Among regular polygons, the pentagon is considered to be barely used in medieval architectural compositions, due to its odd spatial appearance and difficult method of construction. The pentagon, representing the number five has a rich semantic role in Christian symbolism. Even though the proper way of construction was already invented in the Antiquity, there is no evidence of medieval architects having been aware of this knowledge. Contemporary sources only show approximative construction methods. In the Middle Ages the form has been used in architectural elements such as window traceries, towers and apses. As opposed to the general opinion supposing that this polygon has rarely been used, numerous examples bear record that its application can be considered as rather common. Our paper attempts to give an overview of the different methods architects could have used for regular pentagon construction during the Middle Ages, and the ways of applying the form.
{"title":"Pentagons in medieval architecture","authors":"K. Fehér, B. Halmos, B. Szilágyi","doi":"10.1556/096.2018.008","DOIUrl":"https://doi.org/10.1556/096.2018.008","url":null,"abstract":"Among regular polygons, the pentagon is considered to be barely used in medieval architectural compositions, due to its odd spatial appearance and difficult method of construction. The pentagon, representing the number five has a rich semantic role in Christian symbolism. Even though the proper way of construction was already invented in the Antiquity, there is no evidence of medieval architects having been aware of this knowledge. Contemporary sources only show approximative construction methods. In the Middle Ages the form has been used in architectural elements such as window traceries, towers and apses. As opposed to the general opinion supposing that this polygon has rarely been used, numerous examples bear record that its application can be considered as rather common. Our paper attempts to give an overview of the different methods architects could have used for regular pentagon construction during the Middle Ages, and the ways of applying the form.","PeriodicalId":40047,"journal":{"name":"Epites-Epiteszettudomany","volume":"164 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67648621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cikkunkben egy ujfajta szerkezeti megoldas, a kotellel tortenő csigasoros felfuggesztes szabadrezgesre gyakorolt hatasat vizsgaljuk meg egy hajlitott gerendacsalad eseten. A gerendacsalad minden tagja szimmetrikus kettamaszu tarto, amit egy csigasoron atvezetett, vegtelen merevnek es elhanyagolhato tomegűnek tekintett kotel is megtamaszt a szimmetrikusan elhelyezkedő felfuggesztesi pontokban. A felfuggesztes csigainak tehetetlensegi nyomatekat es a surlodast elhanyagoljuk. A fuggesztőkotel ketfele allapota a szerkezet viselkedeset altalanos esetben nemlinearissa teszi, de meg ilyenkor is vizsgalhato szakaszonkent linearis szerkezetkent. A fuggesztőkotel megfeszitett allapotahoz tartozo sajatkorfrekvenciak es rezgesalakok ismerete lehetőve teszi a modalanalizis alkalmazasat a szerkezet rezgesenek szamitasa soran. A rezgesalakokat es a sajatfrekvenciakat a frekvenciaparameter es egy, a felfuggesztesi pontok helyzetet meghatarozo parameter fuggvenyeben allitjuk elő. Ehhez a parameterek segitsegevel irjuk fel a folytonossagi es peremfelteteleket kifejező frekvenciamatrixot. A frekvenciamatrix determinansanak zerushelyeit keresve bemutatjuk, hogyan vezethető vissza a determinans szamitasa egy kisebb meretű matrix determinansanak szamitasara. E kisebb meretű matrix determinansa ugyanazokra a frekvenciaparameterekre ad zerust, mint a frekvenciamatrix determinansa. | In this paper the effects of a new kind of structure, the block-and-tackle suspension system, are investigated on the free vibration of a beam family subjected to bending. The beam family consists of symmetric pinned-pinned beams that are supported by an infinitely stiff cable with neglectable mass connected symmetrically by the block-and-tackle system. The inertia of the pulleys and their friction is neglected. Two possible states of the cable results in a typically nonlinear structural behavior, but each state can be analyzed as a linear problem. In view of the natural frequencies and vibration modes corresponding to the tightened state of the cable, the use of modal analysis in the examination of the vibrations of the structure is possible. The vibration modes and natural frequencies are determined as a function of the frequency parameter and a parameter characterizing the position of the suspension points. This is obtained through the frequency matrix expressing the continuity and boundary conditions. Searching for the fix points of the determinant of the frequency matrix we present how the calculation of the determinant leads to the calculation of the determinant of a smaller matrix. The determinant of this smaller matrix vanishes at the same values of the frequency parameter as the determinant of the frequency matrix.
{"title":"Függesztett gerendacsalád szabadrezgése ii.","authors":"N. Károly, Geleji Borbála","doi":"10.1556/096.2017.006","DOIUrl":"https://doi.org/10.1556/096.2017.006","url":null,"abstract":"Cikkunkben egy ujfajta szerkezeti megoldas, a kotellel tortenő csigasoros felfuggesztes szabadrezgesre gyakorolt hatasat vizsgaljuk meg egy hajlitott gerendacsalad eseten. A gerendacsalad minden tagja szimmetrikus kettamaszu tarto, amit egy csigasoron atvezetett, vegtelen merevnek es elhanyagolhato tomegűnek tekintett kotel is megtamaszt a szimmetrikusan elhelyezkedő felfuggesztesi pontokban. A felfuggesztes csigainak tehetetlensegi nyomatekat es a surlodast elhanyagoljuk. A fuggesztőkotel ketfele allapota a szerkezet viselkedeset altalanos esetben nemlinearissa teszi, de meg ilyenkor is vizsgalhato szakaszonkent linearis szerkezetkent. A fuggesztőkotel megfeszitett allapotahoz tartozo sajatkorfrekvenciak es rezgesalakok ismerete lehetőve teszi a modalanalizis alkalmazasat a szerkezet rezgesenek szamitasa soran. A rezgesalakokat es a sajatfrekvenciakat a frekvenciaparameter es egy, a felfuggesztesi pontok helyzetet meghatarozo parameter fuggvenyeben allitjuk elő. Ehhez a parameterek segitsegevel irjuk fel a folytonossagi es peremfelteteleket kifejező frekvenciamatrixot. A frekvenciamatrix determinansanak zerushelyeit keresve bemutatjuk, hogyan vezethető vissza a determinans szamitasa egy kisebb meretű matrix determinansanak szamitasara. E kisebb meretű matrix determinansa ugyanazokra a frekvenciaparameterekre ad zerust, mint a frekvenciamatrix determinansa. \u0000 | \u0000In this paper the effects of a new kind of structure, the block-and-tackle suspension system, are investigated on the free vibration of a beam family subjected to bending. The beam family consists of symmetric pinned-pinned beams that are supported by an infinitely stiff cable with neglectable mass connected symmetrically by the block-and-tackle system. The inertia of the pulleys and their friction is neglected. Two possible states of the cable results in a typically nonlinear structural behavior, but each state can be analyzed as a linear problem. In view of the natural frequencies and vibration modes corresponding to the tightened state of the cable, the use of modal analysis in the examination of the vibrations of the structure is possible. The vibration modes and natural frequencies are determined as a function of the frequency parameter and a parameter characterizing the position of the suspension points. This is obtained through the frequency matrix expressing the continuity and boundary conditions. Searching for the fix points of the determinant of the frequency matrix we present how the calculation of the determinant leads to the calculation of the determinant of a smaller matrix. The determinant of this smaller matrix vanishes at the same values of the frequency parameter as the determinant of the frequency matrix.","PeriodicalId":40047,"journal":{"name":"Epites-Epiteszettudomany","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67648455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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