Frequency analysis of multiple layered cylindrical shells under lateral pressure with asymmetric boundary conditions

Mathematical Problems in Engineering

Wen

2016

An analysis of nonlinear behaviors of pressure thin-wall pipe segment with supported clearance at both ends was presented in this paper. The model of pressure thin-wall pipe segment with supported clearance was established by assuming the restraint condition as the work of springs in the deformation directions. Based on Sanders shell theory, Galerkin method was utilized to discretize the energy equations, external excitation, and nonlinear restraint forces. And the nonlinear governing equations of motion were derived by using Lagrange equation. The displacements in three directions were represented by the characteristic orthogonal polynomial series and trigonometric functions. The effects of supporting stiffness and supported clearance on dynamic behavior of pipe wall were discussed. The results show that the existence of supported clearance may lead to the changing of stiffness of the pipe vibration system and the dynamic behaviors of the pipe system show nonlinearity and become more complex; for example, the amplitude-frequency curve of the foundation frequency showed hard nonlinear phenomenon. The chaos and bifurcation may emerge at some region of the values of stiffness and clearance, which means that the responses of the pressure thin-wall pipe segment would be more complex, including periodic motion, times periodic motion, and quasiperiodic or chaotic motions.

Section: Instructionmentioning

confidence: 99%

Nonlinear Dynamic Behavior Analysis of Pressure Thin-Wall Pipe Segment with Supported Clearance at Both Ends

Mathematical Problems in Engineering

Wen

2016

“…To study the free vibration of the pipe, substituting equation (17) into (16), the eigenvalue problem of the pressure pipe can be obtained as…”

Section: The Differential Equation Of Vibrationmentioning

confidence: 99%

“…Pressure shell was also a popular object for researchers. Isvandzibaei et al 17 investigated the effect of geometrical parameter and effect of the asymmetric boundary conditions on natural frequencies characteristic under lateral pressure. And the studying way is various.…”

Section: Introductionmentioning

confidence: 99%

The sensibility on dynamic characteristics of pre-pressure thin-wall pipe under elastic boundary conditions

Proceedings of the Institution of Mechanical Engineers, Part C:

Boqing

et al. 2016

Consideration is given to dynamic behavior of cylindrical pressure pipe with elastic boundary conditions. Based on Sanders’ shell theory and Hamilton principle, the system equations are established for integrating the uniform distributed pressure into the elastic boundary condition. In the analytical formulation, the Rayleigh–Ritz method with a set of displacement shape functions is used to deduce mass, damping, and stiffness matrices of the pipe system. The displacements in three directions are represented by the characteristic orthogonal polynomial series and trigonometric functions which are satisfied with the elastic boundary conditions, which are represented as four sets of independent springs placed at the ends including three sets of linear springs and one set of rotational spring. The pressure pipe always suffers a uniform distributed pressure in radial direction. To verify the accuracy and reliability of the present method, several numerical examples with classical boundary condition, including free and simply supported supports are listed and comparisons are made with open literature. Then the influences of boundary restraint stiffness and the distributed pressure on natural frequency and the forced vibration response are studied: The natural frequencies increase significantly as the restraint stiffness or the distributed pressure increases. Compared to the rotational spring stiffness, the stiffnesses of axial, radial, and circumferential springs have more significant effect on natural frequency. And the lower modes are more sensitive on restraint stiffness than higher modes. But the variation of natural frequency with respect to the spring stiffness decreases monotonically with the increasing distributed pressure. The forced vibration response is also affected by the restraint stiffness.

“…Based on Sanders' theory, Sun et al [18] studied the vibration studies of rotating cylindrical shells with arbitrary edges using characteristic orthogonal polynomials in the Rayleigh-Ritz method. Isvandzibaei et al [19,20] studied the vibration of multiple layered cylindrical shells under lateral pressure with asymmetric boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…(16)is three degrees of freedom, and M, C, K is three order matrix. Substituting Eqs (19),(20). into Eq.…”

mentioning

confidence: 99%

Natural Characteristic of Thin-Wall Pipe under Uniformly Distributed Pressure

She

et al. 2018

Chin. J. Mech. Eng.

Natural characteristics of thin-wall pipe of the compressor under uniformly distributed pressure were presented in this paper based on a cylindrical shell model. In the traditional method, the beam model was usually used to analyze the pipe system. In actual fact, the pipe segment of the compressor was always broken in the form of a long crack or a partial hole and the phenomenon was hardly explained by beam model. According to the structure characteristic of compressor pipe segment, whose radius is large and thickness is little, shell model shows the advantage in this kind of pipe problem. Based on Sanders' shell theory, the vibration differential equation of pipe was established by applying the energy method. The influences of length to radius ratio (L/R), thickness to radius ratio (h/R), circumferential wave number (n) and pressure (q) on the natural frequencies of pipe were analyzed. The study shows: Pressure and structural parameters have a great effect on the natural characteristics of the pipe. Natural frequency increases as the pressure increases, especially for the higher mode. The sensitivity of natural frequency on pressure becomes stronger with h/R ratio increases; when L/R ratio is greater than a certain critical value, the influence of the pressure on natural frequency will no longer be obvious. The value of n corresponding to the minimum natural frequency also depends on the value of pressure. In the end, analysis of the forced vibration of a specific pipeline model was given and the modal shapes were illustrated to understand the break of the pipe. The research here will provide the theory support for the dynamic design of related pressure pipe and further experiment study should be employed.