In-plane free vibrations of functionally graded sandwich arches using shear and quasi-3D deformation theories

2021 ◽  
pp. 109963622110219
Author(s):  
Ke Xie ◽  
Yuewu Wang ◽  
Hongpan Niu ◽  
Hongyong Chen
Keyword(s):  
Boundary Conditions ◽  
Lagrange Equation ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Displacement Fields ◽  
Various Boundary Conditions ◽  
Shear Deformation Theories ◽  
3D Deformation ◽  
First Time ◽  
Stress Free Boundary

The in-plane vibration problem of functionally graded (FG) sandwich circular arch made up of two layers of power law FGM face sheet and one layer of homogeneous core is investigated. A framework for the vibration analysis of FG sandwich circular arches is presented, and the quasi-3D theories for the arch structures compatible with this framework are established for the first time. The quasi-3D theories take into account the changes of displacement through the thickness of the arch, and satisfy the stress-free boundary conditions naturally. The Lagrange equation is employed to derive the equation of motion, and various boundary conditions are implemented by applying simple algebraic polynomials as admissible functions to discrete the displacement fields of the FG sandwich arches. The comparison study of various high-order shear deformation theories and quasi-3D deformation theories for the FG sandwich circular arches is carried out via different numerical examples. The influences of material distributions and geometric parameters on the vibration characteristics of the FG sandwich circular arches are also presented and discussed for the first time.

Dynamics Sensitivity Analyses of Functionally Graded Porous (FGP) Curved Beams with Variable Curvatures and General Boundary Conditions

2021 ◽  
pp. 2150151
Author(s):  
C. Yu ◽  
J. Lu ◽  
S. Li ◽  
W. Xu ◽  
C. Chiu
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sensitivity Analyses ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Curved Beams ◽  
Displacement Fields ◽  
Various Boundary Conditions

A method is proposed to obtain the exact solution for the dynamic analysis of functionally graded porous (FGP) curved beams with general boundary conditions and variable curvatures. First, the model of a curved beam of variable curvature is constructed, and then the beam is divided into a number of free beam segments via a multi-segment segmentation (MSS) strategy. Second, the first-order shear deformation theory (FSDT) is adopted to obtain the displacement fields of each segment, and then the kinetic energy and potential energy of the structure are expressed by the displacement field. Finally, the exact solution is obtained by the Hamilton principle. Using the springs to simulate various boundary conditions, the frequency parameters, modal shapes and forced vibration responses of the structure with elastic boundary conditions are calculated, with the convergence and correctness verified. Finally, effects of the FGP curved beams, such as porosity distribution types, porosity ratios, boundary condition types, geometry parameters and load types, are investigated in detail.

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

A Nonlinear Shear Deformable Nanoplate Model Including Surface Effects for Large Amplitude Vibrations of Rectangular Nanoplates with Various Boundary Conditions

2015 ◽  
Vol 07 (05) ◽  
pp. 1550076 ◽  
Author(s):  
Reza Ansari ◽  
Mostafa Faghih Shojaei ◽  
Vahid Mohammadi ◽  
Raheb Gholami ◽  
Mohammad Ali Darabi
Keyword(s):  
Boundary Conditions ◽  
Surface Stress ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Free Vibrations ◽  
Model Parameters ◽  
Geometrically Nonlinear ◽  
Residual Surface Stress ◽  
Various Boundary Conditions ◽  
Shear Deformable

In this paper, a geometrically nonlinear first-order shear deformable nanoplate model is developed to investigate the size-dependent geometrically nonlinear free vibrations of rectangular nanoplates considering surface stress effects. For this purpose, according to the Gurtin–Murdoch elasticity theory and Hamilton's principle, the governing equations of motion and associated boundary conditions of nanoplates are derived first. Afterwards, the set of obtained nonlinear equations is discretized using the generalized differential quadrature (GDQ) method and then solved by a numerical Galerkin scheme and pseudo arc-length continuation method. Finally, the effects of important model parameters including surface elastic modulus, residual surface stress, surface density, thickness and boundary conditions on the vibration characteristics of rectangular nanoplates are thoroughly investigated. It is found that with the increase of the thickness, nanoplates can experience different vibrational behavior depending on the type of boundary conditions.

Computational Development of a 4-Unknowns Trigonometric Quasi-3D Shear Deformation Theory to Study Advanced Sandwich Plates and Shells

2016 ◽  
Vol 08 (04) ◽  
pp. 1650049 ◽  
Author(s):  
J. L. Mantari
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Sandwich Plates And Shells ◽  
Plates And Shells ◽  
First Time ◽  
Stretching Effect

In this paper, a simple and accurate sinusoidal trigonometric theory (STT) for the bending analysis of functionally graded single-layer and sandwich plates and shells is presented for the first time. The principal feature of this theory is that models the thickness stretching effect with only 4-unknowns, even less than the first order shear deformation theory (FSDT) which as it is well-known has 5-unknowns. The governing equations and boundary conditions are derived by employing the principle of virtual work. Then, a Navier-type closed-form solution is obtained for functionally graded plates and shells subjected to bi-sinusoidal load for simply supported boundary conditions. Consequently, numerical results of the present STT are compared with other refined theories, FSDT, and 3D solutions. Finally, it can be concluded that: (a) An accurate but simple 4-unknown STT with thickness stretching effect is developed for the first time. (b) Optimization procedure (described in the paper) appear to be of paramount importance for 4-unknown higher order shear deformation theories (HSDTs) of this gender, so deserves a lot of further research. (c) Transverse shear stresses results are sensitive to the theory and need carefully attention.

scholarly journals Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method

2016 ◽  
Vol 2016 ◽  
pp. 1-23 ◽  
Author(s):  
Peng Liu ◽  
Kun Lin ◽  
Hongjun Liu ◽  
Rong Qin
Keyword(s):  
Boundary Conditions ◽  
Transverse Vibration ◽  
Spline Interpolation ◽  
Computational Cost ◽  
Functionally Graded ◽  
Point Method ◽  
Finite Point ◽  
Various Boundary Conditions ◽  
Finite Point Method ◽  
Free Transverse Vibration

A new model for the free transverse vibration of axially functionally graded (FG) tapered Euler-Bernoulli beams is developed through the spline finite point method (SFPM) by investigating the effects of the variation of cross-sectional and material properties along the longitudinal directions. In the proposed method, the beam is discretized with a set of uniformly scattered spline nodes along the beam axis instead of meshes, and the displacement field is approximated by the particularly constructed cubic B-spline interpolation functions with good adaptability for various boundary conditions. Unlike traditional discretization and modeling methods, the global structural stiffness and mass matrices for beams of the proposed model are directly generated after spline discretization without needing element meshes, generation, and assembling. The proposed method shows the distinguished features of high modeling efficiency, low computational cost, and convenience for boundary condition treatment. The performance of the proposed method is verified through numerical examples available in the published literature. All results demonstrate that the proposed method can analyze the free vibration of axially FG tapered Euler-Bernoulli beams with various boundary conditions. Moreover, high accuracy and efficiency can be achieved.

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