Rayleigh-Lamb Waves in an Elastic Plate With Voids

1987 ◽  
Vol 54 (3) ◽  
pp. 509-512 ◽  
Author(s):  
D. S. Chandrasekharaiah

Rayleigh-Lamb waves in a homogeneous and isotropic linear elastic plate containing a distribution of vacuous pores (voids) are studied. Assuming that the plate is of uniform thickness and that its faces are stress-free, it is found that the waves move, in general, in two uncoupled families, of which one is symmetrical with respect to the midplane of the plate and the other antisymmetrical; each of these families is affected by the presence of voids. If the plate is thin and the frequency is small, the voids influence only the symmetric waves and, because of this influence, the waves propagate slower than their classical counterparts. If the plate thickness and the frequency are large, each of the two families degenerates into two uncoupled waves; one of these is a classical Rayleigh wave and the other is a new wave not encountered in the classical theory.

Author(s):  
Shi Yan ◽  
Binbin He ◽  
Naizhi Zhao

Pipeline structure may generate damages during its service life due to the influence of environment or accidental loading. The damages need to be detected and repaired if they are severe enough to influence the transportation work. Non-destructive detection using smart materials combined with suitable diagonal algorithms are widely used in the field of structural health monitoring (SHM). Piezoelectric ceramics (such as Lead Zirconate Titanate, PZT) is one of the smart materials to be applied in the SHM due to the piezoelectric effect. So far, the PZT-based wave method is widely used for damage detection of structures, in particular, pipeline structures. A series of piezoelectric patches are bonded on the surface of the pipeline structure to monitor the damages such as local crack or effective area reduction due to corrosion by using diagonal waves. The damage of the pipeline structure can be detected by analysis of the received diagonal waves which peak value, phase, and arriving time can be deferent from the health ones. The response of the diagonal wave is not only correlated to the damage location through estimation of the arrival time of the wave peak, but also associated with the peak value of the wave for the reduction of wave energy as the guided wave passing through the damages. Therefore, the presence of damages in the pipeline structure can be detected by investigating the parameter change of the guided waves. The change of the wave parameters represents the attenuation, deflection and mode conversion of the waves due to the damages. In addition, the guided wave has the ability of quick detecting the damage of the pipeline structure and the simplicity of generating and receiving detection waves by using PZT patches. To verify the proposed method, an experiment is designed and tested by using a steel pipe bonded the PZT patches on the surface of it. The PZT patches consist of an array to estimate the location and level of the damage which is simulated by an artificial notch on the surface of the structure. The several locations and deep heights of the notches are considered during the test. A pair of the PZT patches are used at the same time as one is used as an actuator and the other as a sensor, respectively. A tone burst of 5 cycles of wave shape is used during the experiment. A wave generator is applied to create the proposed waves, and the waves are amplified by an amplifier to actuate the PZT patch to emit the diagonal waves with appropriately enough energy. Meanwhile, the other PZT patch is used as a sensor to receive the diagonal signals which contain the information of the damages for processing. For data processing, an index of root mean square deviation (RMSD) of the received data is used to estimate the damage level by compare of the data between the damaged and the health peak valves of the received signals. The time reversal method which aimed at increasing the efficiency of the detection is also used to detect the damage location by estimating the arrival time of the reflected wave passing with a certain velocity. The proposed method experimentally validates that it is effective for application in damage detection of pipeline structure.


Author(s):  
Yu Cheng Liu ◽  
Jin Huang Huang

This paper mainly analyzes the wave dispersion relations and associated modal pattens in the inclusion-reinforced composite plates including the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Using the Mori-Tanaka mean-field theory, the effective elastic moduli which are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior can be predicted explicitly. Then, the dispersion relations and the modal patterns of Lamb waves determined from the effective elastic moduli can be obtained by using the dynamic stiffness matrix method. Numerical simulations have been given for the various inclusion types and the resulting dispersions in various wave types on the composite plate. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions about the midplane of the plate. For an orthotropic composite plate, it can also be classified as either symmetric or antisymmetric waves by analyzing the dispersion curves and inspecting the calculated modal patterns. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns.


