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Showing 10 results for Linearity


Volume 11, Issue 3 (7-2009)
Abstract

Investigation of the interrelationships between yield and its components will improve the efficiency of a breeding program with appropriate selection criteria. In this study, the relationship among yield components and their direct and indirect influences on the total yield of melon were investigated. The study was based on evaluation of 49 entries gener-ated from a 7×7 diallel involving Iranian melon landraces under two conditions of cultiva-tion, pruning and non-pruning. A sequential path model was used for ordering the vari-ous variables in first and second-order paths based on their maximum direct effect and minimal colinearity. Two first-order variables, namely the number of fruits per plant and average weight of fruits per plant accounted for 91% and 83% of total variation in total weight per plant under the pruning and non-pruning conditions, respectively. The direct effects of these two variables on total weight per plant under non-pruning conditions were nearly equal, but the direct effect of average weight of fruits per plant in the pruning data set was much higher than the number of fruits per plant (1.14 vs. 0.73). All direct effects were found to be significant as indicated by bootstrap analysis. The results indicated the utility of the sequential path model for determining the interrelationships between yield and related traits in melon.

Volume 12, Issue 1 (3-2012)
Abstract

Progressive collapse of buildings has raised questions on adequacy of the existing regulations to prevent local and, in turn, global collapses. The present study mostly focuses on the performance of welded moment connections against progressive collapse. The performance of moment connections suggested in the FEMA 350, which are proper for seismic forces, Welded Flange Plate (WFP), Reduced Beam Seaction (RBS), Welded Unreinforced Flange- Welded Web (WUF-W) and Free Flange (FF), has been studied. The models used include non-linear behavior of materials and geometrical nonlinear behavior. The behavior of steel materials used in the structure is the true behavior of steel was stress-strain, which has been considered in the model completely. The nonlinear stress-strain behavior of steel selected for modeling the real behavior of beam and column members in the structure. The material properties of all steel components were modeled using elastic-plastic material model from ABAQUS. For connection region porous material plasticity was used. The diagram of vertical force against vertical displacement for each connection was drawn, and the state of each connection failure was investigated. Making the large scale experimental models to study the progressive collapse of structures seems too difficult. Using finite element models to study the behavior of structures are relatively appropriate option with regard to time and cost. In all of the numerical models, shell (S4) element has been used to simulate the beams, columns and connections. This is a four-node element, which contains four integration points on the element. During the calculations, full integration method with more precision was used. For analysis of the models, dynamic explicit method was used. This method is suitable to analyze the models with more members having nonlinear characteristics of materials and large deformations. In this method, the central difference integrating is used to solve the dynamic equations. In every time step, this method performs simpler than other methods in solving dynamic equations since there is no need to inverse stiffness matrix in any time stage. The used numerical method has compared using the laboratorial results, which have tested in 2010 by NIST. The analytical results showed a good agreement with laboratory models. The results of numerical analyses illustrated that RBS connection has less strength in comparison with other connections and this connection reaches maximum vertical displacement with less force. Performance of FF and WUF-W connections is similar to each other. These connections more resistant in comparison with RBS. WFP connection is more resistant as compared with the WUF-W, FF and RBS connections against the failure of the column. Failure load in WFPconnection is twice of other connection, and according to the analytical results, this connection is suitable for HLOP structures. In all connections, rotation capacity corresponding to collapse prevention against column removal scenario is about twice of the accepted criteria that FEMA 350 has suggested for seismic loads.
Amer Gheitury, Arsalan Golfam,
Volume 15, Issue 1 (1-2008)
Abstract

The non-linear order of revelations is often considered by many scholars to signify lack of coherence, disunity, and fragmentariness. It seems that 'coherence' and the related terms have veiled a significant linguistic feature of the Qur’an, namely, the non-linear nature of revelations, which might be used to make a distinction between ordinary and Quranic discourse. We will argue that to unveil the non-linearity, we should consider revelations in relation to God who reveals Himself in language not as an ordinary speaker whose speech is limited to a certain context, with a beginning and an end. We should not expect God to speak like a man. The Qur’an, thus, is seen here as a non-temporal, non-linear text that reflects its divine origin, by systematically destructing the spacio-temporal context and the linear order of language.

