Free vibration analysis of laminated composite conical, cylindrical shell and annular plate with variable thickness and general boundary conditions

This paper presents a unified solution method to investigate the free vibration behaviors of laminated composite conical shell, cylindrical shell and annular plate with variable thickness and arbitrary boundary conditions using the Haar wavelet discretization method (HWDM). Theoretical formulation is established based on the first order shear deformation theory(FSDT) and displacement components are extended Haar wavelet series in the axis direction and trigonometric series in the circumferential direction. The constants generating by the integrating process are disposed by boundary conditions, and thus the equations of motion of total system including the boundary condition are transformed into an algebraic equations. Then natural frequencies of the laminated composite structures are directly obtained by solving these algebraic equations. Stability and accuracy of the present method are verified through convergence and validation studies. Effects of some material properties and geometric parameters on the free vibration of laminated composite shells are discussed and some related mode shapes are given. Some new results for laminated composite conical shell, cylindrical shell and annular plate with variable thickness and arbitrary boundary conditions are presented, which may serve as benchmark solutions.

Investigation on vibration of the functionally graded material–stepped cylindrical shell coupled with annular plate in thermal environment

This article is concerned with thermal vibration behaviors of the functionally graded material–stepped cylindrical shell coupled with annular plate, including free vibration, transient response, and steady state response. The stepped cylindrical shell is divided into N s segments at locations of thickness and radius variations, which is coupled with N p annular plates. The boundary and coupling conditions are achieved by introducing the artificial virtual spring technology. Under the framework of FSDT, the displacement function of arbitrary shell segment and annular plate is expanded with Chebyshev polynomials and Fourier series for circumferential direction. Compared with results obtained by the finite element method and the references, a series of numerical examples and validations are presented to verify the convergence and accuracy of the current method. The effects of the relevant parameters containing the geometric parameters, boundary conditions, various loadings, and the thermal environment are investigated in detail.

Heat transfer at the step of a CANDU calandria during a severe accident

During the in-vessel stage of a severe accident in a CANDU 6 reactor, decay heat from a collapsed core would be rejected through the calandria walls into the surrounding water. At the step in the calandria wall, the subshell and annular plate meet at a right angle pointing into the calandria. The geometry at this joint could concentrate the exiting heat flux, potentially leading to calandria failure. Finite element analysis is used to study the heat transfer near the welded joint. Different weld profiles, boundary conditions, and decay heat characteristics are considered, and the local concentration of exiting heat flux is calculated.

Temperature Effect on Stability of Clamped–Clamped Composite Annular Plate with Damages

The paper presents the response of a three-layered annular plate with different damaged laminate facings to the action of the static or dynamic temperature field model. Various damages of laminate, composite facings change the plate structure reaction under the temperature fields. Obtained results indicate practical meaning of analyses in failure diagnostic process. The thermal sensitivity of two kinds of plate structures, undamaged and damaged, offers both new practical and scientific possibilities in evaluation of the plate behavior. The relations between macro-damage, i.e., the buckling of the plate structure and micro-damages of plate layers subjected to temperature gradient, are shown. The numerical solution is proposed as the most effective in examinations of the various transversally symmetrical and asymmetrical plate structures with a different rate of damages. The graphical distribution of changes in values of static and dynamic critical loads illustrate the process of structural damaging during its exploitation. They have practical importance in the evaluation of the structure capacity. The knowledge of the effect of laminate degradation process on plate buckling phenomenon located in thermal environment complements previous investigations and designates complex, multi-parameter problems as having scientifically new elements.

Propagation of Transverse Wave for the Piezoelectric Radial Phononic Crystal Annular Plate in a Fibonacci Order

Based on the previous conventional phononic crystal (PC) structures infinitely periodic in Cartesian coordinates, this paper addresses a new radial phononic crystal annular plate (RPCAP) modeled in a Fibonacci order along the radial direction. In this study, piezoelectric material PZT4 is simultaneously inserted into this RPCAP model to investigate the stop band behaviors. In order to clearly show the transmission characteristics of transverse wave, in cylindrical coordinates, the transfer matrix is deduced through combining the general solutions, piezoelectric governing equations, and continuity conditions. Compared with conventional PC structures, transmission response of transverse vibration for the Fibonacci RPCAP model is calculated theoretically to analyze the stop band phenomenon. Finite element simulation method (FEM) is conducted here to verify the theoretical results. The results show that the Fibonacci RPCAP model presents two newly emerging resonance frequencies while the radial periodic order is disorganized. To thoroughly understand the RPCAP, the effects of structural parameters, material parameters, and piezoelectric parameters on the stop band are discussed in detail. The proposed Fibonacci RPCAP can be employed in many engineering applications, such as in rotating parts which are often coupled with transverse vibration (like gear driving systems).