References
- S. Paunikar, "Wave propagation in adhesively bonded single lap joints: solution of forward and inverse problems," Ph.D. Thesis, Indian Institute of Science, Bangalore, India, 2021.
- J. Seelig and W. Hoppmann, “Normal mode vibrations of systems of elastically connected parallel bars,” J. Acoust. Soc. Am., vol. 36, no. 1, pp. 93–99, 1964. DOI: https://doi.org/10.1121/1.1918919.
- S. S. Rao, “Natural vibrations of systems of elastically connected Timoshenko beams,” J. Acoust. Soc. Am., vol. 55, no. 6, pp. 1232–1237, 1974. DOI: https://doi.org/10.1121/1.1914690.
- Y.-H. Chen and J.-T. Sheu, “Dynamic characteristics of layered beam with flexible core,” J. Vib. Acoust., vol. 116, no. 3, pp. 350–356, 1994. DOI: https://doi.org/10.1115/1.2930435.
- S. Kukla, “Free vibration of the system of two beams connected by many translational springs,” J. Sound Vib., vol. 172, no. 1, pp. 130–135, 1994. DOI: https://doi.org/10.1006/jsvi.1994.1163.
- S. M. Hashemi and M. J. Richard, “Free vibrational analysis of axially loaded bending-torsion coupled beams: A dynamic finite element,” Comput. Struct., vol. 77, no. 6, pp. 711–724, 2000. DOI: https://doi.org/10.1016/S0045-7949(00)00012-2.
- Z. Oniszczuk, “Free transverse vibrations of elastically connected simply supported double-beam complex system,” J. Sound Vib., vol. 232, no. 2, pp. 387–403, 2000. DOI: https://doi.org/10.1006/jsvi.1999.2744.
- Z. Oniszczuk, “Forced transverse vibrations of an elastically connected complex simply supported double-beam system,” J. Sound Vib., vol. 264, no. 2, pp. 273–286, 2003. DOI: https://doi.org/10.1016/S0022-460X(02)01166-5.
- H. Vu, A. Ordonéz, and B. Karnopp, “Vibration of a double-beam system,” J. Sound Vib., vol. 229, no. 4, pp. 807–822, 2000. DOI: https://doi.org/10.1006/jsvi.1999.2528.
- J. Li and H. Hua, “Spectral finite element analysis of elastically connected double-beam systems,” Finite Elem. Anal. Des., vol. 43, no. 15, pp. 1155–1168, 2007. DOI: https://doi.org/10.1016/j.finel.2007.08.007.
- Y. Zhang, Y. Lu, S. Wang, and X. Liu, “Vibration and buckling of a double-beam system under compressive axial loading,” J. Sound Vib., vol. 318, no. 1–2, pp. 341–352, 2008. DOI: https://doi.org/10.1016/j.jsv.2008.03.055.
- M. Şimşek and S. Cansız, “Dynamics of elastically connected double-functionally graded beam systems with different boundary conditions under action of a moving harmonic load,” Compos. Struct., vol. 94, no. 9, pp. 2861–2878, 2012. DOI: https://doi.org/10.1016/j.compstruct.2012.03.016.
- L. Xiaobin, X. Shuangxi, W. Weiguo, and L. Jun, “An exact dynamic stiffness matrix for axially loaded double-beam systems,” Sadhana, vol. 39, no. 3, pp. 607–623, 2014. DOI: https://doi.org/10.1007/s12046-013-0214-5.
- V. Stojanović and P. Kozić, Vibrations and Stability of Complex Beam Systems. Springer, Switzerland, 2015,
- Q. Mao and N. Wattanasakulpong, “Vibration and stability of a double-beam system interconnected by an elastic foundation under conservative and nonconservative axial forces,” Int. J. Mech. Sci., vol. 93, pp. 1–7, 2015. DOI: https://doi.org/10.1016/j.ijmecsci.2014.12.019.
- Y. Song, S. Kim, I. Park, and U. Lee, “Dynamics of two-layer smart composite Timoshenko beams: Frequency domain spectral element analysis,” Thin-Walled Struct., vol. 89, pp. 84–92, 2015. DOI: https://doi.org/10.1016/j.tws.2014.12.016.
