the refill of the lake after explosions, as the lake is recharged by a combination of magma that has already partially degassed, and that vesiculates rapidly in response to the drop in magmastatic pressure at the lake.TI acknowledges doctoral grants from the AXA Research Fund and the William Georgetti trust. Fieldwork was carried out with the support of the G-081 Erebus team and the US Antarctic Program, funded by NSF grant ANT1142083. The original FTIR retrieval code was written by Mike Burton with modifications made by Georgina Sawyer. Thermal IR images and lake velocity data were supplied by Nial Peters. Support was also received from grant 202844 from the European Research Council under the European FP7 and the NERC Centre for the Observation and Modelling of Earthquakes, Volcanoes and Tectonics (COMET), part of the NERC-funded National Centre for Earth Observation (http://comet.nerc.ac.uk/).This is the final version. It first appeared at http://www.sciencedirect.com/science/article/pii/S2214242815000327