On Free Vibrations of Fiber Reinforced Doubly Curved Panels, Part 2: Applications

1998 ◽  
Vol 120 (1) ◽  
pp. 295-300 ◽  
Author(s):  
A. V. Singh ◽  
V. Kumar
Keyword(s):  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Free Vibrations ◽  
Cylindrical Panel ◽  
Curvilinear Coordinates ◽  
Displacement Fields ◽  
Element Analysis ◽  
Surface Patches ◽  
Orthogonal Curvilinear Coordinates ◽  
Doubly Curved

The applications of a Ritz-type numerical scheme, in which the displacement fields are prescribed by Bezier surface patches, are presented for the analysis of doubly curved laminated open panels. The fundamental strain-displacement relations and energy expressions are developed in orthogonal curvilinear coordinates. The higher-order shear deformation theory and the effects of rotary inertia are considered in the formulation. Good comparisons of the results are obtained for a class of open panels. For example, values of the natural frequencies of open cylindrical and spherical panels made of isotropic material are compared with the results from the finite element analysis. Cases of cantilevered and simply supported angle-ply laminated cylindrical panel and a fully clamped isotropic conical panel are also examined for comparison with the available sources in the literature. In addition, the natural frequencies are presented for angle-ply laminated circular cylindrical, conical and spherical panels and the influence of the fiber orientation on the fundamental frequency is also examined for the angle ply having one, two [φ/−φ] and four [φ/−φ/φ/−φ] laminae arrangements.

On Free Vibrations of Fiber Reinforced Doubly Curved Panels, Part 1: Formulation/Convergence Study

1998 ◽  
Vol 120 (1) ◽  
pp. 287-294 ◽  
Author(s):  
A. V. Singh ◽  
V. Kumar
Keyword(s):  
Shear Deformation Theory ◽  
Solution Procedure ◽  
Free Vibrations ◽  
Curvilinear Coordinates ◽  
Displacement Fields ◽  
Eighth Order ◽  
Bézier Surface ◽  
Surface Patches ◽  
Bezier Surface ◽  
Doubly Curved

This paper presents a Ritz-type numerical scheme for the analysis of doubly curved laminated open panels. The fundamental strain-displacement relations and energy expressions are developed in orthogonal curvilinear coordinates. Higher-order shear deformation theory and the effects of rotary inertia are included in the formulation. The displacement fields are prescribed by Bezier surface patches and the procedure to implement the boundary conditions in this context is also described. The numerical method is developed such that any arbitrary open panel bounded by four curved edges can be analyzed. Two examples namely: cantilevered cross-ply cylindrical and spherical panels are used to demonstrate the convergence of the solution procedure. Bezier surface patches formed by the eighth order polynomials yield good values of the natural frequencies.

A third-order shear deformation theory for nonlinear vibration analysis of stiffened functionally graded material sandwich doubly curved shallow shells with four material models

2017 ◽  
Vol 21 (4) ◽  
pp. 1316-1356 ◽  
Author(s):  
Dang T Dong ◽  
Dao Van Dung
Keyword(s):  
Functionally Graded Material ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Shallow Shells ◽  
Graded Material ◽  
Doubly Curved

This study presents a nonlinear vibration analysis of function graded sandwich doubly curved shallow shells, which reinforced by functionally graded material stiffeners and rested on the Pasternak foundation. The shells are subjected to the combination of mechanical, thermal, and damping loading. Four models of the sandwich shells with general sigmoid and power laws distribution are considered. The governing equations are established based on the third-order shear deformation theory. Von Kármán-type nonlinearity and smeared stiffener technique are taken into account. The explicit expressions for determining natural frequencies, nonlinear frequency–amplitude relation, and time–deflection curves are obtained by employing the Galerkin method. Finally, the fourth-order Runge–Kutta method is applied to investigate the influences of functionally graded material stiffeners, the boundary conditions, the models of the shells, thermal environment, foundation and geometrical parameters on the natural frequencies and dynamic nonlinear responses of the sandwich shells.

scholarly journals Dynamic stiffness method for free vibrations analysis of partial fluid-filled orthotropic circular cylindrical shells

2015 ◽  
Vol 37 (1) ◽  
pp. 43-56
Author(s):  
Tran Ich Thinh ◽  
Nguyen Manh Cuong ◽  
Vu Quoc Hien
Keyword(s):  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Cylindrical Shells ◽  
Computational Cost ◽  
Shear Deformation Theory ◽  
Free Vibrations ◽  
Various Boundary Conditions ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Circular Cylindrical Shells

Free vibrations of partial fluid-filled orthotropic circular cylindrical shells are investigated using the Dynamic Stiffness Method (DSM) or Continuous Element Method (CEM) based on theFirst Order Shear Deformation Theory (FSDT) and non-viscous incompressible fluid equations. Numerical examples are given for analyzing natural frequencies and harmonic responses of cylindrical shells partially and completely filled with fluid under various boundary conditions. The vibration frequencies for different filling ratios of cylindrical shells are obtained and compared with existing experimental and theoretical results which indicate that the fluid filling can reduce significantly the natural frequencies of studiedcylindrical shells. Detailed parametric analysis is carried out to show the effects of some geometrical and material parameters on the natural frequencies of orthotropic cylindrical shells. The advantages of this current solution consist in fast convergence, low computational cost and high precision validating for all frequency ranges.

