Natural frequencies and modes of tapered skew plates

The vibration of simply supported skew plates having a linear variation in thickness in one direction is considered. Approximate analysis is made by using Lagrange's equations employing the double Fourier sine series in oblique co-ordinates to represent the deflected surface. Natural frequencies are obtained for rhombic plates for several ranges of thickness variation and skew angle. The nodal patterns plotted for a few typical configurations show interesting metamorphoses with variation in thickness and skew angle.

A three-dimensional solution for plates and laminates

A general three-dimensional solution is presented for statics and dynamics of plates, homogeneous or laminated, of orthotropic materials. The solution is in series form. Using parts of the general solution a variety of problems, especially of rectangular configurations, can be solved. As Mindlin's approximate analysis for vibration of thick plates is often adequate for specific practical purposes, a general solution for Mindlin's analysis is also given.

Effect of matrix cracking and material uncertainty on composite plates

A laminated composite plate model based on first order shear deformation theory is implemented using the finite element method.Matrix cracks are introduced into the finite element model by considering changes in the A, B and D matrices of composites. The effects of different boundary conditions, laminate types and ply angles on the behavior of composite plates with matrix cracks are studied.Finally, the effect of material property uncertainty, which is important for composite material on the composite plate, is investigated using Monte Carlo simulations. Probabilistic estimates of damage detection reliability in composite plates are made for static and dynamic measurements. It is found that the effect of uncertainty must be considered for accurate damage detection in composite structures. The estimates of variance obtained for observable system properties due to uncertainty can be used for developing more robust damage detection algorithms. (C) 2010 Elsevier Ltd. All rights reserved.

Vibration of simply-supported trapezoidal plates II. Unsymmetric trapezoids

This paper deals with the investigation of the vibration characteristics of simply-supported unsymmetric trapezoidal plates. For numerical calculations, the relationship between the eigenvalue problems of a polygonal simply-supported plate and polygonal membrane is again effectively utilized. The Galerkin method is applied, with the deflection surface expressed in terms of a Fourier sine series in transformed coordinates. Numerical values for the first seven to eight frequencies for different geometries of the unsymmetric trapezoid are presented in the form of tables. Also the nodal patterns for a few representative configurations are presented.

Nonlinear vibration analysis of composite laminated and sandwich plates with random material properties

Nonlinear vibration analysis is performed using a C-0 assumed strain interpolated finite element plate model based on Reddy's third order theory. An earlier model is modified to include the effect of transverse shear variation along the plate thickness and Von-Karman nonlinear strain terms. Monte Carlo Simulation with Latin Hypercube Sampling technique is used to obtain the variance of linear and nonlinear natural frequencies of the plate due to randomness in its material properties. Numerical results are obtained for composite plates with different aspect ratio, stacking sequence and oscillation amplitude ratio. The numerical results are validated with the available literature. It is found that the nonlinear frequencies show increasing non-Gaussian probability density function with increasing amplitude of vibration and show dual peaks at high amplitude ratios. This chaotic nature of the dispersion of nonlinear eigenvalues is also r

On the use of a coordinate transformation for analysis of axisymmetric vibration of polar orthotropic annular plates

Estimates of natural frequencies corresponding to axisymmetric modes of flexural vibration of polar orthotropic annular plates have been obtained for various combinations of clamped, simply supported and free edge conditions. A coordinate transformation in the radial direction has been used to obtain effective solutions by the classical Rayleigh-Ritz method. The analysis with this transformation has been found to be advantageous in computations, particularly for large hole sizes, over direct analysis. Numerical results have been obtained for various values of hole sizes and rigidity ratio. The eigenvalue parameter has been found to vary more or less linearly with the rigidity ratio. A comparison with the results for isotropic plates has brought out some interesting features.

Robust prediction of residual velocities and ballistic limits of projectiles for impact on thin aluminium plates

This paper deals with the simulation-driven study of the impact of hardened steel projectiles on thin aluminium target plates using explicit finite element analysis as implemented in LS-DYNA. The evaluation of finite element modelling includes a comprehensive mesh convergence study using shell elements for representing target plates and the solid element-based representation of ogivalnosed projectiles. A user-friendly automatic contact detection algorithm is used for capturing interaction between the projectile and the target plate. It is shown that the proper choice of mesh density and strain rate-dependent material properties is crucial as these parameters significantly affect the computed residual velocity. The efficacy of correlation with experimental data is adjudged in terms of a 'correlation index' defined in the present study for which values close to unity are desirable.By simulating laboratory impact tests on thin aluminium plates carried out by earlier investigators, extremely good prediction of experimental ballistic limits has been observed with correlation indices approaching unity. Additional simulation-based parametric studies have been carried out and results consistent with test data have been obtained. The simulation procedures followed in the present study can be applied with confidence in designing thin aluminium armour plates for protection against low calibre projectiles.

