Transient Response Of Cylindrical Shells Research Articles

Semi-analytical vibration analysis of FGM cylindrical shells surrounded by elastic foundations in a thermal environment

The natural frequency and transient response of FGM cylindrical shells under arbitrary boundary conditions are performed in present work. A novel semi-analytical method, which integrates Durbin’s inverse Laplace transform and the differential quadrature method, is developed to analyze the dynamical behavior of cylindrical shells. Durbin’s numerical inversion method is selected to gain time domain solutions. The trigonometric series expansion is used in the circumferential direction whereas the use of differential quadrature method provides numerical solutions in terms of axial direction. Comparisons show that the calculated natural frequencies are in good agreement with results in the literature. Convergence study illustrates that the developed method is rapidly convergent with the increase of sampling points, and the calculated transient response of the cylindrical shell is validated by comparing with Navier’s solution. The influences of boundary conditions, material graded indexes, temperature changes, elastic foundation coefficients and geometric parameters on transient response are analyzed. Numerical results indicate that the peak displacement of cylindrical shells increases with the increase of temperature changes and length-radius ratios or the decrease of elastic foundation coefficients and thickness-radius ratios.

Shock initiated instabilities in underwater cylindrical structures

An experimental investigation to understand the mechanisms of dynamic buckling instability in cylindrical structures due to underwater explosive loadings is conducted. In particular, the effects of initial hydrostatic pressure coupled with a dynamic pressure pulse on the stability of metallic cylindrical shells are evaluated. The experiments are conducted at varying initial hydrostatic pressures, below the critical buckling pressure, to estimate the threshold after which dynamic buckling will initiate. The transient underwater full-field deformations of the structures during shock wave loading are captured using high-speed stereo photography coupled with modified 3-D Digital Image Correlation (DIC) technique. Experimental results show that increasing initial hydrostatic pressure decreases the natural vibration frequency of the structure indicating loss in structural stiffness. DIC measurements reveal that the initial structural excitations primarily consist of axisymmetric vibrations due to symmetrical shock wave loading in the experiments. Following their decay after a few longitudinal reverberations, the primary mode of vibration evolves which continues throughout later in time. At the initial hydrostatic pressures below the threshold value, these vibrations are stable in nature. The analytical solutions for the vibration frequency and the transient response of cylindrical shell are discussed in the article by accounting for both (1) the added mass effect of the surrounding water and (2) the effect of initial stress on the shell imposed by the hydrostatic pressure. The analytical solutions match reasonably well with the experimental vibration frequencies. Later, the transient response of a cylindrical shell subjected to a general underwater pressure wave loading is derived which leads to the analytical prediction of dynamic stability.

Comparative studies of the transient response for PECP, MSCP, Barium Titanate, magneto-electro-elastic finite cylindrical shell under constant internal pressure using finite element method

Transient response for (PZT)-epoxy mixed component (PECP), (Terfenol- D)-epoxy mixed components (MSCP), Barium Titanate (BaTiO 3) and magneto-electro-elastic (MEE) cylindrical shell is evaluated by developing the semi-analytical finite element model using the constitutive equations of the piezomagnetic medium employing the fourth-order Runge–Kutta method. Numerical results are presented and compared for the above materials under different clamped boundary conditions. A comparison between the elastic and the coupled response of the MEE shell is also presented. Ansys 8.1 has been used to validate the displacement ( U r ) and potentials ( φ , ψ ) for PECP and MSCP material with code. Studies for the transient response of cylindrical shell made of these materials will be highly useful for the design of sensors and actuators, for the active vibration control of structures

An eigenvector method to determine the transient response of cylindrical shells in a fluid with uniform axial flow

A general time domain approach is presented to evaluate the vibratory response of cylindrical shells in time-invariant axial flows to broadband time-dependent excitations. The approach is based on the use of an in vacuo eigenvector expansion with time-dependent coefficients for the velocity field of the shell. A set of convolution integral equations are developed for the eigenvelocities that are coupled due to the fluid loading. These equations are similiar to those developed for planar vibrators and are readily solved by marching forward in time. The known terms in the equations are the ρc fluid-loaded admittances of each eigenvector and the radition impulse responses. Since these are easily obtained, a large number of eigenvectors can be included in the analysis. Numerical results illustrating the responses of a simply supported cylindrical shell to an impulsive ring excitation are presented.

Transient response of cylindrical shells with arbitrary shaped sections

A new coordinate transformation function is presented, with the help of which a cylindrical shell of arbitrary cross-section can be mapped approximately into a circular cylindrical shell. Using this method, the transient response of a non-circular cylindrical shell subjected to a shock wave is obtained by the finite strip method. The versatility and accuracy of the method are amply demonstrated through a number of numerical examples.

Stationary and Transient Response of Cylindrical Shells Under Random Excitation

This paper presents the random vibration analysis of a simply supported cylindrical shell under a ring load which is uniform around the circumference. The time history of the excitation is assumed to be a stationary wide-band random process. The finite element method and the condition of symmetry along the length of the cylinder are used to calculate the natural frequencies and associated mode shapes. Maximum values of the mean square displacements and velocities occur at the point of application of the load. It is seen that the transient response of the shell under wide band stationary excitation is nonstationary in the initial stages and approaches the stationary solution for large value of time.

Static and transient response of cylindrical shells

Static and transient analysis of composite cylindrical shells is presented using a recently proposed shear deformation theory. The dynamic response is obtained by employing the numerical time integration scheme due to Newmark. The results obtained by using classical shell theory (CST) and Mindlin-type shear deformation theory (SDT) are compared with those obtained by using the proposed theory. The comparison studies reveal that the linear stress distribution, as assumed in CST and SDT, differs considerably from the predicted nonlinear distribution of the proposed theory.

Transient response of cylindrical shells to localized heat sources

An exact analysis of the dynamic problem on the thermal displacements and stresses of cylindrical shells subjected to instantaneous heating is carried out. Equations of motion for cylindrical shells, including the thermal effects, are reduced and solved by using the Fourier and Laplace transformation methods, after obtaining the temperature distribution determined from the nonstationary equation of heat conduction for a shell under a prescribed temperature field. Numerical results are presented for the thermal displacement and stresses due to the time variation together with the quasistatic ones.

The Effect of Pulse Duration on the Transient Response of Cylindrical Shells Subjected to Axial Impact

The Effect of Pulse Duration on the Transient Response of Cylindrical Shells Subjected to Axial Impact