scholarly journals A Semianalytic Method for Vibration Analysis of a Sandwich FGP Doubly Curved Shell with Arbitrary Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Zhongyu Zhang ◽  
Jiayang Gu ◽  
Jianjun Ding ◽  
Yanwu Tao
Keyword(s):  
Boundary Conditions ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Arbitrary Boundary ◽  
Forced Vibration Analysis ◽  
Doubly Curved ◽  
Curved Structure

Due to the excellent mechanical properties of doubly curved structure and functionally graded porous (FGP) material, the study of their vibration characteristics has attracted wide attention. The main aim of this research is to establish a formulation for free and forced vibration analysis of a new Sandwich FGP doubly curved structure. Four models of Sandwich materials are considered. The potential energy and kinetic energy functions are obtained on the foundation of the first-order shear deformation theory (FSDT). The idea of domain energy decomposition is applied to the theoretical modeling, where the structure is segmented along the generatrix direction. The continuity conditions for the interfaces between adjacent segments are balanced by the weighted parameters. For each segment, the displacement functions are selected as the Jacobi orthogonal polynomials and trigonometric series. The boundary conditions of the structure are obtained by the boundary spring simulation technique. The solution is obtained by the variational operation of the structural functional. The convergence performance and correctness of the theoretical model are examined by several numerical examples. Finally, some novel results are given, where free and forced vibration characteristics of Sandwich FGP doubly curved structures are examined in detail.

Forced Vibration Analysis of Functionally Graded Plates With Geometric Nonlinearity

2015 ◽  
Author(s):  
Saurabh Kumar ◽  
Anirban Mitra ◽  
Haraprasad Roy
Keyword(s):  
Boundary Conditions ◽  
Forced Vibration ◽  
Geometric Nonlinearity ◽  
Vibration Analysis ◽  
Mathematical Formulation ◽  
Functionally Graded ◽  
Static Case ◽  
Functionally Graded Plates ◽  
Governing Equations ◽  
Forced Vibration Analysis

Forced vibration analysis has been carried out on functionally graded plates where the material properties vary along axial direction. The geometric nonlinearity is incorporated in the system using nonlinear strain displacement relations. An indirect methodology is adopted in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude, thus reducing the problem to an equivalent static case. The computational points are selected and start functions are generated at those points by satisfying the flexural and membrane boundary conditions of the plate. The start functions are later used for generating higher order functions using Gram-Schmidt orthogonalisation procedure. The mathematical formulation is based on the variational form of energy principles and the governing equations are derived using Hamilton’s principle. The set of nonlinear governing equations is solved using an iterative direct substitution method employing an appropriate relaxation technique. The results are generated for combinations of clamped and simply supported boundary conditions and presented in amplitude-frequency plane. Three dimensional operational deflection shape plots along with contour plots are also provided for some cases. Results are validated with the works available in the literature.

scholarly journals Forced Vibration Analysis of Laminated Composite Shells Reinforced with Graphene Nanoplatelets Using Finite Element Method

2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Trung Thanh Tran ◽  
Van Ke Tran ◽  
Pham Binh Le ◽  
Van Minh Phung ◽  
Van Thom Do ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Thermal Environments ◽  
Forced Vibration Analysis ◽  
Laminated Composite Shells ◽  
Element Method

This paper carries out forced vibration analysis of graphene nanoplatelet-reinforced composite laminated shells in thermal environments by employing the finite element method (FEM). Material properties including elastic modulus, specific gravity, and Poisson’s ratio are determined according to the Halpin–Tsai model. The first-order shear deformation theory (FSDT), which is based on the 8-node isoparametric element to establish the oscillation equation of shell structure, is employed in this work. We then code the computing program in the MATLAB application and examine the verification of convergence rate and reliability of the program by comparing the data of present work with those of other exact solutions. The effects of both geometric parameters and mechanical properties of materials on the forced vibration of the structure are investigated.

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