scholarly journals Analytical and Experimental Vibration of Sandwich Beams Having Various Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Eshagh F. Joubaneh ◽  
Oumar R. Barry ◽  
Hesham E. Tanbour
Keyword(s):  
Finite Element Method ◽  
Boundary Conditions ◽  
Sandwich Panel ◽  
Equations Of Motion ◽  
Sandwich Beam ◽  
Sandwich Beams ◽  
Various Boundary Conditions ◽  
Parametric Studies ◽  
Generalized Differential ◽  
Equations Of Motions

Generalized differential quadrature (GDQ) method is used to analyze the vibration of sandwich beams with different boundary conditions. The equations of motion of the sandwich beam are derived using higher-order sandwich panel theory (HSAPT). Seven partial differential equations of motions are obtained through the use of Hamilton’s principle. The GDQ method is utilized to solve the equations of motion. Experiments are conducted to validate the proposed theory. The results from the analytical model are also compared to those from the literature and finite element method (FEM). Parametric studies are conducted to investigate the effects of different parameters on the natural frequency and response of the sandwich beam under various boundary conditions.

Frequency and Loss Factors of Sandwich Beams under Various Boundary Conditions

1978 ◽  
Vol 20 (5) ◽  
pp. 271-282 ◽  
Author(s):  
D. K. Rao
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Energy Approach ◽  
Sandwich Beams ◽  
Exact Results ◽  
Various Boundary Conditions ◽  
Complete Set ◽  
Loss Factors

A complete set of equations of motion and boundary conditions governing the vibration of sandwich beams are derived by using the energy approach. They are solved exactly for important boundary conditions. The computational difficulties that were encountered in previous attempts at the exact solution of these equations have been overcome by careful programming. These exact results are presented in the form of design graphs and formulae, and their usage is illustrated by examples.

Experimental and Numerical Analysis of a Sandwich Beam With Tip Mass

2018 ◽  
Author(s):  
E. F. Joubaneh ◽  
O. R. Barry ◽  
D. C. D. Oguamanam
Keyword(s):  
Numerical Analysis ◽  
Sandwich Panel ◽  
Equations Of Motion ◽  
Mathematical Formulation ◽  
Sandwich Beam ◽  
Design Parameters ◽  
Governing Equations ◽  
Parametric Studies ◽  
Tip Mass ◽  
Good Agreement

This paper presents experimental and numerical analyses of a vibrating sandwich beam with a tip mass. The mathematical formulation is based on higher order sandwich panel theory (HSAPT) and the governing equations of motion and boundary conditions are obtained using Hamilton’s principle. General Differential Quadrature (GDQ) is employed to solve the system governing equations of motion. Experiments are carried out to validate the proposed formulation and the results show very good agreement. Parametric studies are conducted to investigate the influence of key design parameters on the natural frequency and vibration response of the system.

Piezoelectric Vibration Control of a Sandwich Beam With Tip Mass

2018 ◽  
Author(s):  
Eshagh Farzaneh ◽  
Oumar Barry ◽  
Pablo Tarazaga
Keyword(s):  
Equations Of Motion ◽  
Center Of Mass ◽  
Sandwich Beam ◽  
Sensors And Actuators ◽  
Finite Element Software ◽  
The Face ◽  
Parametric Studies ◽  
Generalized Differential ◽  
Tip Mass ◽  
Piezoelectric Vibration

This paper studies the vibration mitigation of a sandwich beam with tip mass using piezoelectric active control. The core of the sandwich beam is made of foam and the face sheets are made of steel with a bonded piezoelectric actuator and sensor. The three-layer sandwich beam is clamped at one end and carries a payload at the other end. The tip mass is such that its center of mass is offset from the point of attachment. The extended higher-order sandwich panel (HSAPT) theory is employed in conjunction with the Hamilton’s principle to derive the governing equations of motion and boundary conditions. The obtained partial differential equations are solved using the generalized differential quadrature (GDQ) method. Free and forced vibration analyses are carried out and the results are compared with those obtained from the use of the commercial finite element software ANSYS. Derivative feedback control algorithm is employed to control the vibration of the system. Parametric studies are conducted to examine the arrangement impact of the piezoelectric sensors and actuators on the system vibrational behavior.

Upon Impact Numerical Modeling of Foam Materials

2017 ◽  
Vol 54 (2) ◽  
pp. 195-202
Author(s):  
Vasile Nastasescu ◽  
Silvia Marzavan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Numerical Analysis ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
General Character ◽  
Foam Material ◽  
Various Boundary Conditions ◽  
Specific Behaviour

The paper presents some theoretical and practical issues, particularly useful to users of numerical methods, especially finite element method for the behaviour modelling of the foam materials. Given the characteristics of specific behaviour of the foam materials, the requirement which has to be taken into consideration is the compression, inclusive impact with bodies more rigid then a foam material, when this is used alone or in combination with other materials in the form of composite laminated with various boundary conditions. The results and conclusions presented in this paper are the results of our investigations in the field and relates to the use of LS-Dyna program, but many observations, findings and conclusions, have a general character, valid for use of any numerical analysis by FEM programs.

