S.C. Pradhan

VIBRATION CHARACTERISTICS OF FUNCTIONALLY GRADED CYLINDRICAL SHELLS UNDER VARIOUS BOUNDARY CONDITIONS

Abstract In the recent years, functionally gradient materials (FGMs) have gained considerable attention in the high temperature environment applications. In the present work, study of the vibration of a functionally graded cylindrical shell made up of stainless steel and zirconia is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. Effects of boundary conditions and volume fractions (power law exponent) on the natural frequencies of the FG cylindrical shell are studied. Frequency characteristics of the FG shell are found to be similar to those of isotropic cylindrical shells. Further, natural frequencies of these shells are observed to be dependent on the constituent volume fractions and boundary conditions. Strain displacement relations from Loves shell theory are employed. Rayleigh method is used to derive the governing equations. Further, analytical results are validated with those reported in the literature.

Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory

In the present work, nonlocal elasticity theory has been implemented to study the vibration response of single-layered graphene (SLGS) sheets. The nonlocal elasticity theory accounts for the small size effects when dealing with nanostructures. Influence of the surrounding elastic medium on the fundamental frequencies of the SLGS is investigated. Both Winkler-type and Pasternak-type models are employed to simulate the interaction of the graphene sheets with a surrounding elastic medium. On the basis of Hamilton’s principle governing differential equations for the aforementioned problems are derived. The nonlocal small scale coefficients get introduced into the nonlocal theory through the constitutive relations. Differential quadrature method is being employed and numerical solutions for the frequencies are obtained. Numerical results show that the fundamental frequencies of SLGS are strongly dependent on the small scale coefficients. Further, a nonlinear frequency response is observed for the SLGS with lar...

Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity

In this article, nonlocal elasticity theory is applied to investigate the vibration response of nanoplates under uniaxially prestressed conditions. Nonlocal elasticity theory takes into account the small-size effects when dealing with nanostructures. Nonlocal governing equations of the prestressed nanoplate are derived and presented. Differential quadrature method is being utilized and numerical frequency solutions are obtained. Influence of small scale and uniaxial preload on the nonlocal frequency solutions is investigated. It is observed that the frequencies for nanoplates under uniaxially prestressed conditions employing classical plate theory are overestimated compared to nonlocal plate solutions. Considering the nonlocal effects, smaller critical compressive load is required to reach the buckling state of a flexural mode compared to the classical plate theory. The present research work thus reveals that the nonlocal parameter, aspect ratios, boundary conditions, and initial uniaxial prestress have s...

Small-scale effect on vibration analysis of single-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory

Nonlocal elasticity theory is a growing technique for the mechanical analyses of microelectromechanical (MEMS) and nanoelectromechanical (NEMS) based structures. The nonlocal parameter accounts for the small size effects when dealing with nanosize structures such as single-walled carbon nanotubes (SWCNTs). In this article, nonlocal elasticity and Timoshenko beam theory are implemented to study the vibration response of SWCNT embedded in an elastic medium. Influence of the surrounding elastic medium on the fundamental frequencies of the SWCNT is investigated. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of the SWCNT with the surrounding elastic medium. A differential quadrature approach is being utilized and numerical solutions for the natural frequencies are obtained. Influences of nonlocal effects, Winkler modulus parameter, Pasternak shear modulus parameter, and aspect ratio on the frequency of SWCNT are analyzed and discussed. The present study illustr...

Control of laminated composite plates using magnetostrictive layers

In this paper, first-order shear deformation theory (FSDT) is employed to study vibration control of laminated composite plates. The magnetostrictive layers are used to control and enhance the vibration suppression via velocity feedback with a constant gain distributed control. Analytical solutions of the equations governing laminated plates with embedded magnetostrictive layers are obtained for simply-supported boundary conditions. The effects of material properties, lamination scheme, and placement of magnetostrictive layers with respect to laminate midplane on vibration suppression are studied in detail.

A series solution approach to an analytical load-deflection relation for the measurement of mechanical properties of thin films

The load-deflection technique is a popular technique to measure mechanical properties such as internal stress and Youngs modulus of thin films. The measurement of internal stress and Youngs modulus depends on the determination of the analytical load-deflection relation. In this paper, a series solution approach is presented to obtain the analytical load-deflection relation for a circular membrane. To determine the number of terms required for the results to settle to a stable value, a convergence study is carried out. The present study found that to obtain the analytical load-deflection relation using a series solution approach, the transverse displacement can only admit one term solution, while the in-plane displacement can have a series solution. The present approach has been verified with a finite-element solution obtained using Macneal-Schwendler Corporation Nastran by comparing maximum deflections as well as deflection curves. The agreement is excellent.

Galerkin finite element methods for wave problems

We compare here the accuracy, stability and wave propagation properties of a few Galerkin methods. The basic Galerkin methods with piecewise linear basis functions (called G1FEM here) and quadratic basis functions (called G2FEM) have been compared with the streamwise-upwind Petrov Galerkin (SUPG) method for their ability to solve wave problems. It is shown here that when the piecewise linear basis functions are replaced by quadratic polynomials, the stencils become much larger (involving five overlapping elements), with only a very small increase in spectral accuracy. It is also shown that all the three Galerkin methods have restricted ranges of wave numbers and circular frequencies over which the numerical dispersion relation matches with the physical dispersion relation — a central requirement for wave problems. The model one-dimensional convection equation is solved with a very fine uniform grid to show the above properties. With the help of discontinuous initial condition, we also investigate the Gibbs’ phenomenon for these methods.

Three-dimensional finite element modelling of delamination growth in notched composite laminates under compression loading

Abstract Composite materials are widely used in the aerospace industry because of their specific advantages over conventional metals. In these materials, delamination growth leading to failure is one of the major failure mechanisms. In the present work, notched laminates with concentric circular initial delaminations are prepared. Fatigue tests are carried out for various cycles and the delamination growths in the laminates are recorded with a C-scanner. Three-dimensional finite element models are developed to study the delamination growth. Strain energy release rates are used as fracture mechanics parameters to describe the delamination propagation. Variation of the strain energy release rates along the delamination front is determined. Delamination growth patterns are predicted. Experimental and the finite element analysis results are found to be in good agreement.

Parametric study of interfacial debonding in adhesively bonded composite joints

Abstract In composite structures adhesive bonding is preferred to mechanical fasteners because they provide even stress distribution, smooth surface contours and excellent fatigue properties. Interfaces of adherend and adhesive are the potential sources for the initiation of debonding leading to failure. In the present work, composite joints are analysed using the finite element method for the computation of the strain energy release rate, which is used as a measure for possible debonding. Interfaces are modelled by paired nodes and are released one after another in a proper sequence, modelling the crack opening. Joints with various values of elastic moduli, thickness of adherend and adhesive, and overlap lengths for different crack growth lengths along the interfaces are analysed. Laminae of different fibre orientations and lay-up sequences are also considered. Failure loads are estimated and material and geometrical parameters and lay-up sequences are suggested.

Elasto-plastic analysis of adhesive bonded joint

Large scale structures generally consist of an assembly of a number of individual elements. The connections or joints though potentially weak spots are still required. These joints could be discrete, continuous or a combination of both. Continuous joints include adhesively bonded joints, welded joints, brazing, soldering etc. . Discrete (fastener) joints are preferred in structures requiring periodic disassembly and assembly for the purpose of inspection or repair. Adhesive bonded joints have distinct major advantages of excellent fatigue properties, damage tolerance, smooth surface contour, low stress concentration etc.