- I. Bochicchio, C. Giorgi, and E. Vuk, “Buckling and nonlinear dynamics of elastically coupled double-beam systems,” Int. J. Non-Linear Mech., vol. 85, pp. 161–173, 2016. DOI: https://doi.org/10.1016/j.ijnonlinmec.2016.06.009.
- H. Deng, K. Chen, W. Cheng, and S. G. Zhao, “Vibration and buckling analysis of double-functionally graded Timoshenko beam system on Winkler-Pasternak elastic foundation,” Compos. Struct., vol. 160, pp. 152–168, 2017. DOI: https://doi.org/10.1016/j.compstruct.2016.10.027.
- Y. Li and L. Sun, “Transverse vibration of an undamped elastically connected double-beam system with arbitrary boundary conditions,” J. Eng. Mech., vol. 142, no. 2, p. 04015070, 2016. DOI: https://doi.org/10.1061/(ASCE)EM.1943-7889.0000980.
- Y. Li, Z. Hu, and L. Sun, “Dynamical behavior of a double-beam system interconnected by a viscoelastic layer,” Int. J. Mech. Sci., vol. 105, pp. 291–303, 2016. DOI: https://doi.org/10.1016/j.ijmecsci.2015.11.023.
- V. Adámek, “The limits of Timoshenko beam theory applied to impact problems of layered beams,” Int. J. Mech. Sci., vol. 145, pp. 128–137, 2018. DOI: https://doi.org/10.1016/j.ijmecsci.2018.07.001.
- R. Dimitri, F. Tornabene, and G. Zavarise, “Analytical and numerical modeling of the mixed-mode delamination process for composite moment-loaded double cantilever beams,” Compos. Struct., vol. 187, pp. 535–553, 2018. DOI: https://doi.org/10.1016/j.compstruct.2017.11.039.
- F. Han, D. Dan, and W. Cheng, “An exact solution for dynamic analysis of a complex double-beam system,” Compos. Struct., vol. 193, pp. 295–305, 2018. DOI: https://doi.org/10.1016/j.compstruct.2018.03.088.
- H. Fei, D. Danhui, W. Cheng, and P. Jia, “Analysis on the dynamic characteristic of a tensioned double-beam system with a semi theoretical semi numerical method,” Compos. Struct., vol. 185, pp. 584–599, 2018. DOI: https://doi.org/10.1016/j.compstruct.2017.11.010.
- Q. Hao, W. Zhai, and Z. Chen, “Free vibration of connected double-beam system with general boundary conditions by a modified Fourier-Ritz method,” Arch. Appl. Mech., vol. 88, no. 5, pp. 741–754, 2018. DOI: https://doi.org/10.1007/s00419-017-1339-5.
- M. S. Sari, W. G. Al-Kouz, and R. Al-Waked, “Bending–torsional-coupled vibrations and buckling characteristics of single and double composite Timoshenko beams,” Adv. Mech. Eng., vol. 11, no. 3, p. 168781401983445, 2019. DOI: https://doi.org/10.1177/1687814019834452.
- S. Liu and B. Yang, “A closed-form analytical solution method for vibration analysis of elastically connected double-beam systems,” Compos. Struct., vol. 212, pp. 598–608, 2019. DOI: https://doi.org/10.1016/j.compstruct.2019.01.038.
- J. Yang, X. He, H. Jing, H. Wang, and S. Tinmitonde, “Dynamics of double-beam system with various symmetric boundary conditions traversed by a moving force: Analytical analyses,” Appl. Sci., vol. 9, no. 6, p. 1218, 2019. DOI: https://doi.org/10.3390/app9061218.
- F. Han, D. Dan, and W. Cheng, “Exact dynamic characteristic analysis of a double-beam system interconnected by a viscoelastic layer,” Compos. B Eng., vol. 163, pp. 272–281, 2019. DOI: https://doi.org/10.1016/j.compositesb.2018.11.043.
- O. Ragb and M. S. Matbuly, “Nonlinear vibration analysis of elastically supported multi-layer composite plates using efficient quadrature techniques,” Int. J. Comput. Methods Eng. Sci. Mech., pp. 1–18, 2021.
