Linear And Non-linear Dynamical Analysis Of Beams And Cables And Their Combinations

The method of reverberation-ray matrix(MRRM) and the Homotopy analysis method (HAM) proposed in recent years for solving the linear and non-linear dynamics of structures have been successfully applied in many areas.In order to have a thorough understanding of these two methods and extend their applicability as well as provide useful advice for engineering practice,several dynamical problems of beams and cables and their combinations are investigated by making a hybrid use of the two methods mentioned above.Firstly,the optimization of dynamics of a Timoshenko beam with an internal elastic support under axial force is carried out using new formulations of MRRM which are completely in real form.Numerical examples are given to demonstrate the accuracy and numerical stability of the proposed method.Secondly,a recursive algorithm is proposed for the MRRM to exactly analyze the free vibration of beam structures including continuous beams and non-uniform beams.In contrast to the traditional MRRM,the recursive formulation can not only hold the numerical stability,but also can it cut down the heavy computational cost of storage and memory with the increase of elements and nodes.Thirdly,a continuous model describing the dynamic behaviour of cable-stayed beam systems has been presented,which permits us to clarify the characteristics of cable-beam interaction.A parametric analysis of linear modes through MRRM is performed to investigate how the mechanical characteristic influences the occurrence of global,local and coupled modes.Since the single-degree-of-freedom non-linear model is derived through the single-mode discretization,the HAM is successfully applied to obtain the frequency-amplitude relationship,which enables us to characterize the influence of various parameters on the non-linear system behaviour.Finally,based on the analysis of the static equilibrium configuration of inclined cable with damage,the effects on linear modes and non-linear behaviour of the cable-stayed beam systems due to cable damage are studied respectively with the MRRM and HAM.