Analytical approaches to vibration analysis of circular, annular and sectorial plates subjected to classical and arbitrary boundary conditions – a literature survey

Plates are one of the most important structural components used in many industries like aerospace, marine and various other engineering fields and thus motivate designers and engineers to study the vibration characteristics of these structures. A lot of research work and studies have been done to study its vibration characteristics. This paper is a review of existing literature on vibration analysis of circular, annular and sector plates. The aim of this paper is to compile prominent studies related to circular, annular and sector plates subjected to classical and arbitrary boundary conditions under different supports and loadings. This review also identifies the analytical methods and approaches used to study the vibration characteristics of circular, annular and sector plates based on classical plate theories, Mindlin plate theory and higher order shear deformation theories. Few important citations related to functionally graded circular, annular and sector plates have also been included. Apart from helping researchers and engineers to identify relevant literature quickly and easily, this review will also help them to apply some of these analytical methods to study the vibration characteristics of other 2D and 3D built up and coupled structures

Computational approaches to vibration analysis of shells under different boundary conditions – a literature review

Shells are important structural elements widely used in various engineering applications ranging from outer space to deep oceans such as rockets, aircrafts, missiles, submarines and automobiles etc. A huge amount of research efforts has been devoted to vibration analysis and dynamic behaviors of the shells. Furthermore, a large variety of shell theories and computational methods have been proposed and developed by researchers. For different cases different computational approaches have been used in literature to study the vibration characteristics of shells. This review is aimed to provide contemporarily relevant survey of papers on vibrational characteristics of shells and identification of various methods and approaches that have been used to study its vibration characteristics. Focus has been kept to important and prominent studies and its compilation in a single paper to help future researchers to identify relevant literature quickly and easily and also help them to apply these approaches to study vibration characteristics of other built up and coupled structures

Analytical approaches to vibration analysis of circular, annular and sectorial plates subjected to classical and arbitrary boundary conditions – a literature survey

Plates are one of the most important structural components used in many industries like aerospace, marine and various other engineering fields and thus motivate designers and engineers to study the vibration characteristics of these structures. A lot of research work and studies have been done to study its vibration characteristics. This paper is a review of existing literature on vibration analysis of circular, annular and sector plates. The aim of this paper is to compile prominent studies related to circular, annular and sector plates subjected to classical and arbitrary boundary conditions under different supports and loadings. This review also identifies the analytical methods and approaches used to study the vibration characteristics of circular, annular and sector plates based on classical plate theories, Mindlin plate theory and higher order shear deformation theories. Few important citations related to functionally graded circular, annular and sector plates have also been included. Apart from helping researchers and engineers to identify relevant literature quickly and easily, this review will also help them to apply some of these analytical methods to study the vibration characteristics of other 2D and 3D built up and coupled structures

Analytical approaches to vibration analysis of circular, annular and sectorial plates subjected to classical and arbitrary boundary conditions – a literature survey

Plates are one of the most important structural components used in many industries like aerospace, marine and various other engineering fields and thus motivate designers and engineers to study the vibration characteristics of these structures. A lot of research work and studies have been done to study its vibration characteristics. This paper is a review of existing literature on vibration analysis of circular, annular and sector plates. The aim of this paper is to compile prominent studies related to circular, annular and sector plates subjected to classical and arbitrary boundary conditions under different supports and loadings. This review also identifies the analytical methods and approaches used to study the vibration characteristics of circular, annular and sector plates based on classical plate theories, Mindlin plate theory and higher order shear deformation theories. Few important citations related to functionally graded circular, annular and sector plates have also been included. Apart from helping researchers and engineers to identify relevant literature quickly and easily, this review will also help them to apply some of these analytical methods to study the vibration characteristics of other 2D and 3D built up and coupled structures

Free vibration analysis of moderately thick isotropic homogeneous open cylindrical shells using improved Fourier series method

In this paper an Improved Fourier series method has been employed to study the free vibrations of isotropic homogeneous moderately thick open cylindrical shells with arbitrary subtended angle and general elastic restraints. In this method, regardless of the boundary conditions, each of the displacement components of open shell is invariably expressed as a simple trigonometric series with accelerated and uniform convergence over the solution domain. Distributed elastic restraints are used to specify the elastic boundary conditions along the shell edges and therefore, arbitrary boundary restraints can be achieved by varying the values of spring’s stiffness. All the unknown expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh-Ritz technique. A considerable number of new vibration results for isotropic open cylindrical shells with various geometric parameters and boundary conditions are presented. The effects of boundary stiffness, thickness to radius ratio and subtended angle on the vibration characteristics are also discussed in detail

A Unified method for vibration analysis of moderately thick annular, circular plates and their sector counterparts subjected to arbitrary boundary conditions

