Wave Based Method for Free and Forced Vibration Analysis of Cylindrical Shells With Discontinuity in Thickness

Abstract

Wave based method (WBM) is presented to analyze the free and forced vibration of cylindrical shells with discontinuity in thickness. The hull is first divided into multiple segments according to the locations of thickness discontinuity and/or driving points, and then the Fl€ ugge theory is adopted to describe the motion of cylindrical segments. The dynamic field variables in each segment are expressed as wave function expansions, which accurately satisfy the equations of motion and can be used to analyze arbitrary boundary conditions, e.g., classical or elastic boundary conditions. Finally, the boundary conditions and interface continuity conditions between adjacent segments are used to assemble the final governing equation to obtain the free and forced vibration results. By comparing with the results existing in open literate and calculated by finite element method (FEM), the present method WBM is verified. Furthermore, the influences of the boundary conditions and the locations of thickness discontinuity on the beam mode frequency and fundamental frequency are discussed. The effects of the direction of external force, location of external point force, and the structural damping on the forced vibration are also analyzed.

Free and Forced Vibration Analysis of Airtight Cylindrical Vessels with Doubly Curved Shells of Revolution by Using Jacobi-Ritz Method

“…Tornabene et al [14][15][16] studied the dynamic behavior of functionally graded or laminated composite doubly curved shells and panels of revolution by using the Generalized Differential Quadrature (GDQ) method. Chen et al [17] presented wave based method to analyze the free and forced vibration of cylindrical shells with discontinuity in thickness. Ma et al [18] presented a free and forced vibration analysis of coupled conical-cylindrical shells with arbitrary boundary conditions using a modified Fourier-Ritz method.…”

Free and Forced Vibration Analysis of Stepped Circular Cylindrical Shells with Several Intermediate Supports Using an Extended Wave Method; a Generalized Approach

“…In addition, existence of discontinuity in the shell thickness or shell steps is inevitable in many industrial elements such as accumulators, fluid tanks and pipes. Hence, following the importance of the support characteristics and the nonuniform thickness of the shell in the practical application, the researchers have been encouraged to examine these effects on the vibration analysis of shells like in Zhou et al (2012), Qu et al (2013), Chen et al (2015), Chen et al (2013), and finally Wang et al (1997). In this way, different numerical methods, e.g.…”

“…finite element method (FEM) like in Salahifar and Mohareb (2012), weighted residual method as in Qu et al (2013), generalized differential quadrature method (GDQ) as in Loy et al (1997), and analytical solutions, e.g. close form solutions as those represented by Chen et al (2013), wave based method (WBM) like in Chen et al (2015), transfer function method (TFM) as in Zhou et al (1995) and state space techniques (SST) like in Zhang and Xiang (2007), are proposed for analysis of such systems.…”

“…Kx=0 and Krθ=0, and so on. Tables 1 and 2 are regulated to compare the results of frequency analysis of a stepped shell with elastic ended supports using the proposed method and those reported in Qu et al (2013) and Chen et al (2015). Qu et al (2013) have solved the issue of free and forced vibration analysis in a stepped shell with flexible ended supports using a numerical approach, modified variational principle and leastsquares weighted residual method mixed by domain decomposition method (DDM).…”

“…Qu et al (2013) have solved the issue of free and forced vibration analysis in a stepped shell with flexible ended supports using a numerical approach, modified variational principle and leastsquares weighted residual method mixed by domain decomposition method (DDM). In a same manner, Chen et al (2015) have utilized Flügge thin shell theory and the wave based method or WBM, and they have analyzed the same issue, adopted by Qu et al (2013), under a point load excitation. Hence, by considering the presence of only one step at the shell geometry and neglecting the interior supports, i.e.…”