Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering
Volume:6 Issue: 1, 2013

A type of nonlinearity in vibrational engineering systems emerges when the restoring force is a nonlinear function of displacement. The derivative of this function is known as stiffness. If the stiffness increases by increasing the value of displacement from the equilibrium position, then the system is known as hardening type oscillator and if the stiffness decreases by increasing the value of displacement, then the system is known as softening type oscillator. The restoring force as a nonlinear polynomial function of order three, can describe a wide variety of practical nonlinear situations by proper choosing of constant multipliers. In this paper, a spring-mass system is considered by the restoring force of the introduced type. Choosing suitable values for a, b and n, a hardening and softening type oscillators are constructed and related equations of motion are introduced as second order nonlinear differential equations. The equations are solved directly, using the Adomian’s decomposition method (ADM). In another approach, the equations are converted to systems of first order differential equations and then solved using the same method. The results show that the ADM gives accurate results in both approaches, beside it shows that converting the equation to a system of equations of lower order, tends to more accurate solutions when ADM applies.

In this paper, the resonant frequency and sensitivity of an atomic force microscope (AFM) with an assembled cantilever probe (ACP) are analyzed utilizing the modified couple stress theory. The proposed ACP comprises a horizontal microcantilever, an extension and a tip located at the free end of the extension, which make AFM capable of scanning the sample sidewall. First, the governing differential equation and boundary conditions for dynamic analysis are obtained by a combination of the basic equations of the modified couple stress theory and Hamilton principle. Then, a closed form expression for the resonant frequency are derived, and using this expression the sensitivity are also investigated. The results of the proposed model are compared with those of the classic beam theory. The comparison shows that the difference between the results predicted by these two theories becomes significant when the horizontal cantilever thickness comes approximately close to the material length scale parameter, in which for some values of contact stiffness the difference reaches its maximum. It can also be inferred that a decrease in the microcantilever thickness could have a knock on effect on the shifts of first frequency and first sensitivity caused by an increase in the extension length.

In this paper, natural frequency and response of forced vibration of composite laminated conical shells under different boundary conditions are investigated. To this end, equations of Donnell's thin shell theory are used as governing equations. The analytical Galerkin method together with beam mode shapes as weighting functions is employed to solve the problem. Due to importance of boundary conditions upon the mechanical behavior of conical shells, the analysis is carried out for all possible boundary conditions. The response of forced vibration is calculated via the modal participation factor method. Numerical comparisons of free vibration with the results in the open literature are made to validate the present methodology.

This article describes a numerical study on the TOX-clinching process of the steel sheets. In addition, the influence of plastic anisotropy of the material on joining parameters is analyzed by evolution of the joint parameters such as undercut and neck thickness and punch force-displacement curve. Finite element analysis with ABAQUS/CAE-Explicit program is used to simulate two dimensional and three dimensional model of clinching process based on the above objectives. This work mainly represents the comparison between experimental and the simulation results with respect to process which gives the validation of the simulation results.Three-dimentional simulation of clinching process is used to study the effect of anisotropy. Results indicate that the clinching punch force-displacement curve for connection of anisotropic sheets is higher than that for isotropic sheets. In addition, results indicate that neck thickness increases with the effect of plastic anisotropy and the undercut decreases with it.

Nowadays, the technology intends to use materials such as magnesium alloys due to their high strength to weight ratio in engine components. As usual, engine cylinder heads and blocks has made of various types of cast irons and aluminum alloys. However, magnesium alloys has physical and mechanical properties near to aluminum alloys and reduce the weight up to 40 percents. In this article, a new low cycle fatigue lifetime prediction model is presented for a magnesium alloy based on energy approach and to obtain this objective, the results of low cycle fatigue tests on magnesium specimens are used. The presented model has lower material constants in comparison to other criteria and also has proper accuracy; because in energy approaches, a plastic work-lifetime relation is used where the plastic work is the multiple of stress and plastic strain. According to cyclic softening behaviors of magnesium and aluminum alloys, plastic strain energy can be proper selection, because of being constant the product value of stress and plastic strain during fatigue loadings. In addition, the effect of mean stress is applied to the low cycle fatigue lifetime prediction model by using a correction factor. The results of presented models show proper conformation to experimental results.

Nowadays, the technology intends to use materials such as magnesium alloys due to their high strength to weight ratio in engine components. As usual, engine cylinder heads and blocks has made of various types of cast irons and aluminum alloys. However, magnesium alloys has physical and mechanical properties near to aluminum alloys and reduce the weight up to 40 percents. In this article, a new low cycle fatigue lifetime prediction model is presented for a magnesium alloy based on energy approach and to obtain this objective, the results of low cycle fatigue tests on magnesium specimens are used. The presented model has lower material constants in comparison to other criteria and also has proper accuracy; because in energy approaches, a plastic work-lifetime relation is used where the plastic work is the multiple of stress and plastic strain. According to cyclic softening behaviors of magnesium and aluminum alloys, plastic strain energy can be proper selection, because of being constant the product value of stress and plastic strain during fatigue loadings. In addition, the effect of mean stress is applied to the low cycle fatigue lifetime prediction model by using a correction factor. The results of presented models show proper conformation to experimental results.