Abstract
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.
Highlights
The shallow shell is an open shell with a small curvature and radius of curvature compared with various shell parameters
Conducted the enhanced reverberation-ray matrix (ERRM) method to investigate the transient response of the composite shallow shell
To analyze the free vibration characteristics of the composite laminated shallow shell with arbitrary boundary conditions, the shell structure is considered to be calculated as a whole model and the displacement variable solutions are set as infinite wave function forms; the convergence study of the truncated number does not need to be considered
Summary
The shallow shell is an open shell with a small curvature and radius of curvature compared with various shell parameters (i.e., length and width). Ye et al [14] investigated the free vibration characteristics of the composite laminated shallow shell under general elastic boundary conditions. Conducted the enhanced reverberation-ray matrix (ERRM) method to investigate the transient response of the composite shallow shell In these studies, the kinetic analysis of composite laminated shallow shell is proposed to free vibration, and many analytical and computational methods were developed. According to the author’s literature review of related topics, there has not been any published work with regard to the application of the presented method to analyze the free vibration characteristics of the composite laminated shallow shell with general boundary conditions.
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