Vibrations of complex composite double-column system by extended Laplace transform method

Abstract

PurposeDouble-beam/column systems have drawn much attention in many engineering fields. This work aims to present the free and forced vibrations of a novel and complex double-column system with concentrated masses, axial loads and discrete viscoelastic supports subjected to the excitation of ground acceleration are solved by the extended Laplace transform method (ELTM).Design/methodology/approachIn this work, the authors proposed an extended Laplace transform method (ELTM), which is an exact and explicit analytical method. Firstly, the mathematical model simulating the vibrations of the double-column system is reformulated with Dirac's delta function. Secondly, the exact and explicit mode shape solutions are obtained, based on which the natural frequencies and dynamic responses are obtained. An illustrating example is presented to show the validity of the proposed method. A parametric study is carried out to investigate the influences of the non-dimensional column stiffness ratio and the support stiffness ratio on the peak dynamic displacement and velocity.FindingsIt is shown that the proposed method can give exact and explicit solutions of the mode shapes and natural frequencies. It is found that the asynchronous vibrations of the proposed double-column systems can be implemented to efficiently dissipate seismic energy, as shown in the time-histories of displacement and velocity.Practical implicationsThis research systematically studied the free and forced vibrations of the complex double-column system. The proposed extended ELTM is a general method. Its application to studying the energy dissipation capability implicates that the double-column system can be utilized to reduce responses in structures under earthquake attacks.Originality/valueThe proposed extended ELTM is original and powerful. Its application to study the complex double-columns system with discrete supports, concentrated masses and axial loads is novel.

Obtaining analytical solutions of (2+1)-dimensional nonlinear Zoomeron equation by using modified F-expansion and modified generalized Kudryashov methods

“…Many researchers have recently developed various methods for analytic, symbolic, numeric and soliton solutions to solve nonlinear PDEs. These methods can be listed as; the Euler and Adams–Bashforth methods (Roshan et al ., 2023), the extended Laplace transform method (Zhao and Chang, 2022), He’s variational iteration approaches (Khater, 2023a), He’s homotopy perturbation technique (Attia et al ., 2022), extended Fan-expansion method (Khater, 2023b), the Kudryashov’s methods (Ozisik et al ., 2022), Painlevé analysis (Kudryashov and Lavrova, 2023), Lax pairs (Kudryashov, 2021), Lie symmetry (Li and Zhang, 2019), the extended auxiliary equation method (qiong Xu, 2014), the generalized auxiliary equation method (Zhang, 2007; Abdou, 2007; Yomba, 2008), the improved Bernoulli sub-equation function method (Baskonus and Bulut, 2016), the extended mapping approach (Fang et al ., 2005), the simplified homogeneous balance method (Wang and Li, 2014), the modified exp(−Ω( ζ ))-expansion function method (Özpinar et al ., 2015; Baskonus and Aşkin, 2016), He’s variational iteration method (Momani and Abuasad, 2006; Dehghan and Shakeri, 2008), modified F-expansion method with the Riccati equation (Aasaraai et al ., 2013), the modified generalized Kudryashov’s method (Hassan et al ., 2014), the multiple exp-function method (Yıldırım and Yaşar, 2017), the auxiliary equation method (Ma et al ., 2009; Sirendaoreji, 2003), the simple equation method (Nofal, 2016; Zhao et al ., 2013) and residual power series method (Yusuf et al ., 2019).…”