Abstract
This article deals with free and forced vibration responses of the viscoelastic parabolic arches of variable thickness. Firstly, considering the effects of shear deformation and damping, time-dependent motion equations of in-plane loaded parabolic arches are obtained. Subsequently, the Laplace transform is applied to the obtained equations and solved by a powerful numerical method. Furthermore, the Kelvin viscose model is used to describe the viscoelastic material. Using an effective and suitable inverse numerical Laplace transform method, the results were transferred back to time space. The verification of the presented method is performed by comparing its results with the results of ANSYS. It has been shown in several examples that the proposed method is highly accurate and efficient compared to step-by-step time integration methods.
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