Stochastic Analysis of Free Vibrations in Piezoelectric Bimorphs

2006 ◽  
Author(s):  
Alberto Borboni ◽  
Diego De Santis ◽  
Rodolfo Faglia
Keyword(s):  
Free Vibration ◽  
Weibull Distribution ◽  
Electric Potential ◽  
Electromechanical Coupling ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Free Vibrations ◽  
Piezoelectric Bimorph ◽  
Simply Supported ◽  
Piezoelectric Bimorphs

Piezoelectric bimorph benders are a particular class of piezoelectric devices, which are characterized by the ability of producing flexural deformation greatly larger than the length or thickness deformation of a single piezoelectric layer. Piezoelectric bimorph benders were first developed by Sawyer in 1931 at the Brush Development Company. The performance of these actuators was rudimentary studied and improved much later, with the results of research on smart structures in 1980s. Piezoelectric benders have been used in different applications: in robotics, spoilers on missile fins, actuation for a quick-focusing lens, to control the vibration of a helicopter rotor blade and for many other purposes. Due to extensive dimensional reduction of devices and to high precision requested, the effect of erroneous parameter estimation and the fluctuation of parameters due to external reasons, sometimes, cannot be omitted. So, we consider mechanical, electrical and piezoelectric parameters as uniformly distributed around a nominal value and we calculate the distribution of natural frequencies of the device. We consider an efficient and accurate analytical model for piezoelectric bimorph. The model combines an equivalent single-layer theory for the mechanical displacements with layerwise-type approximation for the electric potential. First-order Timoshenko shear deformation theory kinematics and quadratic electric potentials are assumed in developing the analytical solution. Mechanical displacement and electric potential Fourier-series amplitudes are treated as fundamental variables, and full electromechanical coupling is maintained. Numerical analysis of simply supported bimorphs under free vibration conditions are presented for different length-to-thickness ratios (i.e., aspect ratio), and the results are verified by those obtained from the exact 2D solution. According to Timoshenko theory, a shear correction factor is introduced with a value proposed by Timoshenko (1922) and by Cowper (1966). Free vibration problem of simply supported piezoelectric bimorphs with series or parallel arrangement is investigated for the closed circuit condition, and the results for different length-to-thickness ratios are compared with those obtained from the exact 2D solution. Numerical examples are presented on bimorphs constituted by two orthotropic piezoceramic layers (PZT-5A material). The calculation of natural frequencies is based on a Weibull distribution, because it is capable to properly model a large class of stochastic behaviours. The effect of errors on the Weibull distribution of the natural frequencies is shown in terms of change of the Weibull parameters. The results show how the parameters errors are reflected on the natural frequencies and how an increment of the error is able to change the shape of the frequencies distribution.

Dynamic instability characteristics of doubly curved panels subjected to partially distributed follower edge loading with damping

2004 ◽  
Vol 218 (1) ◽  
pp. 67-81 ◽  
Author(s):  
L Ravi Kumar ◽  
P K Datta ◽  
D L Prabhakara
Keyword(s):  
Shear Deformation ◽  
Dynamic Instability ◽  
Shear Deformation Theory ◽  
Structural Damping ◽  
Element Analysis ◽  
Equivalent Viscous Damping ◽  
Direction Control ◽  
The Stability ◽  
Doubly Curved ◽  
Curved Panels

The vibration and dynamic instability characteristics of doubly curved panels subjected to partially distributed non-conservative follower load are studied using finite element analysis. The first-order shear deformation theory is used to model the doubly curved panels, considering the effects of shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to Sander's first approximation for doubly curved shells, which can be reduced to Love's and Donnell's theories by means of tracers. The modal transformation technique is applied to the resulting equilibrium equation for subsequent analysis. Structural damping is introduced into the system in terms of equivalent viscous damping. The effects of load bandwidth, boundary condition, load direction control parameter and damping are considered for the stability behaviour of the panels. The results show that the load bandwidth has a significant effect on the dynamic instability characteristics of the panels. The analysis also shows that, under follower loading, the system is susceptible to instability due to flutter alone or due to both flutter and divergence, depending upon the system parameters. Structural damping significantly affects the critical flutter loads of the panels.

scholarly journals Free Vibrations and Impact Resistance of a Functionally Graded Honeycomb Sandwich Plate

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Jun-hua Zhang ◽  
Bao-juan Dong ◽  
Bince He ◽  
Ying Sun
Keyword(s):  
Sandwich Plate ◽  
Natural Frequencies ◽  
Impact Resistance ◽  
Shear Deformation Theory ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Inhomogeneous Materials ◽  
Honeycomb Sandwich ◽  
Honeycomb Sandwich Plate

