Volume 3, Issue 4

In this paper we will show how the exact frequency response of the piecewise linear vibration isolator can be reduced to be found by solving only two transcendental equations. Adopting a new nondimensionalization method, the mathematical modeling of the system is presented and the mathematics to determine the exact steadystate response of the system is explained.

The objective of this paper is to present an investigation to analyze the vibration of a conservative nonlinear oscillator in the form u" + lambda u + u^(2n-1) + (1 + epsilon^2 u^(4m))^(1/2) = 0 for any arbitrary power of n and m. This method converts the differential equation to sets of algebraic equations and solve numerically. We have presented for three different cases: a higher order Duffing equation, an equation with irrational restoring force and a plasma physics equation. It is also found that the method is valid for any arbitrary order of n and m. Comparisons have been made with the results found in the literature the method gives accurate results.

The present manuscript reports a numerical investigation of fully developed mixed convective flow in a parallel channel filled with porous medium. The motion in the channel is induced by external pressure gradient and buoyancy force. The non-Darcy Brinkman-Forchheimer extended model has been used. The Chebyshev spectral collocation method has been used to solve the coupled differential equations numerically. The main emphesize has been given on the influence of Forchheimer number (F), Darcy number (Da) and Rayleigh number (Ra) on velocity and temperature profiles. From this investegation we have found that the velocity aswell as temperature profiles possess point of inflection beyond a threshold value of Ra. The back flow starts near the center of the channel on increasing the value of Ra beyond the threshold value of Ra. The point of inflection on the velocity as well as temperature profile dies out on decreasing of Da. The strength of the velocity is decreases on the increasing of F', it also changes the velocity profile drastically. The point of inflection on the basic flow dies out on increasing of F'.

In this note, traveling wave solutions for (3 + 1) dimensional fluid models of incompressible flow are considered. The governing partial differential equations of two models are reduced to ordinary differential equation by employing wave parameter and exact solutions are obtained. It is shown that these fluid models allow 3 + 1 dimensional solutions amongst each other. The methodology used in this work is independent of symmetric consideration and other restrictive assumption. Finally, a set of example of boundary condition is discussed for the couple stress fluid. It is observed that velocity profile strongly depends upon couple stress parameter.

The two-dimensional differential transform method (DTM) is applied to solve the one-dimensional coupled heat and moisture diffusion problem for a slab with temperature-dependent thermal and moisture diffusivities, which are expressed by a linear function and an exponential function of temperature, respectively. One surface of the slab is subjected to convective hygrothermal loading and the other has constant prescribed temperature and moisture. Approximate analytical (series) solutions for the temperature and moisture profiles in the slab are derived. The transformed functions included in the solutions are obtained through a simple recursive procedure. Numerical results for a slab subjected to a sudden change in surface temperature illustrate the effects of temperature-dependent diffusivities on the transient temperature and moisture profiles of the slab. The results indicate that the nonlinear effect originating from the varying moisture diffusivity is not negligible for resin composites. The DTMis a useful new analytical method for solving nonlinear coupled transient problems.

For a class of steady-state metal-forming problems, with rigid-plastic, incompressible, strain-rate dependent material model and with unilateral contact and nonlocal Coulomb’s frictional boundary conditions, a variational inequality formulation is derived and by proving the convergence of a modified secant-modulus method, existence and uniqueness results are obtained. A finite element - modified secant-modulus computational algorithm is developed and applied for solving illustrative problems.

In present work, joint flexibility (or looseness) of the free-free beam is investigated by using a two noded beam finite element formulation with transverse displacement and joint rotations as the degrees of freedom per node at joint location. Flexibility of the joint is primarily represented by means of a rotational spring analogy, where the stiffness of the rotational spring characterizes the looseness of the flexible joint for an applied bending moment. Influence of joint location as well as joint stiffness on modal behavior of first five modes of slender, uniform free-free beams are discussed for various values of non-dimensional rotational spring stiffness parameter. Numerical accuracy of the results obtained from the present finite element formulation are validated by using the commercially available finite element software which shows the confidence gained on the numerical results discussed in the present study.

The sea level projection of a 1 meter rise for the 21st century depends on climate models that have projected a given amount of anthropogenic warming during the same period. However, these same climate models predicted a warming also from 2000 to 2014, which has not been seen in the global surface temperature. Researchers have proposed several solutions such as the fact that the “missing heat” was accumulated in the deep ocean. However, no evidences of a sufficient warming of the deep oceans have been observed. Other arguments has been proposed as well and found unsatisfactory. There is the opportunity that the “heat” is not “real” but “missing” or “hiding” somewhere. If the climate model projected “heat” that simply does not exist in reality in the first place, consequently the models overestimate the anthropogenicwarming and also the sea level projections for the 21st century are overestimated.