Babel ◽  
1994 ◽  
Vol 40 (1) ◽  
pp. 21-37
Author(s):  
Ivo R.V. Hoefkens

Marguerite Yourcenar, known as an author, is also the translator of about a dozen works. My purpose here is to trace the evolution of her oeuvre in the field of translation in relation to her literary output. I have divided the former into three distinct periods, the first of which covers the closing years of the 1930s, when Marguerite Yourcenar translated Virginia Woolf's The Waves and Henry James's What Maisie Knew. Her interest in these authors is to a large extent stylistic. On the other hand, the translation of Constantin Cavafy's poetry, which was begun during the same period, reflects the intimist themes to be found in Marguerite Yourcenar's early narratives {Alexis and the others), although she was then already seeking out other thematic sources. The translation was only published in 1958. It consequently falls within a second period: that of the "présentations critiques" (critical commentaries). These major efforts in translation {Présentation critique de Constantin Cavafy, La Couronne et la Lyre, Fleuve profonde, Sombre rivière) are marked by a manifest preoccupation with the aesthetic. But themes of a more universal character and engagement in the socio-political sphere also enter into the choice of the texts for translation (negro spirituals, Présentation critique d'Hortense Flexner). These translations were contemporaneous with the creation of Marguerite Yourcenar's most important novels, namely Mémoires d'Hadrien and L'OEuvre au Noir. The last of the three periods, the 1980s, finds her tackling far less ambitious projects, the function of which tends increasingly towards ethical communication. The only one of them that bears any resemblance to the "présentations critiques" is the essay on Yukio Mishima and the translation of Cinq Nô Modernes, assuming that these are to be considered as an ensemble. Here, as elsewhere, it also emerges that Marguerite Yourcenar is largely indifferent to the existence of other translations.


1940 ◽  
Vol 30 (2) ◽  
pp. 139-178
Author(s):  
J. Emilio Ramirez

Summary Over a period of six months, from July to December, 1938, an investigation on microseismic waves has been carried out in the Department of Geophysics of St. Louis University. Four electromagnetic seismographs, specially designed for recording microseisms, were installed in the city of St. Louis in the form of a triangular network. Two of these were E-W components, one at the St. Louis University Gymnasium and the other 6.4 km. due west at Washington University. The other two were arranged as N-S components, one at the St. Louis University Gymnasium and one 6.3 km. due south at Maryville College. The speed of the photographic paper was 60 mm/min., and time signals were recorded automatically and simultaneously on each paper from the same clock every minute and at shorter intervals from a special pendulum and “tickler” combination by means of telephone wires. The results have demonstrated beyond doubt that microseismic waves are traveling and not stationary waves. The same waves have been identified at each one of the stations of the network, and also at Florissant, 21.8 km. away from St. Louis University. The speed of microseismic waves at St. Louis was determined from several storms of microseisms and it was found to be 2.67±0.03 km/sec. The direction of microseisms was also established for most of the storms and it was found that about 80 per cent of incoming microseisms at St. Louis were from the northeast quadrant during the interval from July to December, 1938. No microseisms were recorded from the south, west, or southwest. The period of the waves varied between 3.5 and 7.5 sec. The average period was about 5.4 sec. The microseismic wave length was therefore of the order of 14¼ km. A study of the nature of microseismic waves from the three Galitzin-Wilip components of the Florissant station reveals in the waves many of the characteristics of the Rayleigh waves; that is, the particles in the passage of microseismic waves move in elliptical orbits of somewhat larger vertical axis and with retrograde motion. A comparison carried over a period of more than a year between microseisms and microbarometric oscillations recorded by specially designed microbarographs showed no direct relationship between the two phenomena in wave form, group form, period, or duration of storms. The source of microseisms is to be found not over the land, but rather out over the surface of the ocean. The amplitudes of microseisms depend only on the intensity and widespread character of barometric lows traveling over the ocean. Several correlations between the two phenomena seem to make this conclusion rather evident. Special emphasis is laid on the fact that all the determined directions of incoming microseisms at St. Louis point to a deep barometric low over the ocean. The period of microseisms seems to be a function of the distance between the station and the source of microseisms. The exact mechanism by which barometric lows over the ocean water result in the production of microseisms needs further investigation. Large microseisms have been produced without any indication of surf near the coasts, or with winds blowing from the land toward the ocean.


2009 ◽  
Vol 409 ◽  
pp. 154-160 ◽  
Author(s):  
Petr Frantík ◽  
Zbyněk Keršner ◽  
Václav Veselý ◽  
Ladislav Řoutil

The paper is focussed on numerical simulations of the fracture of a quasi-brittle specimen due to its impact onto a fixed rigid elastic plate. The failure of the specimen after the impact is modelled in two ways based on the physical discretization of continuum: via physical discrete elements and pseudo-particles. Advantages and drawbacks of both used methods are discussed. The size distribution of the fragments of the broken specimen resulting from physical discrete element model simulation follows a power law, which indicates the ability of the numerical model to identify the fractal nature of the fracture. The pseudo-particle model, on the other side, can successfully predict the kinematics of the fragments of the specimen under impact failure.