Analysis of effects of ambients (temperature and light intensity) on the electrical breakdown in bipolar transistors

This paper presents an analysis of the effects of ambients-temperature and light intensity on the V-l characteristics of bipolar transistors under electrical breakdown. The analysis is based on the transportation and storage of majority carriers in the base region. It is shown that this analysis can explain the observed shift in the V-l characteristics to lower voltages with increase in either temperature or light intensity.

A two-dimensional model for crack closure effect in plates under bending

A two-dimensional model is proposed for taking into account the establishment of contact on the compression side of crack faces in plates under bending. An approximate but simple method is developed for evaluating reduction of stress intensity factor due to such ‘crack closure’. Analysis is first carried out permitting interference of the crack faces. Contact forces are then introduced on the crack faces and their magnitudes determined from the consideration that the interference is just eliminated. The method is based partly on finite element analysis and partly on a continuum analysis using Irwin's solution for point loads on the crack line.

Cognitive functioning and its heritability in bipolar I disorder

Bipolar I disorder is a severe psychiatric disorder characterized by episodic mood alterations that can be manic, depressive or mixed. Bipolar disorder seems to be highly genetic, but the etiology of this complex disorder has remained elusive. In recent years, studies have found that euthymic patients with bipolar disorder may have impairments particularly in executive functioning, verbal learning and memory. These impairments may be present also among some of the relatives of these patients, who may be vulnerable to the disorder. Using neuropsychological variables as endophenotypes, i.e. intermediate phenotypes between genes and the phenotypes, has been suggested to aid search for the etiological background of the disorder, but evidence is sparse on whether these variables fulfill the criteria for endophenotypes. The present thesis is part of the Genetic Epidemiology and Molecular Genetics of Severe Mental Disorders in Finland project. The specific aim was to investigate whether neuropsychological test variables would indicate genetic liability to the disorder and could therefore be regarded as endophenotypes. Thus, cognitive functions and their heritability were studied in bipolar I disorder patients and in their unaffected first-degree relatives from a population-based sample of families, comparing them to a population-based control group. In order to add homogeneity to the subgroups of bipolar disorder patients and their relatives, cognitive functions and their heritability were further studied in a group of families affected by bipolar I disorder only (bipolar families) and another group of families affected by both bipolar I disorder and schizophrenia or schizoaffective disorders (mixed families). Finally, the effect of processing speed on other cognitive functions was investigated. The study showed that especially executive functioning and processing speed fulfilled the endophenotype criteria. Impairments in these functions were found in bipolar patients and in their relatives irrespective of other severe psychopathology in the family. These functions were highly heritable in these families. Study also showed that generalized impairment in verbal memory may associate more with bipolar disorder than to vulnerability to other psychotic disorders, and be more related to fully developed disease; impairments in verbal learning and memory were found only in patients, and they were not found to be highly heritable. Finally, the most potential endophenotype, i.e. processing speed, seemed to contribute to a range of other cognitive dysfunctions seen in bipolar disorder patients. Processing speed, in particular, has also been shown to be a valid endophenotype in subsequent association analyses in psychiatric genetics in Finland and internationally. Information concerning cognitive impairments and their association with the psychosocial consequences of bipolar disorder is important in planning treatment. It is also important to understand and acknowledge that patients may have cognitive impairments that affect their everyday life. Psychosocial interventions and neuropsychological rehabilitation may supplement other conventional treatments for bipolar patients.

Non-darcy double-diffusive mixed convection from heated vertical and horizontal plates in saturated porous media

The non-darcy mixed convection flows from heated vertical and horizontal plates in saturated porous media have been considered using boundary layer approximations. The flows are considered to be driven by multiple buoyancy forces. The similarity solutions for both vertical and horizontal plates have been obtained. The governing equations have been solved numerically using a shooting method. The heat transfer, mass transfer and skin friction are reduced due to inertial forces. Also, they increase with the buoyancy parameter for aiding flow and decrease for the opposing flow. For aiding flow, the heat and mass transfer coefficients are found to approach asymptotically the forced or free convection values as the buoyancy parameter approaches zero or infinity.