A modeling method for vibration analysis of cracked beam with arbitrary boundary condition

This paper establishes a cracked Timoshenko beams model to investigate the vibration behavior based on the ultraspherical polynomials.Timoshenko beam theory is applied to model the free vibration analysis of the cracked beam and the numerical results are obtained by using ultraspherical orthogonal polynomials.The boundary conditions of both ends of the cracked beam are modeled as the elastic spring and the beam is divided into two parts by the crack section,and continuous conditions at the connecting face are modeled by the inverse of the flexibility coefficients of fracture mechanics theory.Ignoring the influence of boundary conditions,displacements admissible functions of cracked Timoshenko beam can be set up as ultraspherical orthogonal polynomials.The accuracy and robustness of the present method are evidenced through comparison with previous literature and the results achieved by the finite element method(FEM).In addition,the effects of flexibility coefficient on the natural frequencies are also investigated by using the proposed method.Numerical examples are given for free vibration analysis of cracked beams with various boundary conditions,which may be provided as reference data for future study.

Haar wavelet discretization method for free vibration study of laminated composite beam under generalized boundary conditions

Investigation on vibration of laminated composite beam(LCB)is an important issue owing to its wide use as fundamental component.In the present work,we study the free vibration of arbitrarily LCB with generalized elastic boundary condition(BC)by using Haar wavelet discretization method(HWDM).Timoshenko beam theory is utilized to model the free vibration of LCB.The LCB is first split into several segments,and then the displacement for each segment is obtained from the Haar wavelet series and their integral.Hamilton’s principle is applied to construct governing equations and the artificial spring boundary technique is adopted to obtain the general elastic boundary and continuity conditions at two ends of LCB.The vibration characteristics of beam with different fiber orientations and lamina numbers is investigated and its displacements are compared with those in previous works.Numerical results are shown graphically and demonstrate the validation of our method.

A semi-analytical method for forced vibration analysis of cracked laminated composite beam with general boundary condition

In this paper,a semi-analytical method for the forced vibration analysis of cracked laminated composite beam(CLCB)is investigated.One computational model is formulated by Timoshenko beam theory and its dynamic solution is solved using the Jacobi-Ritz method.The boundary conditions(BCs)at both ends of the CLCB are generalized by the application of artificial elastic springs,the CLCB is separated into two elements along the crack,the flexibility coefficient of fracture theory is used to model the essential continuous condition of the connective interface.All the allowable displacement functions used to analyze dynamic characteristics of CLCB are expressed by classical Jacobi orthogonal polynomials in a more general form.The accuracy of the proposed method is verified through the compare with results of the finite element method(software ABAQUS is used in this paper).On this basis,the parametric study for dynamic analysis characteristics of CLCB is performed to provide reference datum for engineers.

A solution method for free vibration analysis of coupled laminated composite elliptical-cylindrical-elliptical shell with elastic boundary conditions

In this paper,an efficient,convenient and explicit method based on the Haar wavelet discretization ap-proach for analyzing the free vibration of the coupled laminated composite elliptical-cylindrical-elliptical shells(ECESs)with elastic boundary conditions is presented.Two elliptical double curved shells are cou-pled on both end of cylindrical shell.Based on the first-order shear deformation theory the equations of motion for ECES are derived by means of Hamilton’s principle.The separation of variables is first per-formed;i.e.displacement components and rotations of any point of the ECES are expanded to the Haar wavelet series in the meridian direction and Fourier series in circumferential direction.The constants appearing from the integrating process are determined by boundary conditions,and thus the partial dif-ferential equations are transformed into algebraic equations.By solving the characteristic equation,the natural frequencies and mode shapes of coupled laminated composite ECES are obtained.The present re-sults have been compared with those of the published literature.The comparison results show that this method has high accuracy,high reliability and also a higher convergence rate in attaining the frequencies of the coupled laminated composite ECESs.Then,the effects of the main parameters such as material properties,geometrical parameters,and various boundary conditions,on the vibrational behavior of the coupled ECESs,are investigated.Finally,new free vibration analysis results of the coupled laminated com-posited ECES,which can be used as benchmark data for researchers in this field,are reported through the parameter study.