Forced vibration of non-uniform axially functionally graded (AFG) Timoshenko beam on elastic foundation is performed under harmonic excitation. A linear elastic foundation is considered with three different classical boundary conditions. AFG materials are an advanced class of materials that have potential for application in various engineering fields. In the present work, variation of material properties along the longitudinal axis of the beam are considered according to power-law forms. Five values of material gradation parameter provides different functional variation and their effect on the frequency response of the system is studied. The present approximate method is displacement based and Von-Karman type of geometric nonlinearity is considered with rotational component to incorporate transverse shear. Hamilton’s principle is used to derive nonlinear set of governing equation and Broyden method is implemented to solve the nonlinear equations numerically. The results are successfully validated with previously published article. Frequency vs. amplitude curve corresponding to different combinations of system parameters are presented and are capable of serving as benchmark results. A separate free vibration analysis is undertaken to include backbone curves with the frequency response curves in the non-dimensional plane.

In the present paper, a flattening contact analysis of CNT-Al nanocomposite is presented for both loading and unloading phases. APDL code is used in ANSYS framework to create the FE model to analyse the contact behaviour between a frictionless cylinder (CNT-Al) and a rigid flat. The developed model has been validated against established results of certain problems with lesser complexity. The contact force, contact area, von Mises stresses and nodal displacements are extracted from the simulated solution. These parameters are noted at the end of the loading step and also once unloading is completed from a certain interference. It has been found that as CNT radius increases, the contact properties get decreased. It's also observed that beyond a certain CNT radius, the contact properties of CNT-Al nanocomposite materials start to resemble those of the matrix material and eventually fall below the matrix material.

A dynamic analysis of a hemispherical and cylindrical contact, material properties of which are graded elastically and plastically along the radius, is presented. The static force–displacement behavior of a hemisphere and a semi-cylinder in contact with a rigid flat is obtained using finite element software. The force–displacement is used in a further dynamic analysis for undamped-free as well as for forced-damped vibration of the contact interface. For the undamped free vibration, variation of natural frequency w.r.t. initial displacement is furnished for different values of elastic and plastic gradation parameter. In addition, variation of maximum initial displacement for contact loss is also demonstrated. The forced-damped vibration characteristics of the spherical and cylindrical contact interfaces are presented in the form of frequency response curves with jump up and jump down frequencies. Spherical and cylindrical contact interfaces are found to exhibit softening and hardening type nonlinearity, respectively.

This article presents geometrically nonlinear forced vibration analysis of an axially functionally graded (AFG) non-uniform beam resting on an elastic foundation. The mathematical formulation is displacement based and derivation of governing equations is accomplished following Hamilton's principle. The foundation has been mathematically incorporated into the analysis as a set of linear springs. According to the basic assumption of the present method force equilibrium condition is satisfied at a maximum excitation amplitude value. Thus, the dynamic problem is equivalently represented as a static one, which is solved by following a numerical implementation of the Broyden method. It is a method that utilizes the Jacobian matrix and subsequent correction of the initial Jacobian to solve a system of nonlinear equations. The large amplitude dynamic behaviour of the system in terms of non-dimensional frequency response curves is validated against established results and new results are furnished for a parabolic tapered AFG beam on a linear elastic foundation.

The focus of the present study is to simulate the indentation type contact behaviour of single walled carbon nanotube (SWCNT) based nanocomposite. The contact system consists of a deformable Aluminium matrix, reinforced with a group of SWCNTs, and a conical indenter which is assumed as rigid. Downward and upward displacement is imparted on the conical indenter in order to simulate the loading and unloading phases of the contact. The model has been developed using APDL code on the ANSYS platform. Adequacy and validity of the model has been established by comparison with results from already published papers available in literature and the matching between the two sets of results is found to be excellent. In terms of results, contact forces, contact area, contact pressure and deformation behaviour are extracted from the analysis with varying wall thickness of CNTs. Detailed analysis of the obtained results has been carried out and it is found that sink in and pile up (in one particular scenario) behaviour is exhibited. It is also found that due to high deformation of the tubes at high indentation depth, there is material flow towards the axis of symmetry and creation of small elastic zones in the matrix material.

The present study examines the effects of changes in single-wall carbon nanotube (SWCNT) volume % in an Al reinforced nanocomposite under loading and unloading in a cylindrical flattening contact. Flattening action is provided by a rigid flat, which moves downward and upward to simulate the loading and unloading stages, respectively. The cylinder is modelled as a 2D quarter-circle, which consists of the embedded CNTs. Volume % of the nanotubes is varied by changing the wall thickness and number of CNTs, while the overall radius is kept fixed. Finite element model to perform a plane stress quasi-static analysis is created using ANSYS. The simulated results are compared with results from published studies to satisfactorily validate it. Various parameters, in the contact zone and in the vicinity of the CNTs, are presented as results. It is found that above a certain CNT thickness, higher volume percentage of CNTs result in higher contact force as well as contact area. Additionally, more matrix material in the asperity is found to yield plastically for higher volume percentage of CNTs.