Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Kongresse
Themenseiten
Künstliche Intelligenz Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Veranstaltungskalender Awards MyNewsletter Firmensuche
Kunden Login
Über Einzelzugang informieren
Über Unternehmenszugang informieren
Referenzkunden
Zukunftswerkstatt Sales Excellence 2025 | 08. Mai 2025

KI als Booster im Vertrieb

Lernen Sie von Digital-Experten, wie der gezielte Einsatz von KI-Unterstützung Ihrem Unternehmen in vielen Bereichen hilft, im Vertrieb einen Schritt voraus zu sein. Jetzt wieder live vor Ort teilnehmen in Frankfurt am Main!
Erweiterte Suche
Anmelden
nach oben
Journal of Engineering Mathematics
Erschienen in:

01.10.2024

Approximate frequency analysis of isotropic shear beams using initial value method

verfasst von: Reha Artan, Ceyda Nur, Gokhan Guclu, Erol Demirkan, Murat Çelik

Erschienen in: Journal of Engineering Mathematics | Ausgabe 1/2024

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This study investigates the vibration of isotropic shear beams (ISBs) using the unified shear deformation theory for various shear stress distribution functions. The governing differential equations and boundary conditions are obtained using the principle of virtual work. Using the initial values method, the first five frequencies for various end conditions were calculated with four digits. Frequencies for different shear stress distributions can be easily determined using the approximate transfer matrices provided in this study. To verify the accuracy of the obtained results, we compared the frequencies with the findings in the existing literature.
Vorheriger Artikel Acceleration of a projected gradient algorithm for the Bingham flow problem by rigidity enforcement with penalty