- C. C. H. Guyott, P. Cawley, and R. Adams, “The non-destructive testing of adhesively bonded structure: A review,” J. Adhes., vol. 20, no. 2, pp. 129–159, 1986. DOI: https://doi.org/10.1080/00218468608074943.
- J.-M. Baik and R. B. Thompson, “Ultrasonic scattering from imperfect interfaces: A quasi-static model,” J. Nondestruct. Eval., vol. 4, no. 3-4, pp. 177–196, 1984. DOI: https://doi.org/10.1007/BF00566223.
- P. B. Nagy, “Ultrasonic classification of imperfect interfaces,” J. Nondestruct. Eval., vol. 11, no. 3–4, pp. 127–139, 1992. DOI: https://doi.org/10.1007/BF00566404.
- M. Golub, “Propagation of elastic waves in layered composites with microdefect concentration zones and their simulation with spring boundary conditions,” Acoust. Phys., vol. 56, no. 6, pp. 848–855, 2010. DOI: https://doi.org/10.1134/S1063771010060084.
- A. Pilarski and J. Rose, “Ultrasonic oblique incidence for improved sensitivity in interface weakness determination,” NDT Int., vol. 21, no. 4, pp. 241–246, 1988. DOI: https://doi.org/10.1016/0308-9126(88)90337-9.
- P. B. Nagy and L. Adler, “Nondestructive evaluation of adhesive joints by guided waves,” J. Appl. Phys., vol. 66, no. 10, pp. 4658–4663, 1989. DOI: https://doi.org/10.1063/1.343822.
- M. Lowe, R. Challis, and C. Chan, “The transmission of lamb waves across adhesively bonded lap joints,” J. Acoust. Soc. Am., vol. 107, no. 3, pp. 1333–1345, 2000. DOI: https://doi.org/10.1121/1.428420.
- B. Hosten and M. Castaings, “Finite elements methods for modeling the guided waves propagation in structures with weak interfaces,” J. Acoust. Soc. Am., vol. 117, no. 3, pp. 1108–1113, 2005. DOI: https://doi.org/10.1121/1.1841731.
- V. Vlasie, S. De Barros, M. Rousseau, and L. Champaney, “Ultrasonic rheological model of cohesive and adhesive zones in aluminum joints: Validation by mechanical tests,” Arch. Appl. Mech., vol. 75, no. 4–5, pp. 220–234, 2006. DOI: https://doi.org/10.1007/s00419-005-0401-x.
- G. Ghosh, R. Duddu, and C. Annavarapu, “On the robustness of the stabilized finite element method for delamination analysis of composites using cohesive elements,” Int. J. Comput. Methods Eng. Sci. Mech., pp. 1–21, 2021.
- J. Neto, R. D. Campilho, and L. Da Silva, “Parametric study of adhesive joints with composites,” Int. J. Adhes. Adhes., vol. 37, pp. 96–101, 2012. DOI: https://doi.org/10.1016/j.ijadhadh.2012.01.019.
- T. Ribeiro, R. Campilho, L. Da Silva, and L. Goglio, “Damage analysis of composite–aluminium adhesively-bonded single-lap joints,” Compos. Struct., vol. 136, pp. 25–33, 2016. DOI: https://doi.org/10.1016/j.compstruct.2015.09.054.
- T. Carlberger, K. S. Alfredsson, and U. Stigh, “Explicit FE-formulation of interphase elements for adhesive joints,” Int. J. Comput. Methods Eng. Sci. Mech., vol. 9, no. 5, pp. 288–299, 2008. DOI: https://doi.org/10.1080/15502280802229590.
- J. Reddy, An Introduction to the Finite Element Method. Tata McGraw-Hill, New Delhi, 2005.
- I. Shames and C. Dym, Energy and Finite Element Methods in Structural Mechanics. New Age International Publishers, New Delhi, 2009.
- J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, USA, 2003.
- R. D. Cook, Concepts and Applications of Finite Element Analysis. John Wiley & Sons, Singapore, 2007.