The vibrations of circular, annular and sector plates are different boundary value problems due to different edge conditions and thus have been treated separately using different solution algorithms and procedures. In this paper, a unified method is proposed for vibration analysis of moderately thick annular, circular plates and their sector counterparts with arbitrary boundary conditions. The unification of these plates is physically achieved by applying the coupling spring’s technique at the radial edges to ensure appropriate continuity conditions. Irrespective of the shape of the plate and the type of boundary conditions, each of the displacement function is expressed as a new form of trigonometric expansion with high convergence rate. Unlike most of the previous studies the current method can be universally applied to a wide range of vibration problems involving different shapes, boundary conditions, varying materials and geometric properties without modifying the solution algorithms and procedure. Furthermore, the current method can easily be applied to sector plates with an arbitrary inclusion angle of 2π. The accuracy, reliability and versatility of the proposed method are fully demonstrated with several numerical examples for different shapes of plates and under different boundary conditions

An improved Fourier series method for vibration analysis of moderately thick annular and circular sector plates subjected to elastic boundary conditions

In this paper, an improved Fourier series method is presented for vibration analysis of moderately thick annular and circular sector plates subjected to general elastic boundary conditions along its edges. In literature, annular and circular sector plates subjected to classical boundary conditions have been studied in detail however in practical engineering applications the boundary conditions are not always classical in nature. Therefore, study of vibration response of these plates subjected to general elastic boundary conditions is far needed. In the method presented, artificial boundary spring technique has been employed to simulate the general elastic boundary conditions and first order shear deformation theory has been employed to formulate the theoretical model. Irrespective of the boundary conditions, each of the displacement function is expressed as a new form of trigonometric expansion with accelerated convergence. Rayleigh-Ritz method has been employed to determine the expansion coefficients. Unlike most of the studies on vibration analysis of moderately thick annular sector plates, the present method can be universally applied to a wide range of vibration problems involving different boundary conditions, varying material and geometric properties without modifying the solution algorithms and procedure. The effectiveness, reliability and accuracy of the present method is fully demonstrated and verified by several numerical examples. Bench mark solutions for moderately thick annular sector and circular plates under general elastic boundary conditions are also presented for future computational methods

