Journal of Solid Mechanics
Volume:5 Issue: 2, Spring 2013

Many wearing processes are a result of the oblique impacts. Knowing the effective impact parameters on the wear mechanism would be helpful to have the more reliable designs. The H-DD (Hertz-Di Maio Di Renzo) nonlinear model of impact followed by the time increment procedure is used to simulate the impact process of a ball on a flat plate. Restitution parameters are extracted and compared with the experimental data to ensure the accuracy of the impact model. The constant parameters of a wear equation are determined by comparing the results with the experimental data. The results obtained suggest that this simulation method could be used as a predictive way to study the practical design problems and to explain some phenomena associated with impact erosion.

In this paper, the effect of the temperature change on the vibration frequency of mono-layer graphene sheet embedded in an elastic medium is studied. Using the nonlocal elasticity theory, the governing equations are derived for single-layered graphene sheets. Using Levy and Navier solutions, analytical frequency equations for single-layered graphene sheets are obtained. Using Levy solution, the frequency equation and mode shapes orthotropic rectangular nanoplate are considered for three cases of boundary conditions. The obtained results are subsequently compared with valid result reported in the literature. The effects of the small scale, temperature change, different boundary conditions, Winkler and Pasternak foundations, material properties and aspect ratios on natural frequencies are investigated. It has been shown that the non-dimensional frequency decreases with increasing temperature change. It is seen from the figure that the influence of nonlocal effect increases with decreasing of the length of nanoplate and also all results at higher length converge to the local frequency. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration proper ties of the nanoplates.

This study is concerned to check the validity and applicability of a five parameter viscoelastic model for harmonic wave propagating in the non-homogeneous viscoelastic rods of varying density. The constitutive relation for five parameter model is first developed and validity of these relations is checked. The non-homogeneous viscoelastic rods are assumed to be initially unstressed and at rest. In this study, it is assumed that density, rigidity and viscosity of the specimen i.e. rod are space dependent. The method of non-linear partial differential equation (Eikonal equation) has been used for finding the dispersion equation of harmonic waves in the rods. A method for treating reflection at the free end of the finite non-homogeneous viscoelastic rod is also presented. All the cases taken in this study are discussed numerically and graphically with MATLAB.

The normal human running has been simulated by two-dimensional biped model with 7 segments. Series of normal running experiments were performed and data of ground reaction forces measured by force plate was analyzed and was fitted to some Fourier series. The model is capable to simulate running for different ages and weights at different running speeds. A proportional derivative control algorithm was employed to grant stabilization during each running step. For calculation of control algorithm coefficients, an optimization method was used which minimized cinematic differences between normal running model and that of the experimentally obtained from running cycle data. This yielded the estimated torque coefficients of the different joints. The estimated torques and the torque coefficients were then applied to specific below-knee prosthesis (a SACH foot) to simulate healthy-running motion of joints. Presently the SACH foot is designed for amputee’s walking; our data was used to modify such construct for running purposes. The goal was to minimize the differences between normal human model and a subject wearing a SACH foot during running. Kinematical curves of models for the obtained optimum mechanical properties indicated thatprosthetic leg can reasonably produce the kinematics of normal running under normal joint driving torques.

An accurate solution procedure based on the three-dimensional elasticity theory for the free vibration analysis of Functionally Graded Sandwich (FGS) plates is presented. Since no assumptions on stresses and displacements have been employed, it can be applied to the free vibration analysis of plates with arbitrary thickness. The two-constituent FGS plate consists of ceramic and metal graded through the thickness, from one surface of the each sheet to the other according to a generalized power-law distribution with four parameters. The benefit of using generalized power-law distribution is to illustrate and present useful results arising from symmetric, asymmetric and classic profiles. Using the Generalized Differential Quadrature (GDQ) method through the thickness of the plate, further allows one to deal with FG plates with an arbitrary thickness distribution of material properties. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The effects of different geometrical parameters such as the thickness-to-length ratio, different profiles of materials volume fraction and four parameters of power-law distribution on the vibration characteristics of the FGS plates are investigated. Interesting result shows that by utilizing a suitable four-parameter model for materials volume fraction, frequency parameter can be obtained more than the frequency parameter of the similar FGS plate with sheets made of 100% ceramic and at the same time lighter. Also, results show that frequencies of symmetric and classic profiles are smaller and larger than that of other types of FGS plates respectively. The solution can be used as benchmark for other numerical methods and also the refined plate theories.

This paper presents the dynamic modeling and design of micro motion compliant parallel mechanism with flexible intermediate links and rigid moving platform. Modeling of mechanism is described with closed kinematic loops and the dynamic equations are derived using Lagrange multipliers and Kane’s methods. Euler-Bernoulli beam theory is considered for modeling the intermediate flexible link. Based on the Assumed Mode Method theory, the governing differential equations of motion are derived and solved using both Runge-Kutta- Fehlberg4, 5th and Perturbation methods. The mode shapes and natural frequencies are calculated under clamped-clamped boundary conditions. Comparing perturbation method with Runge-Kutta-Fehlberg4, 5th leads to same results. The mode frequency and the effects of geometry of flexure hinges on intermediate links vibration are investigated and the mode frequency, calculated using Fast Fourier Transform and the results are discussed.

In this study, thermo-nonlocal vibration of double bonded graphene sheet (DBGS) subjectedto 2D-magnetic field under biaxial in-plane pre-load are presented. The elastic forces between layers of graphene sheet (GS) are taken into account by Pasternak foundation and the classical plate theory (CLPT) and continuum orthotropic elastic plate are used. The nonlocal theory of Eringen and Maxwell’s relations are employed to incorporate the smallscale effect and magnetic field effects, respectively, into the governing equations of the GSs. The differential quadrature method (DQM) is used to solve the governing differential equations for simply supported edges. The detailed parametric study is conducted, focusing on the remarkable effects of the angle and magnitude of magnetic field, different type of loading condition for couple system, tensile and compressive in-plane pre-load, aspect ratio and nonlocal parameter on the vibration behavior of the GSs. The result of this study can be useful to design of micro electro mechanical systems and nano electro mechanical systems.

In this work, nonlocal vibration of double of carbon nanotubes (CNTs) system conveying fluid coupled by visco-Pasternak medium is carried out based on nonlocal elasticity theory where CNTs are placed in uniform temperature change and magnetic field. Considering Euler-Bernoulli beam (EBB) model and Knudsen number, the governing equations of motion are discretized and Ritz method is applied to obtain the frequency of coupled CNTs system. The detailed parametric study is conducted, focusing on the remarkable effects of the Knudsen number, aspect ratio, small scale, thermo-magnetic fields, velocity of conveying fluid and visco-Pasternak medium on the stability of coupled system. The resultsindicate that magnetic field has significant effect on stability of coupled system. Also, it is found that trend of figures have good agreement with the previous researches. Results of this investigation could be applied for optimum design of nano/micro mechanical devices for controlling stability of coupled systems conveying fluid under thermo-magnetic fields.