2014 ◽  
Vol 758 ◽  
Author(s):  
S. Karimpour Ghannadi ◽  
Vincent H. Chu

AbstractNumerical simulations of the transverse dam-break waves (TDWs) produced by the sudden removal of a gate on the side of a waterway are conducted based on the shallow-water equations to find solutions to a family of water-diversion problems. The Froude numbers in the main flow identify the members of the family. The depth and discharge profiles are analysed in terms of Ritter’s similarity variable. For subcritical main flow, the waves are comprised of a supercritical flow expansion followed by a subcritical outflow. For supercritical main flow, on the other hand, the waves are analogous to the Prandtl–Meyer expansion in gas dynamics. The diversion flow rate of two-dimensional TDWs on a flat bed is 55 % greater than the one-dimensional flow rate of Ritter in the limiting case of zero main flow, and approaches the rate of Ritter in the other limit when the value of the Froude number in the main flow approaches infinity. The diversion flow rate over a weir is generally higher than the rate over a flat bed depending on the Froude number of the main flow. These numerical simulation results are consistent with laboratory observations.


2021 ◽  
Vol 6 ◽  
Author(s):  
Anna Urbaniak

In the institutionalized life course transition from work to retirement is the transition that culturally defines the beginning of later life. However, there is no universal way of experiencing retirement or understanding retirees’ social roles. Especially in the context of the post-communist, liquid modern reality in Poland. The social role of the retiree, defined as a set of rules and expectations generated for individuals occupying particular positions in the social structure, is constructed at the intersection of what is culturally defined and individually negotiated. Therefore, the way in which individuals (re)define term “retiree” and “do retirement” reflects not only inequalities in individual resources and attitudes, but also in social structure in a given place and at a given time. In this contribution, I draw upon data from 68 qualitative interviews with retirees from Poland to analyze retirement practices and meanings assigned to the term “retiree.” Applying practice theory, I explore the inequalities they (re)produce, mirror and reinforce at the same time. Results show that there are four broad types of retirement practices: caregiving, working, exploring and disengaging. During analysis of meanings assigned by participants to the term “retiree,” two definitions emerged: one of a “new wave retiree” and the other of a “stagnant retiree.” Results suggest that in the post-communist context, retirement practices and meanings assigned to the term “retiree” are in the ongoing process of (re)negotiation and are influenced on the one hand by the activation demands resulting from discourses of active and productive aging, and on the other by habitus and imaginaries of retirement formed in the bygone communist era. Retirement practices and definitions of the term “retiree” that emerged from the data reflect structural and individual inequalities, highlighting intersection of gender, age and socioeconomic status in the (re)production of inequalities in retirement transition in the post-communist context.


1835 ◽  
Vol 125 ◽  
pp. 355-358 ◽  

The Fourth Memoir, published in my Zoological Researches and Illustrations, No. III. page 69, &c., having first made known the real nature of the Cirripedes , the key of which remained concealed in their metamorphosis, it might have been expected that some naturalist favourably situated to investigate the oceanic tribe of these animals, would have been the first to make the same discovery in regard to these, and thereby complete their natural history. It was scarcely to be expected that the honour of this discovery also should be reserved for the author, fixed to one spot, where none of them naturally exist, and are but casually thrown upon our shores by the waves of the Atlantic, attached to pieces of wreck, or brought into port fixed to the bottoms of ships returning from distant voyages. Fortunately, however, two ships of this description came into this harbour (Cork), one from the Mediterranean, the other from North America, which, not being sheathed with copper, had their bot­toms literally covered with Barnacles of the three genera of Lepas , Cineras , and Otion ; and having persons employed expressly for the purpose, numbers of these were brought alive in sea water, amongst which were many with the ova in various stages of their progress, and some ready to hatch, which they eventually did in prodigious numbers, so as to enable him to add the proof of their being, like the Balani, natatory Crusta­cea in their first stage , but of a totally different facies and structure; a circumstance which determines the propriety of the separation of the Cirripedes into two tribes, and evinces the sagacity of Mr. MacLeay in being the first to indicate that these two tribes, the Balani and Lepades , were not so closely related as generally supposed. The larvæ of the Balani , described in Memoir IV. under the external appearance of the bivalve Monoculi ( Astracoda ), have a pair of pedunculated eyes, more numerous and more completely developed members, approximating to those of Cyclops , and of the perfect Triton ; while, in the present type, or Lepades , the larva resembles some­what that of the Cyclops , which Müller, mistaking for a perfect animal, named Amymone , and which can be shown to he common to a great many of the Entomostraca ; or the resemblance is still more striking to that of the Argulus Armiger of Latreille, which, in fact, is but an Amymone furnished with a tricuspidate shield at the back.


1980 ◽  
Vol 7 (2) ◽  
pp. 384-388 ◽  
Author(s):  
T. I. Campbell ◽  
W. H. Siu

The natural frequencies of skewed slabs (in the shape of a parallelogram) of uniform thickness and linear elastic isotropic material are considered. It is shown that the natural frequencies of a skewed slab can be related to those of the corresponding rectangular slab by means of an equivalent rectangular slab concept. Charts are presented to allow the computation of the natural frequencies of one-, two-, and three-span symmetric skewed slabs, which are simply supported at each end and free along each edge.


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