Archives of Acoustics, 47, 1, pp. 97–112, 2022

Acoustic Response of an Isotropic Beam Under Axially Variable Loads Using Ritz and Rayleigh Integral Methods

National Institute of Technology Karnataka Surathkal, Mangalore

National Institute of Technology Karnataka Surathkal, Mangalore 575 025

Vellore Institute of Technology Chennai, Tamilnadu 600 127

Aditya Engineering College, Surampalem, Andhra Pradesh

Vibro-acoustic response of an isotropic beam under the action of variable axial loads (VALs), is presented in the study. Effects of six different types of VALs and three types of end conditions on buckling, free vibration and sound radiation characteristics are investigated. Static buckling and free vibration behaviours using shear and normal deformable theorem and Ritz method. However, the forced vibration response is evaluated using modal superposition method and the acoustic radiation characteristics are obtained using Rayleigh integral. The nature of variation of VALs and end conditions are influencing buckling and free vibration characteristics remarkably. Results indicate that the acoustic response is highly sensitive to the nature of VAL and intensity of the VAL. In general, sound power at resonance decreases when the magnitude of VAL is increased.
Keywords: Ritz method; variable axial load; buckling; vibration; sound radiation.
Full Text: PDF


Abo-bakr R.M., Abo-bakr H.M., Mohamed S.A., Eltaher M.A. (2021), Optimal weight for buckling of FG beam under variable axial load using Pareto optimality, Composite Structures, 258: 113193, doi: 10.1016/j.compstruct.2020.113193.

Alshabatat N.T., Naghshineh K. (2014), Optimization of natural frequencies and sound power of beams using functionally graded material, Advances in Acoustics and Vibration, 2014: Article ID 752361, doi: 10.1155/2014/752361.

Aydogdu M. (2005), Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method, International Journal of Mechanical Sciences, 47(11): 1740–1755, doi: 10.1016/j.ijmecsci. 2005.06.010.

Aydogdu M. (2006), Buckling analysis of cross-ply laminated beams with general boundary conditions by Ritz method, Composites Science and Technology, 66(10): 1248–1255, doi: 10.1016/j.compscitech.2005. 10.029.

Chakraverty S., Behera L. (2015), Free vibration of non-uniform nanobeams using Rayleigh-Ritz method, Physica E: Low-Dimensional Systems and Nanostructures, 67: 38–46, doi: 10.1016/j.physe.2014.10.039.

Denli H., Sun J.Q. (2007), Structural-acoustic optimization of sandwich structures with cellular cores for minimum sound radiation, Journal of Sound and Vibration, 301(1–2): 93–105, doi: 10.1016/j.jsv.2006. 09.025.

Eltaher M.A., Mohamed S.A. (2020a), Buckling and stability analysis of sandwich beams subjected to varying axial loads, Steel and Composite Structures, 34(2): 241–260, doi: 10.12989/scs.2020.34.2.241.

Eltaher M.A., Mohamed S.A., Melaibari A. (2020b), Static stability of a unified composite beams under varying axial loads, Thin-Walled Structures, 147: 106488, doi: 10.1016/j.tws.2019.106488.

Ghannadpour S.A., Mohammadi B., Fazilati J. (2013), Bending, buckling and vibration problems of nonlocal Euler beams using Ritz method, Composite Structures, 96: 584–589, doi: 10.1016/j.compstruct. 2012.08.024.

Gunasekaran V., Pitchaimani J., Chinnapandi L.B.M. (2020a), Vibro-acoustics response of an isotropic plate under non-uniform edge loading: an analytical investigation, Aerospace Science and Technology, 105: 106052, doi: 10.1016/j.ast.2020.106052.

Gunasekaran V., Pitchaimani J., Chinnapandi L.B.M., Kumar A. (2020b), Analytical solution for sound radiation characteristics of graphene nanocomposites plate: Effect of porosity and variable edge load, International Journal of Structural Stability and Dynamics, 21(06): 2150087, doi: 10.1142/S02194 55421500875.

Gunasekaran V., Pitchaimani J., Chinnapandi L.B.M. (2021), Acoustic radiation and transmission loss of FG-Graphene composite plate under nonuniform edge loading, European Journal of MechanicsA/Solids, 88: 104249, doi: 10.1016/j.euromechsol.2021. 104249.

Hamed M.A., Mohamed S.A., Eltaher M.A. (2020a), Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads, Steel and Composite Structures, 34(1): 75–89, doi: 10.12989/scs.2020.34.1.075.

Hamed M.A., Abo-bakr R.M., Mohamed S.A., Eltaher M.A.(2020b), Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous core, Engineering with Computers, 36(4): 1929-1946, doi: 10.1007/ s00366-020-01023-w.

Harsha B., Jeyaraj P., Lenin B. (2021), Effect of porosity and profile axial loading on elastic buckling and free vibration of functionally graded porous beam, [in:] IOP Conference Series: Materials Science and Engineering, 1128: 012025, IOP Publishing, doi: 10.1088/1757-899X/1128/1/012025.

Hu H., Badir A., Abatan A. (2003), Buckling behaviour of a graphite/epoxy composite plate under parabolic variation of axial loads, International Journal of Mechanical Sciences, 45(6–7): 1135–1147, doi: 10.1016/j.ijmecsci.2003.08.003.

