Semnan University Press Journal of Modeling in Engineering 2008-4854 11 34 2013 09 23 FREE VIBRATION ANALYSIS OF CRACKED POST-BUCKLED BEAM BY DIFFERENTIAL QUADRATURE METHOD FREE VIBRATION ANALYSIS OF CRACKED POST-BUCKLED BEAM BY DIFFERENTIAL QUADRATURE METHOD 1 16 1647 10.22075/jme.2017.1647 FA P. Jamshidi Moghadam mm S. Moradi Journal Article 2017 01 28 The vibration analysis of cracked post-buckled beam is investigated using the differential quadrature method. Crack, assumed to be open, is modeled by a massless rotational spring. The beam is divided into two segments and the governing nonlinear equations of motion for the post-buckled state are derived. The solution consists of static and dynamic parts, which both result in nonlinear differential equations. Application of differential quadrature to the static differential equations results in a nonlinear algebraic system of equations, which will be solved utilizing an arc length strategy. Next, the differential quadrature is applied to the linearized dynamic differential equations of motion and their corresponding boundary and continuity conditions. Upon solution of the resulting eigenvalue problem, the natural frequencies and mode shapes of the beam are extracted. Several numerical case studies on cracked beams are conducted to ensure the integrity and accuracy of the proposed method. The results confirm the efficiency and accuracy of the differential quadrature method in dealing with this class of engineering problems. The vibration analysis of cracked post-buckled beam is investigated using the differential quadrature method. Crack, assumed to be open, is modeled by a massless rotational spring. The beam is divided into two segments and the governing nonlinear equations of motion for the post-buckled state are derived. The solution consists of static and dynamic parts, which both result in nonlinear differential equations. Application of differential quadrature to the static differential equations results in a nonlinear algebraic system of equations, which will be solved utilizing an arc length strategy. Next, the differential quadrature is applied to the linearized dynamic differential equations of motion and their corresponding boundary and continuity conditions. Upon solution of the resulting eigenvalue problem, the natural frequencies and mode shapes of the beam are extracted. Several numerical case studies on cracked beams are conducted to ensure the integrity and accuracy of the proposed method. The results confirm the efficiency and accuracy of the differential quadrature method in dealing with this class of engineering problems. https://modelling.semnan.ac.ir/article_1647_866c81963edea7428bb051e9e1186032.pdf