THE GENERAL SOLUTION FOR THE STRESS PROBLEM OF CIRCULAR CYLINDRICAL SHELLS WITH AN ARBITRARY CUTOUT

In this paper a complex variable analytic method for solving stress concentrations in the circular cylindrical shell is proposed. The problem to be solved can be summarized into the solution of an infinite algebraic equation series. The solution can be normal and effective by means of this method. Numerical results for stress concentrations in the shell with a circular, elliptic cutout are graphically presented.

Exact free vibration analysis of open circular cylindrical shells by the method of reverberation-ray matrix

This paper is concerned with the free vibration analysis of open circular cylindrical shells with either the two straight edges or the two curved edges simply supported and the remaining two edges supported by arbitrary classical boundary conditions. Based on the Donnell-Mushtari-Vlasov thin shell theory, an analytical solution of the traveling wave form along the simply supported edges and the modal wave form along the remaining two edges is obtained. With such a unidirectional traveling wave form solution, the method of the reverberation-ray matrix is introduced to derive the equation of natural frequencies of the shell with different classical boundary conditions. The exact solutions for natural frequencies of the open circular cylindrical shell are obtained with the employment of a golden section search algorithm. The calculation results are compared with those obtained by the finite element method and the methods in the available literature. The influence of length, thickness, radius, included angle, and the boundary conditions of the open circular cylindrical shell on the natural frequencies is investigated. The exact calculation results can be used as benchmark values for researchers to check their numerical methods and for engineers to design structures with thin shell components.

NONLINEAR VIBRATION RESPONSE AND BIFURCATION OF CIRCULAR CYLINDRICAL SHELLS UNDER TRAVELING CONCENTRATED HARMONIC EXCITATION

The nonlinear vibration of a cantilever cylindrical shell under a concentrated har- monic excitation moving in a concentric circular path is proposed. Nonlinearities due to large- amplitude shell motion are considered, with account taken of the effect of viscous structure damp- ing. The system is discretized by Galerkin＇s method. The method of averaging is developed to study the nonlinear traveling wave responses of the multi-degrees-of-freedom system. The bifur- cation phenomenon of the model is investigated by means of the averaged system in detail. The results reveal the change process and nonlinear dynamic characteristics of the periodic solutions of averaged equations.

New matrix method for analyzing vibration and damping effect of sandwich circular cylindrical shell with viscoelastic core

Based on the linear theories of thin cylindrical shells and viscoelastic materials, a governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation is derived. The equation can be written as a matrix differential equation of the first order, and is obtained by considering the energy dissipation due to the shear deformation of the viscoelastic core layer and the interaction between all layers. A new matrix method for solving the governing equation is then presented With an extended homogeneous capacity precision integration approach. Having obtained these, vibration characteristics and damping effect of the sandwich cylindrical shell can be studied. The method differs from a recently published work as the state vector in the governing equation is composed of displacements and internal forces of the sandwich shell rather than displacements and their derivatives. So the present method can be applied to solve dynamic problems of the kind of sandwich shells with various boundary conditions and partially constrained layer damping. Numerical examples show that the proposed approach is effective and reliable compared with the existing methods.

Acoustic radiation from the submerged circular cylindrical shell treated with active constrained layer damping

Based on the transfer matrix method of exploring the circular cylindrical shell treated with active constrained layer damping（i.e., ACLD）, combined with the analytical solution of the Helmholtz equation for a point source, a multi-point multipole virtual source simulation method is for the first time proposed for solving the acoustic radiation problem of a submerged ACLD shell. This approach, wherein some virtual point sources are assumed to be evenly distributed on the axial line of the cylindrical shell, and the sound pressure could be written in the form of the sum of the wave functions series with the undetermined coefficients, is demonstrated to be accurate to achieve the radiation acoustic pressure of the pulsating and oscillating spheres respectively. Meanwhile, this approach is proved to be accurate to obtain the radiation acoustic pressure for a stiffened cylindrical shell. Then, the chosen number of the virtual distributed point sources and truncated number of the wave functions series are discussed to achieve the approximate radiation acoustic pressure of an ACLD cylindrical shell. Applying this method, different radiation acoustic pressures of a submerged ACLD cylindrical shell with different boundary conditions, different thickness values of viscoelastic and piezoelectric layer, different feedback gains for the piezoelectric layer and coverage of ACLD are discussed in detail. Results show that a thicker thickness and larger velocity gain for the piezoelectric layer and larger coverage of the ACLD layer can obtain a better damping effect for the whole structure in general. Whereas, laying a thicker viscoelastic layer is not always a better treatment to achieve a better acoustic characteristic.

Nonlinear Dynamics of Clamped Initial Imperfect Functionally Graded Material Circular Cylindrical Shell Considering the Axisymmetric Mode

This paper investigates the dynamic responses of clamped-clamped functionally graded material circular cylindrical shell at both ends with small initial geometric imperfection and subjected to complex loads.The small initial geometric imperfection of the cylindrical shell is characterized with the shape of hyperbolic function.The effects of radial harmonic excitation combined with thermal loads are considered.The classical theory and von-Karman type nonlinear geometric equation are applied to obtain partial differential equation of the functionally gradient material circular cylindrical shell by the Hamilton’s principle.The partial differential dynamic equations are truncated by the Galerkin technique,using the modal expansion with the inclusion of axisymmetric and asymmetric modes.The effective material properties vary in the radial direction following a power-law distribution accordancewith the volume fractions.The effects of volume fraction indexes,ratios of thickness-radius and lengthradius on the first three dimensionless natural frequencies of the perfect cylindrical shell and its counterpart with imperfection are given.The effects of radial external loads,initial geometric imperfections and volume fraction index on the nonlinear dynamic response of the clamped-clamped FGM circular cylindrical shell are discussed by numerical calculation.