Ilanko S., Monterrubio L., Mochida Y. (2014), The Rayleigh-Ritz Method for Structural Analysis, John Wiley & Sons.

Jaworski J.W., Dowell E.H. (2008), Free vibration of a cantilevered beam with multiple steps: Comparison of several theoretical methods with experiment, Journal of Sound and Vibration, 312(4–5): 713–725, doi: 10.1016/j.jsv.2007.11.010.

Karamanli A., Aydogdu M. (2019a), Buckling of laminated composite and sandwich beams due to axially varying in-plane loads, Composite Structures, 210: 391–408, doi: 10.1016/j.compstruct.2018.11.067.

Karamanli A., Aydogdu M. (2019b), On the vibration of size dependent rotating laminated composite and sandwich microbeams via a transverse shearnormal deformation theory, Composite Structures, 216: 290–300, doi: 10.1016/j.compstruct.2019.02.044.

Kanade S.A., Chinnapandi L.B.M., Jeyaraj P., Subramanian J. (2021), Buckling and vibration behavior of composite beam due to axially varying in-plane loads, [in:] IOP Conference Series: Materials Science and Engineering, 1128: 012043, IOP Publishing, doi: 10.1088/1757-899X/1128/1/012043.

Leissa A.W. (2005), The historical bases of the Rayleigh and Ritz methods, Journal of Sound and Vibration, 287(4–5): 961–978, doi: 10.1016/j.jsv.004.12.021.

Li Q., Yang D. (2020), Vibro-acoustic performance and design of annular cellular structures with graded auxetic mechanical metamaterials, Journal of Sound and Vibration, 466: 115038, doi: 10.1016/j.jsv.2019. 115038.

Majkut L. (2006), Acoustical diagnostics of cracks in beam like structures, Archives of Acoustics, 31(1): 17–28.

Melaibari A., Abo-bakr R.M., Mohamed S.A., Eltaher M.A. (2020b), Static stability of higher order functionally graded beam under variable axial load, Alexandria Engineering Journal, 59(3): 1661– 1675, doi: 10.1016/j.aej.2020.04.012.

Melaibari A., Khoshaim A.B., Mohamed S.A., Eltaher M.A. (2020a), Static stability and of symmetric and sigmoid functionally graded beam under variable axial load, Steel and Composite Structures, 35(5): 671– 685, doi: 10.12989/scs.2020.35.5.671.

Nguyen N.-D., Nguyen T.-K., Vo T.P., Thai H.-T. (2018), Ritz-based analytical solutions for bending, buckling and vibration behavior of laminated composite beams, International Journal of Structural Stability and Dynamics, 18(11): 1850130, doi: 10.1142/S0219 455418501304.

Omidi Soroor A., Asgari M., Haddadpour H. (2021), Effect of axially graded constraining layer on the free vibration properties of three layered sandwich beams with magnetorheological fluid core, Composite Structures, 255: 112899, doi: 10.1016/j.compstruct. 2020.112899.

Ruzzene M. (2004), Vibration and sound radiation of sandwich beams with honeycomb truss core, Journal of Sound and Vibration, 277(4–5): 741–763, doi: 10.1016/ j.jsv.2003.09.026.

Spadoni A., Ruzzene M. (2006), Structural and acoustic behavior of chiral truss-core beams, Journal of Vibration and Acoustics, Transactions of the ASME, 128(5): 616–626, doi: 10.1115/1.2202161.

Tang H.B., Xu B.G. (2017), Vibroacoustic modeling of an elastic beam in low subsonic flows with mean velocities, European Journal of Mechanics, A/Solids, 66: 322–328, doi: 10.1016/j.euromechsol.2017.08.004.

Tiryakioglu B. (2020), Radiation of sound waves by a semi-infinite duct with outer lining and perforated end, Archives of Acoustics, 45(1): 77–84 doi: 10.24425/aoa.2020.132483.

Tiryakioglu B., Demir A. (2019), Sound wave radiation from partially lined duct, Archives of Acoustics, 44(2): 239–249, doi: 10.24425/aoa.2019.128487.

Torres-Romero J., Cardenas W., Carbajo J., Segovia Eulogio E.-G., Ramis-Soriano J. (2018), An experimental approach to vibro-acoustic study of beam-type structures, Archives of Acoustics, 43(2): 283–295, doi: 10.24425/122376.

Vo T.P., Thai H.-T., Aydogdu M. (2017), Free vibration of axially loaded composite beams using a fourunknown shear and normal deformation theory, Composite Structures, 178: 406–414, doi: 10.1016/j.comp struct.2017.07.022.

Zheng H., Cai C. (2004), Minimization of sound radiation from based beams through optimization of partial constrained layer damping treatment, Applied Acoustics, 65(5): 501–520, doi: 10.1016/j.apacoust. 2003.11.008.

Zhu T.L. (2011), The vibrations of pre-twisted rotating Timoshenko beams by the Rayleigh-Ritz method, Computational Mechanics, 47(4): 395–408, doi: 10.1007/s00466-010-0550-9.

DOI: 10.24425/aoa.2022.140736

Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN)