Effect of static deflection on natural frequency of non-linear spring mass system by direct linearization method

An exact expression for the frequency of a non-linear cubic spring mass system is obtained considering the effect of static deflection. An alternative expression for the approximate frequency is also obtained by the direct linearization procedure; it is shown that this is very accurate as compared with the exact method. This approximate frequency equation is used to explain a “dual behaviour” of the frequency amplitude curves.

Response spectrum of non-linear spring mass system subjected to transient disturbances

The transient response spectrum of a cubic spring mass system subjected to a step function input is obtained. An approximate method is adopted where non-linear restoring force characteristic is replaced by two linear segments, so that the mean square error between them is a minimum. The effect of viscous damping on the peak response is also discussed for various values of the damping constant and the non-linearity restoring force parameter.

Step function response of non-linear spring mass systems in the presence of Coulomb damping

The transient response of non-linear spring mass systems with Coulomb damping, when subjected to a step function is investigated. For a restricted class of non-linear spring characteristics, exact expressions are developed for (i) the first peak of the response curves, and (ii) the time taken to reach it. A simple, yet accurate linearization procedure is developed for obtaining the approximate time required to reach the first peak, when the spring characteristic is a general function of the displacement. The results are presented graphically in non-dimensional form.

Free vibrations of non-linear cubic spring mass systems in the presence of coulomb damping

An exact solution for the free vibration problem of non-linear cubic spring mass system with Coulomb damping is obtained during each half cycle, in terms of elliptic functions. An expression for the half cycle duration as a function of the mean amplitude during the half cycle is derived in terms of complete elliptic integrals of the first kind. An approximate solution based on a direct linearization method is developed alongside this method, and excellent agreement is obtained between the results gained by this method and the exact results. © 1970 Academic Press Inc. (London) Limited.

Non-enzymatic Degradation of (1→3)(1→4)-β-D-glucan in Aqueous Processing of Oats

Cereal water-soluble β-glucan [(1→3)(1→4)-β-D-glucan] has well-evidenced health benefits and it contributes to the texture properties of foods. These functions are characteristically dependent on the excellent viscosity forming ability of this cell wall polysaccharide. The viscosity is affected by the molar mass, solubility and conformation of β-glucan molecule, which are further known to be altered during food processing. This study focused on demonstrating the degradation of β-glucan in water solutions following the addition of ascorbic acid, during heat treatments or high pressure homogenisation. Furthermore, the motivation of this study was in the non-enzymatic degradation mechanisms, particularly in oxidative cleavage via hydroxyl radicals. The addition of ascorbic acid at food-related concentrations (2-50 mM), autoclaving (120°C) treatments, and high pressure homogenisation (300-1000 bar) considerably cleaved the β-glucan chains, determined as a steep decrease in the viscosity of β-glucan solutions and decrease in the molar mass of β-glucan. The cleavage was more intense in a solution of native β-glucan with co-extracted compounds than in a solution of highly purified β-glucan. Despite the clear and immediate process-related degradation, β-glucan was less sensitive to these treatments compared to other water-soluble polysaccharides previously reported in the literature. In particular, the highly purified β-glucan was relatively resistant to the autoclaving treatments without the addition of ferrous ions. The formation of highly oxidative free radicals was detected at the elevated temperatures, and the formation was considerably accelerated by added ferrous ions. Also ascorbic acid pronounced the formation of these oxidative radicals, and oxygen was simultaneously consumed by ascorbic acid addition and by heating the β-glucan solutions. These results demonstrated the occurrence of oxidative reactions, most likely the metal catalysed Fenton-like reactions, in the β-glucan solutions during these processes. Furthermore, oxidized functional groups (carbonyls) were formed along the β-glucan chain by the treatments, including high pressure homogenisation, evidencing the oxidation of β-glucan by these treatments. The degradative forces acting on the particles in the high pressure homogenisation are generally considered to be the mechanical shear, but as shown here, carbohydrates are also easily degraded during the process, and oxidation may have a role in the modification of polysaccharides by this technique. In the present study, oat β-glucan was demonstrated to be susceptible to degradation during aqueous processing by non-enzymatic degradation mechanisms. Oxidation was for the first time shown to be a highly relevant degradation mechanism of β-glucan in food processing.

Spring Warming of the Eastern Arabian Sea and Bay of Bengal from Buoy Data

Observations from moored buoys during spring of 1998-2000 suggest that the warming of the mixed layer (similar to20 m deep) of the north Indian Ocean warm pool is a response to net surface heat flux Q(net) (similar to100 W m(-2)) minus penetrative solar radiation Q(pen) (similar to45 W m(-2)). A residual cooling due to vertical mixing and advection is indirectly estimated to be about 25 W m(-2). The rate of warming due to typical values of Q(net) minus Q(pen) is not very sensitive to the depth of the mixed layer if it lies between 10 m and 30 m.

Static Balancing of Spring-loaded Planar Revolute-joint Linkages without Auxiliary Links

We present a method to statically balance a general treestructured,planar revolute-joint linkage loaded with linear springs or constant forces without using auxiliary links. The balancing methods currently documented in the literature use extra links; some do not apply when there are spring loads and some are restricted to only two-link serial chains. In our method, we suitably combine any non-zero-free-length load spring with another spring to result in an effective zero-free-length spring load. If a link has a single joint (with the parent link), we give a procedure to attach extra zero-free-length springs to it so that forces and moments are balanced for the link. Another consequence of this attachment is that the constraint force of the joint on the parent link becomes equivalent to a zero-free-length spring load. Hence, conceptually,for the parent link, the joint with its child is removed and replaced with the zero-free-length spring. This feature allows recursive application of this procedure from the end-branches of the tree down to the root, satisfying force and moment balance of all the links in the process. Furthermore, this method can easily be extended to the closed-loop revolute-joint linkages, which is also illustrated in the paper.

Exploring isospectral spring-mass systems with firefly algorithm

This paper investigates in-line spring-mass systems (An), fixed at one end and free at the other, with n-degrees of freedom (d.f.). The objective is to find feasible in-line systems (B(n)) that are isospectral to a given system. The spring-mass systems, A(n) and B(n), are represented by Jacobi matrices. An error function is developed with the help of the Jacobi matrices A(n) and B(n). The problem of finding the isospectral systems is posed as an optimization problem with the aim of minimizing the error function. The approach for creating isospectral systems uses the fact that the trace of two isospectral Jacobi matrices A(n) and B(n) should be identical. A modification is made to the diagonal elements of the given Jacobi matrix (A(n)), to create the isospectral systems. The optimization problem is solved using the firefly algorithm augmented by a local search procedure. Numerical results are obtained and resulting isospectral systems are shown for 4 d.f. and 10 d.f. systems.

On the magnetization reversal of the oxide-based exchange spring magnet

The role of the soft phase (Ni0.8Zn0.2Fe2O4) on the magnetization reversal and coercivity mechanism of the Ni0.8Zn0.2Fe2O4/BaFe12O19 nanocomposite has been investigated. The presence of the interacting field and the disorder in the nanocomposite has been confirmed by the variation of Jr/Jr(∞) vs Jd/Jr(∞) and the irreversible magnetization. To understand the relative strength of the pinning and the nucleation, the magnetic viscosity measurement has been done and the thermal activation volume has been estimated. From the Barbier plot and the activation volume measurement, the dominant mechanism governing the magnetization reversal process has been proposed.

A spring-mass-lever model, stiffness and inertia maps for single-input, single-output compliant mechanisms

A spring-mass-lever (SML) model is introduced in this paper for a single-input-single-output compliant mechanism to capture its static and dynamic behavior. The SML model is a reduced-order model, and its five parameters provide physical insight and quantify the stiffness and inertia(1) at the input and output ports as well as the transformation of force and displacement between the input and output. The model parameters can be determined with reasonable accuracy without performing dynamic or modal analysis. The paper describes two uses of the SML model: computationally efficient analysis of a system of which the compliant mechanism is a part; and design of compliant mechanisms for the given user-specifications. During design, the SML model enables determining the feasible parameter space of user-specified requirements, assessing the suitability of a compliant mechanism to meet the user-specifications and also selecting and/or re-designing compliant mechanisms from an existing database. Manufacturing constraints, material choice, and other practical considerations are incorporated into this methodology. A micromachined accelerometer and a valve mechanism are used as examples to show the effectiveness of the SML model in analysis and design. (C) 2012 Published by Elsevier Ltd.

Exchange-spring mechanism of soft and hard ferrite nanocomposites

The paper reports exchange-spring soft and hard ferrite nanocomposites synthesized by chemical co-precipitation with or without the application of ultrasonic vibration. The composites contained BaFe12O19 as the hard phase and CoFe2O4/MgFe2O4 as the soft phase. X-ray diffraction patterns of the samples in the optimum calcined condition indicated the presence of soft ferrites as face-centred cubic (fcc) and hard ferrites as hexagonal close packed (hcp) structure respectively. Temperature dependence of magnetization in the range of 20-700 degrees C demonstrated distinct presence of soft and hard ferrites as magnetic phases which are characterized by wide difference in magnetic anisotropy and coercivity. Exchange-spring mechanism led these nanocomposite systems to exchange-coupled, which ultimately produced convex hysteresis loops characteristic of a single-phase permanent magnet. Fairly high value of coercivity and maximum energy product were observed for the samples in the optimum calcined conditions with a maximum applied field of 1600 kA/m (2 T).

Investigation on non-exchange spring behaviour and exchange spring behaviour: A first order reversal curve analysis

The First Order Reversal Curve (FORC) method has been utilised to understand the magnetization reversal and the extent of the irreversible magnetization of the soft CoFe2O4-hard SrFe12O19 nanocomposite in the nonexchange spring and the exchange spring regime. The single peak switching behaviour in the FORC distribution of the exchange spring composite confirms the coherent reversal of the soft and hard phases. The onset of the nucleation field and the magnetization reversal by domain wall movement are also evident from the FORC measurements. (C) 2013 AIP Publishing LLC.