• Structural Engineering and Mechanics
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• v.21 no.5
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• pp.539-551
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• 2005

Finite elements based on isoparametric formulation are known to suffer spurious stiffness properties and corresponding stress oscillations, even when care is taken to ensure that completeness and continuity requirements are enforced. This occurs frequently when the physics of the problem requires multiple strain components to be defined. This kind of error, commonly known as locking, can be circumvented by using reduced integration techniques to evaluate the element stiffness matrices instead of the full integration that is mathematically prescribed. However, the reduced integration technique itself can have a further drawback - rank deficiency, which physically implies that spurious energy modes (e.g., hourglass modes) are introduced because of reduced integration. Such instability in an existing stiffness matrix is generally detected by means of an eigenvalue test. In this paper we show that a knowledge of the dimension of the solution space spanned by the column vectors of the strain-displacement matrix can be used to identify the instabilities arising in an element due to reduced/selective integration techniques a priori, without having to complete the element stiffness matrix formulation and then test for zero eigenvalues.

• Smart Structures and Systems
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• v.17 no.5
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• pp.753-771
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• 2016

This paper addresses the free and transient responses of a SDOF linear complex stiffness system by making use of the Hilbert transform and the convolution integral. Because the second-order differential equation of motion having the complex stiffness give rise to the conjugate complex eigen values, its time-domain analysis using the standard time integration scheme suffers from the numerical instability and divergence. In order to overcome this problem, the transient response of the linear complex stiffness system is obtained by the convolution integral of a green function which corresponds to the unit-impulse free vibration response of the complex system. The damped free vibration of the complex system is theoretically derived by making use of the state-space formulation and the Hilbert transform. The convolution integral is implemented by piecewise-linearly interpolating the external force and by superimposing the transient responses of discretized piecewise impulse forces. The numerical experiments are carried out to verify the proposed time-domain analysis method, and the correlation between the real and imaginary parts in the free and transient responses is also investigated.

• Geomechanics and Engineering
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• v.1 no.2
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• pp.121-142
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• 2009

The paper deals with the applications of spectral finite element method to the dynamic analysis of framed foundations supporting high speed machines. Comparative performance of approximate dynamic stiffness methods formulated using static stiffness and lumped or consistent or average mass matrices with the exact spectral finite element for a three dimensional Euler-Bernoulli beam element is presented. The convergence of response computed using mode superposition method with the appropriate dynamic stiffness method as the number of modes increase is illustrated. Frequency proportional discretisation level required for mode superposition and approximate dynamic stiffness methods is outlined. It is reiterated that the results of exact dynamic stiffness method are invariant with reference to the discretisation level. The Eigen-frequencies of the system are evaluated using William-Wittrick algorithm and Sturm number generation in the $LDL^T$ decomposition of the real part of the dynamic stiffness matrix, as they cannot be explicitly evaluated. Major's method for dynamic analysis of machine supporting structures is modified and the plane frames are replaced with springs of exact dynamic stiffness and dynamically flexible longitudinal frames. Results of the analysis are compared with exact values. The possible simplifications that could be introduced for a typical machine induced excitation on a framed structure are illustrated and the developed program is modified to account for dynamic constraint equations with a master slave degree of freedom (DOF) option.

• Journal of the Korea Institute of Military Science and Technology
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• v.12 no.1
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• pp.97-105
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• 2009

In this paper, the performance of AP(Alternating Projection) and EM(Expectation Maximization) algorithms is investigated in terms of detection of multiple signals, resolvability of coherent signals and the efficiency of sensor array processing. The basic idea of these algorithms is utilization of relaxation technique of successive 1D maximization to solve a direction finding problem by maximizing the multidimensional likelihood function. It means that the function is maximized over only for a single parameter while the other parameters are fixed at each step of the iteration. According to simulation results, the algorithms showed good performance for both incoherent and coherent multiple signals. Moreover, some advantages are identified for direction finding with very small samples and fast convergence. The performance of AP algorithm is compared with that of EM using multiple criteria such as the number of sensor, SNR, the number of samples, and convergence speed over uniform circular array. It is resulted AP algorithm is superior to EM overally except for one criterion, convergence speed. Especially, for EM algorithm there is no performance difference between incoherent and coherent case. In conclusion, AP and EM are viable and practical alternatives, which can be applied to a direction under due to the resolvability of multi-path signals, reliable performance and no troublesome eigen-decomposition of the sample-covariance matrix.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2010.05a
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• pp.469-471
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• 2010

Supercavitating vehicles which cruise under water undergo high longitudinal force caused by thrust and drag. These combination may cause structural buckling. Static and dynamic buckling analysis method by using FEM can be used to predict this structural failure behavior. In this paper, some principles which include method for solution eigenvalue problem for buckling analysis are introduced. And before buckling analysis, we predicted some mode shape and natural frequency of cylindrical shell by using DIAMOND/IPSAP eigen-solver.