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Reddy JN (2004) Mechanics of laminated composite plates and shells: theory and analysis. CRC Press, Boca Raton
2.
Shi YF, Chai GB (2006) Functionally Graded Materials: Nonlinear Analysis of Plates and Shells. CRC Press, London
3.
Zhang N, Khan T, Guo H, Shi S, Zhong W, Zhang W (2019) Functionally graded materials: an overview of stability, buckling, and free vibration analysis. Adv Mater Sci Eng 1354150
4.
Zhang X (2019) Functionally graded materials: design, processing, and applications. Springer, Berlin
5.
Chithambararaj A, Senthilkumar K (2020) Thermal conductivity of functionally graded materials: a review. Mater Today 33:1739–1743
6.
Karthikeyan TK, Arunachalam R, Anandavel A (2019) Thermal and electrical properties of functionally graded composites: a review. Mater Today 33:1744–1748
7.
Kumar P, Singh S, Mishra RK (2017) Electrical and thermal conductivity study of functionally graded materials. Mater Today 4(7):7221–7229
8.
Reddy MS, Ramesh K (2016) Electrical and thermal conductivity enhancement of functionally graded materials: a comprehensive review. Mater Today 3(4):1163–1173
9.
Kim KS, Kim SK, Kim YS (2019) Functionally graded beam structures: a review of recent advances and future challenges. J Korean Soc Adv Compos Struct 10(2):38–49MathSciNet
10.
Mao J-J, Wang Y-J, Yang J (2023) Static and dynamic stability analyses of functionally graded beam with inclined cracks. Int J Struct Stab Dyn 23:04MathSciNetCrossRef
11.
Taleb O, Sekkal M, Bouiadjra RB, Benyoucef S, Khedher KM, Salem MA, Tounsi A (2023) On the free vibration behavior of temperature-dependent bidirectional functionally graded curved porous beams. Int J Struct Stab Dyn 9:2450112MathSciNet
12.
Zahedinejad P, Zhang C, Zhang H, Shuai J (2020) A comprehensive review on vibration analysis of functionally graded beams. Int J Struct Stab Dyn 10:669–689MathSciNet
13.
Cowper GR (1966) The shear coefficient in Timoshenko’s beam theory. J Appl Mech 33(2):335–340CrossRef
14.
Cowper GR (1968) On the accuracy of Timoshenko’s beam theory. J Eng Mech 94(6):1447–1453
15.
Ambartsumyan SA (1958) On the theory of bending plates. Izv Otd Tech Nauk AN SSSR 5:69–77MathSciNet
16.
Baluch MH, Azad AK, Khidir MA (1984) Technical theory of beams with normal strain. J Eng Mech 110(8):1233–1237CrossRef
17.
Bhimaraddi A, Chandrashekhara K (1993) Observations on higher-order beam theory. J Aerosp Eng 6(4):408–413CrossRef
18.
Bickford WB (1982) A consistent higher order beam theory. Dev Theor Appl Mech 11:137–150
19.
Hildebrand FB, Reissner EC (1942) Distribution of stress in built-in beams of narrow rectangular cross section. J Appl Mech 64:109–116
20.
Kruszewski ET (1909) Effect of transverse shear and rotary inertia on the natural frequency of a uniform beam. In: NACA Technical Note, 1949
21.
Turan M, Muhittin V (2024) Mixed series solution for vibration and stability of porous bi-directional functionally graded beams. Arch Appl Mech 94:1785–1806CrossRef
22.
Turan M, Kahya V (2021) Free vibration and buckling analysis of functionally graded sandwich beams by Navier’s method. J Fac Eng Archit Gazi Univ 36:743–757
23.
Turan M (2022) Bending analysis of two-directional functionally graded beams using trigonometric series functions. Arch Appl Mech 92(6):1841–1858CrossRef
24.
Turan M, Adiyaman V (2023) A new higher-order finite element for static analysis of two-directional functionally graded porous beams. Arab J Sci Eng 48(5):13303–13321CrossRef
25.
Turan M, Yaylaci U, Yaylaci M (2023) Free vibration and buckling of functionally graded porous beams using analytical, finite element, and artificial neural network methods. Arch Appl Mech 93:1351–1372CrossRef
26.
Kashani MT, Hashemi SM (2022) On the free vibration and the buckling analysis of laminated composite beams subjected to axial force and end moment: A dynamic finite element analysis. Appl Mech 3(1):210–226CrossRef
27.
Turan M, Adiyaman G (2024) Free vibration and buckling analysis of porous two-directional functionally graded beams using a higher-order finite element model. J Vib Eng Technol 12:1133–1152CrossRef
28.
Karama M, Afaq KS, Mistou S (2003) Mechanical behavior of laminated composite beam by new multi-layered laminated composite structures model with transverse shear stress continuity. Int J Solids Struct 40(6):1525–1546CrossRef
29.
Soldatos KP (1992) A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mech 94:195–200MathSciNetCrossRef
30.
Touratier M (1991) An efficient standard plate theory. Int J Eng Sci 29(8):901–916CrossRef
31.
Vlazov VZ, Leontiev UN (1966) Beams, plates and shells on elastic foundations. Israel Program for Scientific Translations, Springfield, Va., pp 357
32.
Stein M (1989) Vibration of beams and plate strips with three-dimensional flexibility. J Appl Mech 56(1):228–231CrossRef
33.
Ghugal YM, Shimpi RP (2002) A review of refined shear deformation theories for isotropic and anisotropic laminated beams. J Reinf Plast Compos 21:775–813CrossRef
34.
Ghugal YM (2006) A simple higher order theory for beams with transverse shear and transverse normal effect. Dep Rep 4
35.
Sayyad AS (2011) Comparison of various refined beam theories for the bending and free vibration analysis of thick beams. Appl Comput Mech 5:217–230
36.
Gantmakher FR (1959) The Theory of Matrices. Number Bd. 2 in the Theory of Matrices. Chelsea Publishing Company, New York
37.
Akavci SS (2007) Buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation. J Reinf Plast Compos 26:1907–1919CrossRef
38.
Karama M, Afaq KS, Mistou S (2006) A new model for the behaviour of the multi-layer material interfaces. In: Motasoares CA, Martins JAC, Rodrigues HC, Ambrósio JAC, Pina CAB, Motasoares CM, Pereira EBR, Folgado J (eds) III European conference on computational mechanics. Springer Netherlands, Dordrecht, pp 232–232
39.
Reddy JN (1990) A general non-linear third-order theory of plates with moderate thickness. Int J Non-Linear Mech 25(6):677–686CrossRef
Metadaten
Titel
Approximate frequency analysis of isotropic shear beams using initial value method
verfasst von
Reha Artan
Ceyda Nur
Gokhan Guclu
Erol Demirkan
Murat Çelik
Publikationsdatum
01.10.2024
Verlag
Springer Netherlands
Erschienen in
Journal of Engineering Mathematics / Ausgabe 1/2024
Print ISSN: 0022-0833
Elektronische ISSN: 1573-2703
DOI
https://doi.org/10.1007/s10665-024-10401-y

Weitere Artikel der Ausgabe 1/2024

Acceleration of a projected gradient algorithm for the Bingham flow problem by rigidity enforcement with penalty

A mathematical model for the nutrient distribution of a spheroidal avascular cancer tumour within an inhomogeneous environment

Cole–Hopf linearization of the thermocapillary Marangoni dynamics of a two-dimensional bubble with insoluble surfactant

  • Open Access

Instability of thermal convection in an inclined fluid layer with temperature-dependent internal heat source

The effect of asymmetric zeta potentials on the electro-osmotic flow of a generalized Phan–Thien–Tanner fluid

  • Open Access

Effect of magnetic field and hydrodynamic slippage on electro-osmotic Brinkman flow through patterned zeta potential microchannel

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise