K.Y. Lam

Frequency characteristics of a thin rotating cylindrical shell using the generalized differential quadrature method

Abstract In this paper, the generalized differential quadrature (GDQ) method is used for the first time to study the effects of boundary conditions on the frequency characteristics of a thin rotating cylindrical shell. The present analysis is based on Love-type shell theory and the governing equations of motion include the effects of initial hoop tension and the centrifugal and coriolis accelerations due to rotation. The displacement field is expressed as a product of unknown smooth continuous functions in the meridional direction and trigonometric functions along the circumferential direction so that the three-dimensional dynamic problem may be transformed mathematically into a one-dimensional problem. Based on this approach, the results are obtained for the effects of the boundary conditions on the frequency characteristics at different circumferential wave numbers and rotating speeds and various geometric properties; the effect of rotating speed on the relationship between frequency parameter and circumferential wave number is also discussed. To validate the accuracy and efficiency of the GDQ method, the results obtained are compared with those in the literature and very good agreement is achieved.

Generalized differential quadrature for free vibration of rotating composite laminated conical shell with various boundary conditions

By using the generalized differential quadrature (GDQ) method, this paper presents the orthotropic influence of composite materials on frequency characteristics for a rotating thin truncated circular symmetrical cross-ply laminated composite conical shell with different boundary conditions. The present governing equations of free vibration include the effects of initial hoop tension and the centrifugal and Coriolis accelerations due to rotation. Frequency characteristics are obtained to study in detail the orthotropic influences. Effects of boundary condition, rotating speed, circumferential wave number and geometric property are also discussed. To ensure the accuracy of the present results by the GDQ method, comparisons are made with those available in open literature and very good agreements are achieved.

Vibration analysis of a rotating truncated circular conical shell

Abstract In this paper, a method is presented to study the free vibrations of a rotating truncated circular conical shell with simply-supported boundary conditions. The method is based on the use of Love’s first approximation theory and it includes the effects of initial hoop tension and the centrifugal and coriolis accelerations. Results are obtained for the frequency characteristics at different modes and various geometric properties, the effects of cone angle on the frequency characteristics are also discussed. To validate the present analysis, comparisons are made with a very long rotating cylindrical shell and a non-rotating truncated circular conical shell and very good agreement is obtained.

On free vibration of a rotating truncated circular orthotropic conical shell

Abstract This article presents a method to study the free vibration of a rotating truncated circular orthotropic conical shell with simply-supported boundary conditions at both ends. Based on the Love first approximation theory and considering the centrifugal and Coriolis accelerations as well as the initial hoop tension, this article studies the frequency characteristics for various geometric and material properties. A detailed discussion is also made for the effects of material orthotropy and cone angle on the frequency characteristics. The present method proves to be reliable and accurate by comparing with available results in the literature.

Orthotropic influence on frequency characteristics of a rotating composite laminated conical shell by the generalized differential quadrature method

By using the generalized differential quadrature (GDQ) method, this paper presents the influence of orthotropic material on the frequency characteristics for a rotating thin truncated circular symmetrical cross-ply laminated composite conical shell with simply-supported boundary conditions at both edges. The present analysis includes the effects of initial hoop tension and the centrifugal and coriolis accelerations due to rotation. Frequency characteristics is obtained for various orthotropic parameters; the orthotropic influences of material on the frequency characteristics are also discussed for different cone angles. To validate the accuracy and efficiency of present analysis by the GDQ method, comparisons are made with those available in open literature; very good agreements are achieved.

Dynamic analysis of clamped laminated curved panels

Abstract The free vibration and dynamic response of clamped laminated curved panels subjected to the step, triangular and explosive loadings are investigated. The case of rectangular panels having fixed boundary conditions is also considered. The Rayleigh-Ritz method is employed to obtain the natural frequencies of the clamped laminated curved panels by using a set of simple polynomials as admissible functions. The normal mode superposition method is then used in the analysis of the dynamic response. Numerical results of the symmetric angleply, symmetric and antisymmetric cross-ply laminated curved panels under three kinds of dynamic loadings are presented.

Biodynamic response of shipboard sitting subject to ship shock motion.

Underwater shock can produce very high accelerations, resulting in severe human injuries. In this paper, a shock-structure-human interaction model is proposed to study the biodynamic response of a shipboard sitting subject to ship motion induced by underwater shock (ship shock motion) wherein, the human body is modeled using a lumped parameter system with the parameters obtained from dynamic tensile tests. The results obtained from the human model used in this paper and living human drop test are also compared. Numerical results have revealed the characteristics of human response to ship shock motion. The part in direct contact with the structure (like the pelvis) is much more vulnerable than other parts (like the head). The influences of structural damping and stiffness on the peak loads acting on the human body are investigated. Both damping and stiffness have important influences on the pelvis, but have much less influences on other parts. Injury criteria in the literature are also summarized to facilitate injury assessment.

Estimation of complicated distributions using B-spline functions

The distributions of some of random variables are quite complicated and difficult to determine using ordinary statistical models. A method is presented in this paper which gives satisfactory estimation of the complicated distribution of a continuous random variable. There are two key steps in the method: one being that the probability density function (p.d.f.) of a random variable is approximated by a linear combination of B-splines and the other being that the best model is determined by entropy analysis. Extensive numerical experiments have made it clear that the proposed method is useful to determine the p.d.f. directly from a set of sample points without using any prior knowledge of the distribution form.

Influence of initial pressure on frequency characteristics of a rotating truncated circular conical shell

As a new global numerical approximate technique, the generalized differential quadrature (GDQ) method is used in this paper to study the influence of initial pressure load on the free vibration of a rotating thin isotropic truncated circular conical shell. The present motion governing equations include the influence of initial stress field due to the initial uniform pressure. The effects of initial hoop tension and the centrifugal and coriolis accelerations due to rotation are also considered. The influence of initial pressure on the frequency characteristics of the rotating conical shell is discussed in detail. For the examination of present work, frequency numerical comparisons are made with those available in published works, and very good agreement is achieved.

Hydrodynamic influence on ship-hull vibration close to water bottom

The problem of a uniform ship-hull girder vibrating vertically close to water bottom is studied. A simple formula for the added mass is found by use of the method of matched asymptotic expansions. Results obtained from the present method and BEM are compared. They are in good agreement in the range considered here. The obtained added mass is used to predict the natural vibrations of a uniform beam vibrating close to water bottom. Numerical values show that the effects of shallow water are significant. The first- and second-order frequencies of the ship hull studied in this paper in deep water are about 1·4–3 times higher than those in shallow water.