• Structural Engineering and Mechanics
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• v.27 no.2
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• pp.199-222
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• 2007

Composite laminated structures supported on elastic foundations are being increasingly used in a great variety of engineering applications. Composites exhibit larger dispersion in their material properties compared to the conventional materials due to large number of parameters associated with their manufacturing and fabrication processes. And also the dispersion in elastic foundation stiffness parameter is inherent due to inaccurate modeling and determination of elastic foundation properties in practice. For a better modeling of the material properties and foundation, these are treated as random variables. This paper deals with effects of randomness in material properties and foundation stiffness parameters on the free vibration response of laminated composite plate resting on an elastic foundation. A $C^0$ finite element method has been used for arriving at an eigen value problem. Higher order shear deformation theory has been used to model the displacement field. A mean centered first order perturbation technique has been employed to handle randomness in system properties for obtaining the stochastic characteristic of frequency response. It is observed that small amount of variations in random material properties and foundation stiffness parameters significantly affect the free vibration response of the laminated composite plate. The results have been compared with those available in the literature and an independent Monte Carlo simulation.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.3
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• pp.250-255
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• 2012

Face recognition has wide applications in security and surveillance systems as well as in robot vision and machine interfaces. Conventional challenges in face recognition include pose, illumination, and expression, and face recognition at a distance involves additional challenges because long-distance images are often degraded due to poor focusing and motion blurring. This study investigates the effectiveness of applying photon-counting linear discriminant analysis (Pc-LDA) to face recognition in harsh environments. A related technique, Fisher linear discriminant analysis, has been found to be optimal, but it often suffers from the singularity problem because the number of available training images is generally much smaller than the number of pixels. Pc-LDA, on the other hand, realizes the Fisher criterion in high-dimensional space without any dimensionality reduction. Therefore, it provides more invariant solutions to image recognition under distortion and degradation. Two decision rules are employed: one is based on Euclidean distance; the other, on normalized correlation. In the experiments, the asymptotic equivalence of the photon-counting method to the Fisher method is verified with simulated data. Degraded facial images are employed to demonstrate the robustness of the photon-counting classifier in harsh environments. Four types of blurring point spread functions are applied to the test images in order to simulate long-distance acquisition. The results are compared with those of conventional Eigen face and Fisher face methods. The results indicate that Pc-LDA is better than conventional facial recognition techniques.

• Steel and Composite Structures
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• v.51 no.4
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• pp.457-471
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• 2024

In this research, for the first time the instability boundaries for a spinning shaft reinforced with graphene nanoplatelets undergone the principle parametric resonance are determined and examined taking into account the gyroscopic effect. In this respect, the extracted equations of motion in our previous research (Ref. Asadi et al. (2023)) are implemented and efficiently upgraded. In the upgraded discretized equations the effect of the Rayleigh's damping and the varying spinning speed is included that leads to a different dynamical discretized governing equations. The previous research was about the free vibration analysis of spinning graphene-based shafts examined by an eigen-value problem analysis; while, in the current research an advanced mechanical analysis is addressed in details for the first time that is the dynamics instability of the aforementioned shaft subjected to the principal parametric resonance. The spinning speed of the shaft is considered to be varied harmonically as a function of time. Rayleigh's damping effect is applied to the governing equations in order to regard the energy loss of the system. Resorting to Bolotin's route, Floquet theory and β-Newmark method, the instability region and its accompanied boundaries are defined. Accordingly, the effects of the graphene nanoplatelet on the instability region are elucidated.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.1
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• pp.59-64
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• 2005

To achieve a goal of minimum output power, the beamformer tends to cancel the desired signal if there exists correlated interference sources such as multipaths of the desired signal. In this paper, we propose a new method which overcomes the signal cancellation problem for correlated interferences. Instead of decorrelating the correlated interferences, the proposed bramformer regards them as replicas of the desired signal and coherently combines them with desired signal. This method uses an eigenvector constraint that suppresses a noise and uncorrelated interferences but keeps the desired signal and correlated interferences. Indisputably, the beamformer does not require any preliminary information on correlated interferences. Simulation results show that the proposed beamformer overcomes the signal cancellation problem and improves signal-to-noise ratio (SNR) of the array output when the correlated interferences exist.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.4 no.1
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• pp.93-101
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• 1984

New formulas to determine the critical elastic buckling load of long tapered columns are given. This study is restricted to solid round or rectangular columns with fixed-free ends as often used in highway design. The exact solution of the differential equation of the deflection curve is expressed in terms of Bessel Function and the solution is numerically evaluated using Bisection method by computer. In the F.E.M analysis of columns under their own weight, the stability problem can be resulted in a eigen value problem of conservative system. Approximate solution by the F.E.M is evaluted numerically using Jacobi method and compared with exact solution of the prismatic column to increase the precision. In addition, critical buckling load of the tapered column for every shape factor and ratio of cross-sectional change (Diameter of bottom end/Diameter of upper end) was converted into a comparable expression to critical buckling load of the prismatic column.