The functionally graded honeycomb has the characteristic of light weight, low density, high impact resistance, noise reduction, and energy absorption as a kind of new composite inhomogeneous materials. It has the advantages of both functionally graded materials and honeycombs. In this paper, a functionally graded honeycomb sandwich plate with functionally graded distributed along the thickness of the plate is constructed. The equivalent elastic parameters of the functionally graded honeycomb core are given. Based on Reddy’s higher-order shear deformation theory (HSDT) and Hamilton’s principle, the governing partial differential equation of motion is derived under four simply supported boundary conditions. The natural frequencies of the graded honeycomb sandwich plate are obtained by both the Navier method from the governing equation and the finite element model. The results obtained by the two methods are consistent. Based on this, the effects of parameters and graded on the natural frequencies of the functionally graded honeycomb sandwich plate are studied. Finally, the dynamic responses of the functionally graded honeycomb sandwich plate under low-speed impacts are studied. The results obtained in this paper will provide a theoretical basis for further study of the complex dynamics of functionally graded honeycomb structures.

scholarly journals Three-Dimensional Exact Free Vibration Analysis of Spherical, Cylindrical, and Flat One-Layered Panels

2014 ◽  
Vol 2014 ◽  
pp. 1-29 ◽  
Author(s):  
Salvatore Brischetto
Keyword(s):  
Free Vibration ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Closed Shell ◽  
Free Vibrations ◽  
Curvilinear Coordinates ◽  
Shell Panel ◽  
Plates And Shells ◽  
Orthogonal Curvilinear Coordinates

The paper proposes a three-dimensional elastic analysis of the free vibration problem of one-layered spherical, cylindrical, and flat panels. The exact solution is developed for the differential equations of equilibrium written in orthogonal curvilinear coordinates for the free vibrations of simply supported structures. These equations consider an exact geometry for shells without simplifications. The main novelty is the possibility of a general formulation for different geometries. The equations written in general orthogonal curvilinear coordinates allow the analysis of spherical shell panels and they automatically degenerate into cylindrical shell panel, cylindrical closed shell, and plate cases. Results are proposed for isotropic and orthotropic structures. An exhaustive overview is given of the vibration modes for a number of thickness ratios, imposed wave numbers, geometries, embedded materials, and angles of orthotropy. These results can also be used as reference solutions to validate two-dimensional models for plates and shells in both analytical and numerical form (e.g., closed solutions, finite element method, differential quadrature method, and global collocation method).

Dynamic Behaviors of Postbuckled Thin Film on Flexible Substrates Considering Viscoelastic Effects

2021 ◽  
Vol 88 (4) ◽  
Author(s):  
Yi Wang ◽  
Xinbo Cui ◽  
Haoran Fu ◽  
Qi Zhao ◽  
Yuhang Li
Keyword(s):  
Thin Film ◽  
Natural Frequencies ◽  
Flexible Substrate ◽  
Free Vibrations ◽  
Flexible Substrates ◽  
Negative Effects ◽  
Element Analysis ◽  
Dynamic Behaviors ◽  
Practical Applications ◽  
Viscoelastic Effects

Abstract Stretchable electronic systems based on controllable compressive buckling can be further endowed with superior compliance and stretchability. However, such systems are usually restrained by the interference from different loads in practical applications, so it is desirable to study their dynamic behaviors. In this article, an analytical model is developed on the linear free vibrations of a buckled thin film attached to a flexible substrate, whose results can be verified by the finite element analysis (FEA). In the model, the film is considered as an Euler–Bernoulli beam, and the substrate is assumed as a Pasternak foundation with Kelvin viscoelasticity. The natural frequencies and their corresponding vibration modes of the buckled film with the substrate are obtained. The results indicate that the increases of stiffness and damping of the substrate have negative effects on the natural frequencies. The damping influences the low-order modes a lot but not the high-order modes. This study may provide some suggestions for the dynamic design of buckled thin films on flexible substrates. For example, the controllable vibration attenuation can be achieved by choosing the substrate with appropriate viscoelasticity.

Measurement of Young’s Modulus and Shear Modulus of Some Structures Welded Using Flux Cored Wire by Vibration Tests

2014 ◽  
Vol 216 ◽  
pp. 151-156 ◽  
Author(s):  
Liviu Bereteu ◽  
Mircea Vodǎ ◽  
Gheorghe Drăgănescu
Keyword(s):  
Shear Modulus ◽  
Arc Welding ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Vibration Modes ◽  
Cored Wire ◽  
Flux Cored Arc Welding ◽  
Longitudinal Elastic Modulus ◽  
Vibration Tests ◽  
Non Destructive

The aim of this work was to determine by vibration tests the longitudinal elastic modulus and shear modulus of welded joints by flux cored arc welding. These two material properties are characteristic elastic constants of tensile stress respectively torsion stress and can be determined by several non-destructive methods. One of the latest non-destructive experimental techniques in this field is based on the analysis of the vibratory signal response from the welded sample. An algorithm based on Pronys series method is used for processing the acquired signal due to sample response of free vibrations. By the means of Finite Element Method (FEM), the natural frequencies and modes shapes of the same specimen of carbon steel were determined. These results help to interpret experimental measurements and the vibration modes identification, and Youngs modulus and shear modulus determination.

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