Volume 16, Issue 4 (6-2016)
Abstract

Employing piezoelectric systems is one of the suitable methods for harvesting energy from mechanical vibrations available in the environment. In this work,single degree of freedom model for cantilever beam with piezoelectric layer is considered. Simulation contains nonlinear coefficients like: stiffness, damping and coupling coefficient. Governing system of equations is solved by multiple scales method. First with assuming one term in approximate response, the effects of all nonlinear parameters on frequency curve are investigated. Results show that assuming only one term in response evaluates the effect of nonlinear damping correctly. Increasing this coefficient leads to reduce the range of excitation frequency and maximum harvested power. But one term assumption couldn’t assess the effects of nonlinear stiffness and coupling coefficient logically. In this case, the peak of frequency response curve is independent of nonlinear coefficients. So for obtaining accurate results assuming at least two terms of response is necessary. Results show increasing nonlinear stiffness coefficient increase the maximum harvested power and the range of excitation frequency. The effect of nonlinear coupling coefficient is decreasing the maximum power because this coefficient increases the stiffness of the system.

Volume 16, Issue 11 (1-2017)
Abstract

In this paper the effect of artificial noise on the performance of nonlinear system identification method in reconstructing the response of a cantilever beam model having a local nonlinearity is investigated. For this purpose, the weak form equation governing the transverse vibration of a linear beam having a strongly nonlinear spring at the end is discretized by using Rayleigh-Ritz approach. Then, the derived equations are solved via Rung-Kutta method and the simulated response of the beam to impulse force is obtained. By contaminating the simulated response to artificial measurement noise, nonparametric nonlinear system identification is applied to reconstruct the response. Accordingly, intrinsic mode functions of the response are obtained by using advanced empirical mode decomposition, and nonlinear interaction model including intrinsic modal oscillators is constructed. Primary results show that the presence of noise in the response highly affects the sifting process which results in extraction of spurious intrinsic mode functions. In order to eradicate the effect of noise on this process, noise signals are used as masking signals in the advanced empirical mode decomposition method and intrinsic mode functions corresponding to the noise are extracted. Based on this approach, the dynamic of the noise in the response is identified and noise reduced signals are reconstructed by the intrinsic modal oscillators with appropriate accuracy.

Volume 17, Issue 10 (1-2018)
Abstract

With development of micro-electromechanical phase shifter, the study of deformation and instability of micro-switches is very important. The static behavior and pull-in instability of the clamped-clamped micro-beam subjected to local electrostatic loads which is used in DMTL phase shifter is investigated. Taking into account of nonlinear effects caused by radius of curvature for the first time, the nonlinear differential equation of the system is obtained using Euler-Bernoulli beam theory and effects of small sizes by employing the principle of virtual work. By considering the local electrostatic static voltage applied on the micro-beam, the governing partial differential equation is further discretized with the aid of Galerkin’s method, and the effect of system parameters on static deflection and pull-in voltage of the micro-switches are investigated. It is found that curvature nonlinearity has a great effect on the mechanical behavior of the micro-switches. Increasing this parameter leads to hardening behavior in the micro-switches, and also static deflection is decreased with respect to linear beam theory. The results also indicate that with an increase in the applied voltage, nonlinear strains increase and nonlinear effects caused by radius of curvature will be significant. For instance, when the stiffness parameter is increased from 0 to 10, maximum deflections of the micro-switches for applied voltages of 1V, 2V and 3V decreases about 7.7%, 35.8% and 48.6 %, respectively.

Volume 18, Issue 7 (12-2016)
Abstract

Relationship between grain yield and its component traits can improve the efficiency of breeding programs by determining appropriate selection criteria. An investigation was carried out on barnyard millet (Echinochloa spp.) global germplasm collection to investigate the association among yield components and their direct and indirect effects on the grain yield of barnyard millet. The experiment was conducted in 2011 and 2012 in augmented and alpha lattice design, respectively. The results of correlation coefficients indicated that grain yield had high significant and positive association with flag leaf width and culm thickness during both years, whereas negative association of grain yield was observed with basal tillers and peduncle length. Simple path analysis indicated high direct effects of panicle exertion, flag leaf sheath length, flag leaf width and days to maturity in 2011; and flag leaf width and raceme number in 2012. However, these high direct estimates were biased due to multicolinearity. Therefore, ontogeny based sequential path analysis was used to establish the causal relationships determining grain yield in barnyard millet. Based on the results over the years, culm thickness and raceme number were found to be important traits for indirect selection. The other important traits suggested for inclusion in selection index were inflorescence length, plant height, flag leaf length, inflorescence width and number of basal tillers per plant.

