An investigation on the modal properties of a viscoelastically connected cantilever beam carrying mass at its end

Year 2024, Volume: 3 Issue: 2, 24 - 30, 16.01.2025

Aydın Demir

Abstract

In this study, the effects of the connection point stiffness and damping of a cantilever beams with a viscoelastic connection carrying a mass at its end on its modal properties were investigated in detail. Although viscoelastic materials used as surface damping in structures are effective for vibration and sound insulation, they cannot be applied at all times and under all conditions. In this case, the use of viscoelastic materials in connections is one of the preferred methods. The viscoelastic connection was modeled using spring elements with complex rigidity in linear and rotational directions. The problem considered was examined within the framework of simple beam theory and the differential equation and boundary conditions of the Bernoulli-Euler beam were used as starting points. The modal parameters of the cantilever beam were obtained by iteratively solving the extracted characteristic equation. The numerical results were examined as natural frequencies and modal damping ratios of the system by changing the linear and rotational properties of the viscoelastic connection.

Keywords

Viscoelastic connection, Cantilever beam, End mass, Modal properties

Uç kısmında kütle taşıyan viskoelastik bağlantılı bir ankastre kirişin modal özellikleri üzerine bir araştırma

Abstract

Bu çalışmada, ucunda kütle taşıyan viskoelastik bağlantılı ankastre çubuğun bağlantı noktası rijitlik ve sönümünün modal özelliklerine etkisi detaylı olarak incelenmiştir. Yapılarda yüzey sönümü olarak kullanılan viskoelastik malzemeler, titreşim ve ses yalıtımları için etkili bir uygulama olmalarına rağmen, her zaman ve her koşulda uygulama imkânı bulamamaktadır. Bu durumlarda, bağlantılarda viskoelastik malzemeler kullanılması tercih edilen yöntemlerdendir. Viskoelastik bağlantı doğrusal ve dönme yönünde kompleks rijitliğe sahip yay elemanları kullanılarak modellenmiştir. Ele alınan problem basit çubuk teorisi çerçevesinde incelenmiş, Bernoulli-Euler çubuğuna ait diferansiyel denklem ve sınır şartlarından hareket edilmiştir. Ankastre çubuğun modal parametreleri çıkartılan karakteristik denklemin iteratif çözümüyle elde edilmiştir. Sayısal sonuçlar, viskoelastik bağlantının doğrusal ve dönme yönündeki özellikleri değiştirilerek doğal frekans ve modal sönüm oranları olarak incelenmiştir.

Keywords

Viskoelastik bağlantı, Ankastre kiriş, Uç kütle, Modal özellikler

References

• Akbas S.D, Bashiri A.H, Eltaher M.A, 2021. Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support. Journal of Vibration and Control, 27 (13-14):1644-1655.
• Alipour M.M, 2018. Transient forced vibration response analysis of heterogeneous sandwich circular plates under viscoelastic boundary support. Archives of Civil and Mechanical Engineering, 18 (1):12-31.
• Demir C, 2023. Natural Frequencies of a Viscoelastic Supported Axially Functionally Graded Bar With Tip Masses. International Journal of Acoustics and Vibration, 28(1): 50-64.
• Demir C, Oz FE, 2014. Free vibration analysis of a functionally graded viscoelastic supported beam. Journal of Vibration and Control, 20 (16): 2464-2486.
• Ding H, Zhu M.H, Chen L.Q, 2018. Nonlinear vibration isolation of a viscoelastic beam, Nonlinear Dynamics, 92 (2):325-349.
• Fan Z.J, Lee J.H, Kang K.H, Kim K.J, 1998. The forced vibration of a beam with viscoelastic boundary supports. Journal of Sound and Vibration, 210 (5): 673-682.
• Guandong Q, Salam R, 2021. Dynamics of Euler-Bernoulli beams with unknown viscoelastic boundary conditions under a moving load, Journal of Sound and Vibration, 491, 115771:1-19.
• Harris C. M, 1988. Shock and Vibration Handbook, New York: McGraw-Hill.
• Kang K.H., Kim K.J, 1996. Modal properties of beams and plates on resilient supports with rotational and translational complex stiffness. Journal of Sound and Vibration, 190(2):207-220.
• Lei Y, Murmu T, Adhikari S, Friswell M.I, 2013. Dynamic characteristics of damped viscoelastic nonlocal Euler-Bernoulli beams. European Journal of Mechanics A/Solids, 42:125-136.
• Lei Y, Adhikari S, Friswell M.I, 2013. Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams. International Journal of Engineering Science, 66-67:1-13.
• Mohamed N, Mohamed S.A, Eltaher MA, 2024. Nonlinear Forced Vibration of Curved Beam with Nonlinear Viscoelastic Ends. International Journal of Applied Mechanics, 16 (03):2450031.
• Nayak D.K, Dash P.R, 2021. Parametric Stability Analysis of a Spring Attached, Pre-Twisted, Rotating Sandwich Beam with Tip Mass and Viscoelastic Support. International Journal of Structural Stability and Dynamics, 21 (10):2150143.
• Patil R, Joladarashi S, Kadoli R, 2023. Bending and vibration studies of FG porous sandwich beam with viscoelastic boundary conditions: FE approach. Mechanics of Advanced Materials and Structures, 30 (17):3588-3607.
• Peng L, Ding H, Chen L.Q, 2016. Frequencies, Modes and Orthogonality of Vibrating Timoshenko Beams on Viscoelastic Foundation. Journal of Vibration Engineering & Technologies, 4 (6):527-537.
• Sun Lu, 2002. A closed-form solution of beam on viscoelastic subgrade subjected to moving loads. Computers and Structures, 80:1-8.
• Wineman A, Min J.H, 2000. Viscoelastic hinge formation in beams. Acta Mechanica, 140:183-205.
• Zhang D.P, Lei Y.J, Shen Z.B, 2017. Vibration analysis of viscoelastic single-walled carbon nanotubes resting on a viscoelastic foundation. Journal of Mechanical Science and Technology, 31 (1):87-98.