Abstract
Forced vibration of thin-wall cylindrical shell under nonlinear boundary condition was discussed in this paper. The nonlinear boundary was modeled as supported clearance in one end of shell and the restraint was assumed as linearly elastic in the radial direction. Based on Sanders’ shell theory, Lagrange equation was utilized to derive the nonlinear governing equations of cylindrical shell. The displacements in three directions were represented by beam functions and trigonometric functions. In the study of nonlinear dynamic responses of thin-wall cylindrical shell with supported clearance under external loads, the Newmark method is used to obtain time history, frequency spectrum plot, phase portraits, Poincare section, bifurcation diagrams, and three-dimensional spectrum plot with different parameters. The effects of external loads, supported clearance, and support stiffness on nonlinear dynamics behaviors of cylindrical shell with nonlinear boundary condition were discussed.
Highlights
Circular cylindrical shell structures are commonly used in various engineering applications in the aerospace, petrochemical engineering, marine, and so on
In order to study the complexity of vibration, the bifurcation diagrams, time histories, frequency spectrum plots, phase portraits, and Poincare sections are selected as tools to study the nonlinear dynamic responses of the cylindrical shell
The nonlinear boundary was considered as supported clearance in one end of the cylindrical shell. m = 1 and n = 8 were set to calculate the numerical results of dynamic response
Summary
Circular cylindrical shell structures are commonly used in various engineering applications in the aerospace, petrochemical engineering, marine, and so on. Zhou et al [20] applied the method of wave propagations to investigate the effects of elastic restraints on the frequency parameters for cylindrical shells of different geometrical characteristics Jin and his coauthors [21,22,23,24,25] used this energy oriented modified Fourier method to carry out the vibration problem of isotropic and composite structures with general boundary conditions. Singh [31] studied the free vibration of open skewed circular cylindrical shells under partial support at the edges They discussed the effects of different shell parameters on the natural frequency and mode shapes. The effects of external loads, supported clearance, and support stiffness on nonlinear dynamic behaviors of the system were discussed
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