Abstract
This paper presents elasticity solutions for the vibration analysis of isotropic and orthotropic open shells and plates with arbitrary boundary conditions, including spherical and cylindrical shells and rectangular plates. Vibration characteristics of the shells and plates have been obtained via a unified three-dimensional displacement-based energy formulation represented in the general shell coordinates, in which the displacement in each direction is expanded as a triplicate product of the cosine Fourier series with the addition of certain supplementary terms introduced to eliminate any possible jumps with the original displacement function and its relevant derivatives at the boundaries. All the expansion coefficients are then treated equally as independent generalized coordinates and determined by the Rayleigh-Ritz procedure. To validate the accuracy of the present method and the corresponding theoretical formulations, numerical cases have been compared against the results in the literature and those of 3D FE analysis, with excellent agreements obtained. The effects of boundary conditions, material parameters, and geometric dimensions on the frequencies are discussed as well. Finally, several 3D vibration results of isotropic and orthotropic open spherical and cylindrical shells and plates with different geometry dimensions are presented for various boundary conditions, which may be served as benchmark solutions for future researchers as well as structure designers in this field.
Highlights
In many applications and fields of modern technology, for example, civil aviation, space industry, and deep-ocean exploitation, the engineering structures often work in complex environment conditions and can be subjected to various forms of external loads, which may result in violent vibrations and lead the structures to failure
A unified, reliable, and efficient method for predicting the 3D vibration characteristics of thick deep and shallow open shells with arbitrary boundary conditions would be highly desirable. In view of these voids, this paper presents an endeavor to investigate the vibrations of isotropic and orthotropic open shells with arbitrary boundary conditions and variable circumferential dimensions in the framework of 3D shell theory
This paper presents a unified method for the free vibration analysis of isotropic and orthotropic plates and shells with arbitrary boundary conditions and geometry dimensions in the framework of three-dimensional displacement-based energy formulation, including rectangular plates, open cylindrical shells, and the spherical ones
Summary
In many applications and fields of modern technology, for example, civil aviation, space industry, and deep-ocean exploitation, the engineering structures often work in complex environment conditions and can be subjected to various forms of external loads, which may result in violent vibrations and lead the structures to failure. An important step in vibration design of an engineering structure is the evaluation of its vibration modal characteristics. This modal information plays a key role in the structure design and vibration suppression when subjected to dynamics excitations. Plate and shells, such as rectangular plates and cylindrical, conical, and spherical shells, are basic structural elements of most engineering structures. The vibration analysis of shells has received much attention. The literature on this subject is vast. The vibration of thick shells has conventionally been solved using the first-order
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