Volume 19, Issue 9 (9-2019)
Abstract

The equations of nonlinear motion of clamped-hinged beam with an open crack were extracted and through solving them, the internal resonance in the cracked beam was studied. To this end, the crack was modeled as a torsional spring and the cracked beam was considered as two beam segments connected by a torsional spring. The equations of motion of the cracked beam were extracted considering the geometrical nonlinearity. Then, using the Galerkin’s method, these equations were changed to a set of nonlinear differential equations for vibration modes which were solved by the perturbation method. Since the mechanical energy of the beam in each mode depends on the instantaneous amplitude of vibration of the beam at the corresponding mode, so to analyze the influence of the crack on the energy exchange between the modes, the instantaneous amplitudes of the vibration modes were obtained. The results show that in the cracked beam the magnitude of the energy exchanged between the modes is less and the frequency is more than that in the intact beam. Also, by increasing the crack depth the frequency of energy exchange between the modes increases. The Vibration response obtained for the cracked beam with various amounts of the damping ratios shows that the frequency and the amplitude of energy exchange between the modes are independent of the system damping. To validate the results by the perturbation method, the equations of motions are also solved by a numerical method and the obtained results are in agreement with the results of the analytical method.


Volume 20, Issue 7 (6-2020)
Abstract

Employing nonlinear dynamic signature of the host structure for early damage detection and remaining useful life estimation purposes, is an emerging idea in the area of piezoelectric patches based structural health monitoring. Clamped support loosening is one of the defects that not only may cause disorder in system’s functioning, but also obstruct damage identification process through distorting the signals. In this study, support loosening induced contact acoustic nonlinearity (CAN) behavior was monitored by vibro-acoustic modulation (VAM) technique. Using miniaturized PZT patches with the capability to be installed on the host structure permanently for both pump and probe actuation as well as sensing the modulated signal, enabled online monitoring via VAM technique. An appropriate filter was designed to eliminate the unintentionally excited natural frequencies and to reveal the sidebands. In this study, the sensitivity of modulation strength to the pump excitation frequency was also investigated. According to the results, appearance of sidebands around the central probe frequency is an appropriate indicator for CAN identification. In order to study the mechanism of modulation phenomenon, a coupled field electromechanical finite element (FE) model was developed. Proper matching of the numerical and experimental results indicates sufficient accuracy of the developed FE model and its potential to predict the modulation behavior.


Volume 21, Issue 6 (12-2021)
Abstract

Occurrence of the nonlinear behavior can be a sign of changes in structural parameters and the presence of damage in systems. This paper presents a method for detecting and quantifying of nonlinearity, as an indication of damage, using the indicators that are extracted from the frequency response functions (FRFs) and Hilbert transform of FRFs, for steel moment frame structural systems. Using time history analysis under selected harmonic ground motions, the results of FRFs for the studied 4-story system are illustrated and discussed.
Nonlinear behavior is a result of formation plastic hinges under earthquake loading. FRFs and Hilbert transform of FRFs are extracted from both the linear and nonlinear behavior of 4, 8, and 12-stories steel moment frames under fifteen different earthquake records with different characteristics in their time histories. Some near and far field well-known earthquakes records have been selected for the present study as the ground motions input in time history analysis. Different levels of nonlinearity are determined based on the maximum rotation of hinges in column members of structures equal to 2θy, 4θy and 6θy, in which θy is yield limit rotation. The indicators of the studied systems are calculated and evaluated for linear and different levels of nonlinearity based on the mathematical power of changes for FRFs and Hilbert transform of FRFs. The presented indicators are extracted based on the frequency response functions (FRFs) and Hilbert transform of FRFs for the responses of absolute acceleration and relative displacement of stories. The indicators are calculated at the location of acceleration sensors (accelerometer) in four levels of the structural systems, while the formation of plastic hinges in the columns of the structures will occur only at the level of the distance between the adjacent sensors.It is shown that the proposed method and calculated indicators have enough accuracy and sensitivity in detecting the “existence”, “location” and “extent” of damage.


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