The vibrations of circular, annular, and sector plates are traditionally considered as different boundary value problems and often treated using different solution algorithms and procedures. This problem is further compounded by the fact that the solution for each type of plate typically needs to be adapted to different boundary conditions. In this paper, a simple solution method is proposed for a unified vibration analysis of annular, circular and sector plates with arbitrary boundary conditions. Regardless of the shapes of the plates and the types of boundary conditions, the displacement solutions are invariably expressed as a new and simple form of trigonometric series expansion with an accelerated convergence rate. The unification of seemingly different boundary value problems for the circular and annular plates and their sector counterparts is physically accomplished by applying a set of coupling springs to ensure appropriate continuity conditions along the radial edges. The accuracy, reliability and versatility of the current method are fully demonstrated and verified through numerical examples involving plates with various shapes and boundary conditions. It should be noted that the current method can be easily applied to sector plates with an arbitrary inclusion angle up to 2π.

In this investigation, an accurate solution method is presented for the free vibrations of Timoshenko beams with general elastic restraints at the end points, a class of problems which are rarely attempted in the literatures. Unlike in most existing studies where solutions are often developed for a particular type of boundary conditions, the current method can be generally applied to a wide range of boundary conditions with no need of modifying solution algorithms and procedures. Under the current framework, the displacement and rotation functions are generally sought, regardless of boundary conditions, as an improved trigonometric series in which several supplementary functions introduced to remove the potential discontinuities with the displacement components and its derivatives at the end points and accelerated the series expansion. Mathematically, the current Fourier series expansion is an exact solution for a class of problems with the Timoshenko beam such that both the governing equations and the boundary conditions simultaneously satisfy any specified degree of accuracy. The effectiveness and reliability of the presented solution are demonstrated by comparing the present results with those results published in literatures and finite element method data, and numerous new results for beams with elastic boundary restraints is presented, which may serve as benchmark solution for future researches.

It is well known that the bubble dynamics and load characteristics of cavitation bubbles depend to a great extent on their proximity to the boundary. The purpose of this study is to explore the relationship between the boundary curvature and bubble dynamics, as well as the load characteristics, and summarize the relevant change laws. This study takes three hemispheres of different curvatures and one flat board as its main research boundaries. The hemisphere was chosen as the curved surface boundary because the hemisphere represents the simplest type of curved surface boundary. This method allowed us to easily observe the experimental results and summarize the change laws of bubble dynamics and load characteristics. A high voltage electricity of 400 V was used to produce stable and repeatable electric spark bubbles in this experiment. Since the pulsation time of the bubbles is very short, we used a high-speed camera to acquire the necessary photographs. We also used a Hopkinson bar (HPB) to measure the bubble collapse load. Suppose that the dimensionless parameter of curvature is ζ and the dimensionless parameter of the explosion distance is γ. By summarizing the 44 groups of the experimental results under different combinations of ζ and γ, we found that the cavitation bubble dynamics and loading characteristics are affected by ζ. With an increase of ζ, the shockwave load and bubble collapse load will decrease. In addition, in terms of load characteristics, this study further verified the change trend of the shockwave load and bubble collapse load with γ. For the bubble shrink shape, this paper illustrates the relationship between the bubble’s shrink shape and its shrinkage speed. Four typical bubble shrink shapes are summarized. The effects of different ζ and γ values on the jet are preliminarily explored using the experimental results, and, by considering the experimental results, the developmental trends of the time of the bubble’s first pulsation period are discussed.

Radomes are usually constructed from sandwich structures made of materials which usually have a low dielectric constant so that they do not interfere with electromagnetic waves. Performance of the antenna is increased by the appropriate assortment of materials enabling it to survive under marine applications, and it depends on composite strength-to-weight ratio, stiffness, and resistance to corrosion. The design of a sandwich core submarine radome greatly depends on the material system, number of layers, orientation angles, and thickness of the core material. In this paper, a conceptual design study for a sandwich core submarine radome is carried out with the help of finite element analysis (FEA) using two unidirectional composite materials—glass fiber reinforced polymer (GFRP) and carbon fiber reinforced polymer (CFRP)—as a skin material and six different core materials. Conceptual designs are obtained based on constraints on the composite materials’ failure, buckling, and strength. The thickness of the core is reduced under constraints on material and buckling strength. Finite element analysis software ANSYS WORKBENCH is used to carry out all the simulations.

A semi-analytic method is adopted to analyze the free vibration characteristics of the moderately thick composite laminated cylindrical shell with arbitrary classical and elastic boundary conditions. By Hamilton’s principle and first-order shear deformation theory, the governing equation of the composite shell can be established. The displacement variables are transformed into the wave function forms to ensure the correctness of the governing equation. Based on the kinetic relationship between the displacement variables and force resultants, the final equation associated with arbitrary boundary conditions is established. The dichotomy method is conducted to calculate the natural frequencies of the composite shell. For verifying the correctness of the present method, the results by the present method are compared with those in the pieces of literatures with various boundary conditions. Furthermore, some numerical examples are calculated to investigate the effect of several parameters on the composite shell, such as length to radius ratios, thickness to radius ratios and elastic restrained constants.