Application of Generalized Differential Quadrature Method to the Bending of Thick Laminated Plates with Various Boundary Conditions

2006 ◽  
Vol 5-6 ◽  
pp. 407-414 ◽  
Author(s):  
Mohammad Mohammadi Aghdam ◽  
M.R.N. Farahani ◽  
M. Dashty ◽  
S.M. Rezaei Niya
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Simple Procedure ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Differential Quadrature ◽  
Governing Equations ◽  
First Order ◽  
Various Boundary Conditions ◽  
Generalized Differential

Bending analysis of thick laminated rectangular plates with various boundary conditions is presented using Generalized Differential Quadrature (GDQ) method. Based on the Reissner first order shear deformation theory, the governing equations include a system of eight first order partial differential equations in terms of unknown displacements, forces and moments. Presence of all plate variables in the governing equations provide a simple procedure to satisfy different boundary condition during application of GDQ method to obtain accurate results with relatively small number of grid points even for plates with free edges .Illustrative examples including various combinations of clamped, simply supported and free boundary condition are given to demonstrate the accuracy and convergence of the presented GDQ technique. Results are compared with other analytical and finite element predictions and show reasonably good agreement.

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.

Large deflection geometrically nonlinear bending of sandwich beams with flexible core and nanocomposite face sheets reinforced by nonuniformly distributed graphene platelets

2019 ◽  
Vol 22 (3) ◽  
pp. 866-895 ◽  
Author(s):  
S Jedari Salami
Keyword(s):  
Sandwich Panel ◽  
Sandwich Beam ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Face Sheet ◽  
Sandwich Beams ◽  
Nonlinear Bending ◽  
Graphene Platelet ◽  
The Face ◽  
Graphene Platelets

This study investigates the nonlinear bending response of a novel class of sandwich beams with flexible core and face sheets reinforced with graphene platelets that are functionally graded distributed through the thickness. Nonlinear governing equations are established based on extended high-order sandwich panel theory and Von Kármán type of geometrical nonlinearity. In this theory, the face sheets follow the first-order shear deformation theory, and the two-dimensional elasticity is adopted for the core. These nonlinear differential equations are discretized into algebraic systems by means of the Ritz-based method from which the static bending solution can be achieved. The effective Young’s modulus of functionally graded graphene platelet-reinforced composite (GPLRC) face sheets is determined through the modified Halpin–Tsai micromechanics model, and associated Poisson’s ratio is evaluated by employing the rule of mixture. Comparison studies are provided for a sandwich beam with graphene-reinforced face sheets and conventional nanocomposite beam reinforced by graphene platelets due to lack of results for introduced sandwich beams. Besides, three-point bending test was carried out in order to assure the validity of nonlinear bending analysis of a sandwich beam based on extended high-order sandwich panel theory. Afterwards, parametric studies are given to examine the influences of graphene platelet distribution pattern, weight fraction, and core-to-face sheet thickness ratio together with the total number of layers on the linear and nonlinear bending performances of the sandwich beams. Numerical results demonstrate that distributing more graphene platelets near the upper and lower surface layers of the face sheets, named X-GPLRC, is capable to improve the bending strength and decrease the local deflection of the top face sheet, and this recovery effect becomes more significant as graphene platelet weight fraction increases. The results also reveal that the graphene platelet distribution pattern of the face sheets plays an important role to decrease the transverse shear stress of the core by dispersing more graphene platelets near surfaces of the face sheets (X-GPLRC). So, reducing the local deflection of the top face sheet tends to be much more safety of the soft core from any failure. Besides, sandwich beams with a lower weight fraction of graphene platelets in face sheets that are symmetrically distributed in such a way, called O-GPLRC, are also less sensitive to the nonlinear deformation.

Static and dynamic analysis of sandwich panel with spatially varying non-Gaussian properties

2018 ◽  
Vol 22 (8) ◽  
pp. 2469-2504 ◽  
Author(s):  
Shuvajit Mukherjee ◽  
B Raja Sekhar ◽  
S Gopalakrishnan ◽  
Ranjan Ganguli
Keyword(s):  
Free Vibration ◽  
Dynamic Response ◽  
Boundary Conditions ◽  
Sandwich Panel ◽  
Gaussian Random Field ◽  
Sandwich Beam ◽  
Gaussian Random Fields ◽  
Static And Dynamic Analysis ◽  
Geometric Uncertainty ◽  
Non Gaussian

In this work, we study the material and geometric uncertainty effects on the static, free vibration and dynamic behaviour of sandwich beam structures. A higher-order sandwich panel theory is considered for the analysis. The elastic properties of the sandwich beam are considered as 1-D non-Gaussian random field which causes local variation in mass and stiffness matrices of the beam. The discretization of the non-Gaussian random fields is performed using the expansion optimal linear estimation. To perform the numerical analysis, Monte-Carlo simulation along with the computationally efficient time-domain spectral element method is proposed. Numerical results are obtained for different boundary conditions as well as for different materials in the sandwich face sheet and core. Results obtained in this work quantify the effects of material and geometric uncertainty in the response behaviour of a sandwich beam. The individual effect of core thickness and Poisson’s ratio of the core on the static, free vibration and dynamic response is quantified. It is observed that the uncertainties in material and geometric properties along with loading and boundary conditions influence the static, free vibration and dynamic response.

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