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.

This paper aims to control the in-plane wave propagation characteristics of two-dimensional functionally graded periodic grid structures by adding local resonators made of the spring oscillator. The in-plane wave dispersion relations of the periodic grid structures with local resonators are calculated by spectral element method combined with Bloch theorem. Meanwhile, the effectiveness of the band gap calculation method is verified by the vibration transmission of the finite-length grid structures calculated based on spectral element method and finite element method. According to the spectral element method, the spectral stiffness matrix of the functionally graded beam element is established at first, then assembled with the additional stiffness matrix of the spring oscillator subsystem to obtain the complete spectral stiffness matrix of the functionally graded oscillator coupled beam. Finally, the whole stiffness matrix of grid structures with local resonators can be obtained by the coordinate transformation matrix, to form the in-plane wave dispersion relations equation based on the Bloch periodic boundary conditions. In addition, the effects of structural and material parameters on the in-plane wave propagation characteristics are analyzed, which can be applied to the vibration reduction design of periodic grid structures.

In this paper, a semi-analytical method is adopted to analyze the free vibration characteristics of composite laminated shallow shells under general boundary conditions. Combining two kinds of shell theory, that is, first-order shear deformation shell theory (FSDT) and classical shell theory (CST), to describe the dynamic relationship between the displacement resultants and force vectors, the theoretical formulations are established. According to the presented work, the displacement and transverse rotational variables are transformed into wave function forms to satisfy the theoretical formulation. Related to diverse boundary conditions, the total matrix of the composite shallow shell can be established. Searching the determinant of the total matrix using the dichotomy method, the natural frequency of composite laminated shallow shells is obtained. Through several classical numerical examples, it is proven that the results calculated by the presented method are more accurate and reliable. Furthermore, to discuss the effect of geometric parameters and material constants on the natural frequencies of composite laminated shallow shells, some numerical examples are calculated to analyze. Also, the influence of boundary elastic restrained stiffness is discussed.

Automobile side door glass squeaks and rattles during use. This abnormal noise can make the driver and occupants irritable and reduce the comfort of the automobile. This reduces the sales of this automobile. This paper analyzes and determines the cause of squeak and rattle during the lifting and lowering process of the side door glass of an automobile. The noise is due to four reasons. One is that the distance between the inner waterproof belt and the automobile side door glass of the automobile is unreasonable, causing excessive friction between the automobile side door glass and the inner waterproof belt during the automobile side door glass up and down movement. Other factors affecting squeak and rattle may be the distance between the automobile side door sheet metal and the automobile side door glass, the thickness of the automobile side door glass and the characteristics of the inner waterproof belt. The first two dimensions are analyzed using the 6 sigma method, and the structure of the inner waterproof belt is improved and the flocking position is adjusted. The squeak and rattle phenomenon is explained using the implicit dynamic analysis method ABAQUS, and the compression load deflection after the installation of the inner waterproof belt is 3–9 N/100 mm. This research completely solves the squeak and rattle problem caused by the up and down movement of the side door glass of the automobile. This research has significance for solving practical engineering problems.

In order to study the influence of the pressure load generated during the pulsation of cavitation bubbles on the oblique 45-degree curved surface boundary. The curved surface boundaries have different curvatures. This study also designs a multi-angle bracket to make the oblique boundary oblique 45 degrees. This research uses high-voltage electric discharge to generate electric spark bubbles, which act as cavitation bubbles. When the explosion source is at different distances from the oblique 45-degree boundary, a high-speed camera is used to capture the pulsation process of electric spark bubbles. A pressure sensor is used to measure the pulsating load of the electric spark bubbles on the oblique 45-degree boundary during the pulsation process. In this study, we use the dimensionless parameter ζ to represent the curvature of the oblique 45-degree boundary. The dimensionless parameter γ is used to represent the shortest distance between the explosion source and the oblique 45-degree boundary. It is found through experiments that the oscillation characteristics and pulsating load of electric spark bubbles will be affected by ζ and γ. This study summarized six types of unique bubble pulse shapes from 44 groups of experiments. They are “mushroom shape without jet”, “mound shape with jet”, “jellyfish shape with jet”, “oval shape with jet”, “drop shape without jet”, and “spherical shape without jet”. In this paper, the ABAQUS/Explicit is used to simulate the ring-shaped bubble that is not clearly captured by the high-speed camera. Finally, the study summarizes the shock wave load generated during the explosion, the first pulsation load, and the second pulsation load of electric spark bubbles, and finds an obvious overall trend of change.