State of the climate in 2022: introduction

Earth’s global climate system is vast, complex, and intricately interrelated. Many areas are influenced by global-scale phenomena, including the “triple dip” La Niña conditions that prevailed in the eastern Pacific Ocean nearly continuously from mid-2020 through all of 2022; by regional phenomena such as the positive winter and summer North Atlantic Oscillation that impacted weather in parts the Northern Hemisphere and the negative Indian Ocean dipole that impacted weather in parts of the Southern Hemisphere; and by more localized systems such as high-pressure heat domes that caused extreme heat in different areas of the world. Underlying all these natural short-term variabilities are long-term climate trends due to continuous increases since the beginning of the Industrial Revolution in the atmospheric concentrations of Earth’s major greenhouse gases.In 2022, the annual global average carbon dioxide concentration in the atmosphere rose to 417.1±0.1 ppm, which is 50% greater than the pre-industrial level. Global mean tropospheric methane abundance was 165% higher than its pre-industrial level, and nitrous oxide was 24% higher. All three gases set new record-high atmospheric concentration levels in 2022.Sea-surface temperature patterns in the tropical Pacific characteristic of La Niña and attendant atmospheric patterns tend to mitigate atmospheric heat gain at the global scale, but the annual global surface temperature across land and oceans was still among the six highest in records dating as far back as the mid-1800s. It was the warmest La Niña year on record. Many areas observed record or near-record heat. Europe as a whole observed its second-warmest year on record, with sixteen individual countries observing record warmth at the national scale. Records were shattered across the continent during the summer months as heatwaves plagued the region. On 18 July, 104 stations in France broke their all-time records. One day later, England recorded a temperature of 40°C for the first time ever. China experienced its second-warmest year and warmest summer on record. In the Southern Hemisphere, the average temperature across New Zealand reached a record high for the second year in a row. While Australia’s annual temperature was slightly below the 1991–2020 average, Onslow Airport in Western Australia reached 50.7°C on 13 January, equaling Australia's highest temperature on record.While fewer in number and locations than record-high temperatures, record cold was also observed during the year. Southern Africa had its coldest August on record, with minimum temperatures as much as 5°C below normal over Angola, western Zambia, and northern Namibia. Cold outbreaks in the first half of December led to many record-low daily minimum temperature records in eastern Australia.The effects of rising temperatures and extreme heat were apparent across the Northern Hemisphere, where snow-cover extent by June 2022 was the third smallest in the 56-year record, and the seasonal duration of lake ice cover was the fourth shortest since 1980. More frequent and intense heatwaves contributed to the second-greatest average mass balance loss for Alpine glaciers around the world since the start of the record in 1970. Glaciers in the Swiss Alps lost a record 6% of their volume. In South America, the combination of drought and heat left many central Andean glaciers snow free by mid-summer in early 2022; glacial ice has a much lower albedo than snow, leading to accelerated heating of the glacier. Across the global cryosphere, permafrost temperatures continued to reach record highs at many high-latitude and mountain locations.In the high northern latitudes, the annual surface-air temperature across the Arctic was the fifth highest in the 123-year record. The seasonal Arctic minimum sea-ice extent, typically reached in September, was the 11th-smallest in the 43-year record; however, the amount of multiyear ice—ice that survives at least one summer melt season—remaining in the Arctic continued to decline. Since 2012, the Arctic has been nearly devoid of ice more than four years old.In Antarctica, an unusually large amount of snow and ice fell over the continent in 2022 due to several landfalling atmospheric rivers, which contributed to the highest annual surface mass balance, 15% to 16% above the 1991–2020 normal, since the start of two reanalyses records dating to 1980. It was the second-warmest year on record for all five of the long-term staffed weather stations on the Antarctic Peninsula. In East Antarctica, a heatwave event led to a new all-time record-high temperature of −9.4°C—44°C above the March average—on 18 March at Dome C. This was followed by the collapse of the critically unstable Conger Ice Shelf. More than 100 daily low sea-ice extent and sea-ice area records were set in 2022, including two new all-time annual record lows in net sea-ice extent and area in February.Across the world’s oceans, global mean sea level was record high for the 11th consecutive year, reaching 101.2 mm above the 1993 average when satellite altimetry measurements began, an increase of 3.3±0.7 over 2021. Globally-averaged ocean heat content was also record high in 2022, while the global sea-surface temperature was the sixth highest on record, equal with 2018. Approximately 58% of the ocean surface experienced at least one marine heatwave in 2022. In the Bay of Plenty, New Zealand’s longest continuous marine heatwave was recorded.A total of 85 named tropical storms were observed during the Northern and Southern Hemisphere storm seasons, close to the 1991–2020 average of 87. There were three Category 5 tropical cyclones across the globe—two in the western North Pacific and one in the North Atlantic. This was the fewest Category 5 storms globally since 2017. Globally, the accumulated cyclone energy was the lowest since reliable records began in 1981. Regardless, some storms caused massive damage. In the North Atlantic, Hurricane Fiona became the most intense and most destructive tropical or post-tropical cyclone in Atlantic Canada’s history, while major Hurricane Ian killed more than 100 people and became the third costliest disaster in the United States, causing damage estimated at $113 billion U.S. dollars. In the South Indian Ocean, Tropical Cyclone Batsirai dropped 2044 mm of rain at Commerson Crater in Réunion. The storm also impacted Madagascar, where 121 fatalities were reported.As is typical, some areas around the world were notably dry in 2022 and some were notably wet. In August, record high areas of land across the globe (6.2%) were experiencing extreme drought. Overall, 29% of land experienced moderate or worse categories of drought during the year. The largest drought footprint in the contiguous United States since 2012 (63%) was observed in late October. The record-breaking megadrought of central Chile continued in its 13th consecutive year, and 80-year record-low river levels in northern Argentina and Paraguay disrupted fluvial transport. In China, the Yangtze River reached record-low values. Much of equatorial eastern Africa had five consecutive below-normal rainy seasons by the end of 2022, with some areas receiving record-low precipitation totals for the year. This ongoing 2.5-year drought is the most extensive and persistent drought event in decades, and led to crop failure, millions of livestock deaths, water scarcity, and inflated prices for staple food items.In South Asia, Pakistan received around three times its normal volume of monsoon precipitation in August, with some regions receiving up to eight times their expected monthly totals. Resulting floods affected over 30 million people, caused over 1700 fatalities, led to major crop and property losses, and was recorded as one of the world’s costliest natural disasters of all time. Near Rio de Janeiro, Brazil, Petrópolis received 530 mm in 24 hours on 15 February, about 2.5 times the monthly February average, leading to the worst disaster in the city since 1931 with over 230 fatalities.On 14–15 January, the Hunga Tonga-Hunga Ha'apai submarine volcano in the South Pacific erupted multiple times. The injection of water into the atmosphere was unprecedented in both magnitude—far exceeding any previous values in the 17-year satellite record—and altitude as it penetrated into the mesosphere. The amount of water injected into the stratosphere is estimated to be 146±5 Terragrams, or ∼10% of the total amount in the stratosphere. It may take several years for the water plume to dissipate, and it is currently unknown whether this eruption will have any long-term climate effect