![](/images/graphics-bg.png)
Analysis of the Spatial Vibration of Nonprismatic Arches by Means of Recurrence Relations for the Coefficients of the Chebyshev Series Expansion of the Solution
المؤلفون المشاركون
المصدر
Mathematical Problems in Engineering
العدد
المجلد 2018، العدد 2018 (31 ديسمبر/كانون الأول 2018)، ص ص. 1-27، 27ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2018-12-31
دولة النشر
مصر
عدد الصفحات
27
التخصصات الرئيسية
الملخص EN
The problem of spatial vibrations, both aperiodically forced and free vibrations, of an arch with an arbitrary distribution of material and geometric parameters is considered.
Approximation with Chebyshev series was used to solve a conjugated system of partial differential equations describing the problem.
The system of differential equations was solved using an algorithm generating a recursive infinite system of equations, developed by S.
Paszkowski in “Numerical applications of Chebyshev polynomials” (in Polish), Warsaw PWN, 1975.
Since the coefficients of the obtained system of equations are defined by closed analytical formulas they can be directly used to solve any nonprismatic arch, without it being necessary to solve again the considered problem.
The algorithm is highly accurate; i.e., already at a small approximation base it yields results agreeing with exact analytical solutions (obviously for problems in the case of which such solutions can be derived).
In order to demonstrate this the eigenfrequencies and eigenvectors obtained for a circular prismatic arch were compared with their precise values determined from the exact analytical solutions.
The results yielded by the proposed method were also compared with the results obtained by other methods and by other authors.
As an illustration, the proposed method was used to solve a more complex problem, i.e., the problem of the free and aperiodically forced vibrations of a nonprismatic arch with its axis described by a catenary curve.
In the example the effect of the lack of cross-sectional symmetry of the arch on the form of the system’s spatial free and forced vibrations was analysed.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Ruta, P.& Meissner, M.. 2018. Analysis of the Spatial Vibration of Nonprismatic Arches by Means of Recurrence Relations for the Coefficients of the Chebyshev Series Expansion of the Solution. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-27.
https://search.emarefa.net/detail/BIM-1205639
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Ruta, P.& Meissner, M.. Analysis of the Spatial Vibration of Nonprismatic Arches by Means of Recurrence Relations for the Coefficients of the Chebyshev Series Expansion of the Solution. Mathematical Problems in Engineering No. 2018 (2018), pp.1-27.
https://search.emarefa.net/detail/BIM-1205639
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Ruta, P.& Meissner, M.. Analysis of the Spatial Vibration of Nonprismatic Arches by Means of Recurrence Relations for the Coefficients of the Chebyshev Series Expansion of the Solution. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-27.
https://search.emarefa.net/detail/BIM-1205639
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-1205639
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
![](/images/ebook-kashef.png)
تقوم هذه الخدمة بالتحقق من التشابه أو الانتحال في الأبحاث والمقالات العلمية والأطروحات الجامعية والكتب والأبحاث باللغة العربية، وتحديد درجة التشابه أو أصالة الأعمال البحثية وحماية ملكيتها الفكرية. تعرف اكثر
![](/images/kashef-image.png)