Chaotic dynamic analysis of viscoelastic plates

The dynamic buckling of viscoelastic plates with large deflection is investigated in this paper by using chaotic and fractal theory. The material behavior is given in terms of the Boltzmann superposition principle. in order to obtain accurate computation results, the nonlinear integro-differential dynamic equation is changed into an autonomic four-dimensional dynamical system. The numerical time integrations of equations are performed by using the fourth-order Runge-Kutta method. And the Lyapunov exponent spectrum, the fractal dimension of strange attractors and the time evolution of deflection are obtained. The influence of geometry nonlinearity and viscoelastic parameter on the dynamic buckling of viscoelastic plates is discussed.

Application of response number for dynamic plastic response of plates subjected to impulsive loading

A dimensionless number, termed response number, is applied to the dynamic plastic response of plates subjected to dynamic loading. Many theoretical and experimental results presented by different researchers are reformulated into new concise forms with the response number. The advantage of the new forms is twofold: (1) they are more physically meaningful, and (2) they are independent of the choice of units, thus, they have wider range of applications.

Suggestion of a new dimensionless number for dynamic plastic response of beams and plates

A dimensionless number, termed response number in the present paper, is suggested for the dynamic plastic response of beams and plates made of rigid-perfectly plastic materials subjected to dynamic loading. It is obtained at dimensional reduction of the basic governing equations of beams and plates. The number is defined as the product of the Johnson's damage number and the square of the half of the slenderness ratio for a beam; the product of the damage number and the square of the half of the aspect ratio for a plate or membrane loaded dynamically. Response number can also be considered as the ratio of the inertia force at the impulsive loading to the plastic limit load of the structure. Three aspects are reflected in this dimensionless number: the inertia of the applied dynamic loading, the resistance ability of the material to the deformation caused by the loading and the geometrical influence of the structure on the dynamic response. For an impulsively loaded beam or plate, the final dimensionless deflection is solely dependent upon the response number. When the secondary effects of finite deflections, strain-rate sensitivity or transverse shear are taken into account, the response number is as useful as in the case of simple bending theory. Finally, the number is not only suitable to idealized dynamic loads but also applicable to dynamic loads of general shape.

Squeeze-film Effects in MEMS Devices with Perforated Plates for Small Amplitude Vibration

Squeeze-film effects of perforated plates for small amplitude vibration are analyzed through modified Reynolds equation (MRE). The analytical analysis reckons in most important influential factors: compressibility of the air, border effects, and the resistance caused by vertical air flow passing through perforated holes. It is found that consideration of air compressibility is necessary for high operating frequency and small ratio of the plate width to the attenuation length. The analytical results presented in this paper agree with ANSYS simulation results better than that under the air incompressibility assumption. The analytical analysis can be used to estimate the squeeze-film effects causing damping and stiffness added to the system. Since the value of Reynolds number involved in this paper is low (< 1), inertial effects are neglected.

Saturated duration of rectangular pressure pulse applied to rectangular plates with finite-deflections

The inequities in health care and housing access experienced by low-income women in the United States are a continuing concern. This article addresses the interrelationships between housing and health as experienced by low-income clients so that health care practitioners can begin to build active and effective health-promoting partnerships with clients, their families, and their communities. A case study is presented that describes the actual experience of a woman living in a low-income housing development and its effect on her health and access to health care. The importance of the role of midwives in addressing the health care and advocacy needs of women in substandard housing is highlighted.

Bending solution of high-order refined shear deformation-theory for rectangular composite plates

A new high-order refined shear deformation theory based on Reissner's mixed variational principle in conjunction with the state- space concept is used to determine the deflections and stresses for rectangular cross-ply composite plates. A zig-zag shaped function and Legendre polynomials are introduced to approximate the in-plane displacement distributions across the plate thickness. Numerical results are presented with different edge conditions, aspect ratios, lamination schemes and loadings. A comparison with the exact solutions obtained by Pagano and the results by Khdeir indicates that the present theory accurately estimates the in-plane responses.

Vibration analysis of laminated plates using a refined shear deformation-theory

A previously published discrete-layer shear deformation theory is used to analyze free vibration of laminated plates. The theory includes the assumption that the transverse shear strains across any two layers are linearly dependent on each other. The theory has the same dependent variables as first order shear deformation theory, but the set of governing differential equations is of twelfth order. No shear correction factors are required. Free vibration of simply supported symmetric and antisymmetric cross-ply plates is calculated. The numerical results are in good agreement with those from three-dimensional elasticity theory.

A finite-element analysis of viscoelastically damped sandwich plates

A finite element analysis associated with an asymptotic solution method for the harmonic flexural vibration of viscoelastically damped unsymmetrical sandwich plates is given. The element formulation is based on generalization of the discrete Kirchhoff theory (DKT) element formulation. The results obtained with the first order approximation of the asymptotic solution presented here are the same as those obtained by means of the modal strain energy (MSE) method. By taking more terms of the asymptotic solution, with successive calculations and use of the Padé approximants method, accuracy can be improved. The finite element computation has been verified by comparison with an analytical exact solution for rectangular plates with simply supported edges. Results for the same plates with clamped edges are also presented.

Analysis of flexural vibration of viscoelastically damped sandwich plates

The simplified governing equations and corresponding boundary conditions of flexural vibration of viscoelastically damped unsymmetrical sandwich plates are given. The asymptotic solution of the equations is then discussed. If only the first terms of the asymptotic solution of all variables are taken as an approximate solution, the result is identical with that obtained from the Modal Strain Energy (MSE) Method. As more terms of the asymptotic solution are taken, the successive calculations show improved accuracy. With the natural frequencies and the modal loss factors of a damped sandwich plate known, one can calculate the response of the plate to various loads providing a reliable basis for engineering design.

Study on cracked plates, shells and 3 dimensional bodies

This paper presents a summary of the authors' recent work in following areas: (1) The stress-strain fields at crack tip in Reissner's plate. (2) The calculations of the stress intensity factors in finite size plates. (3) The stress-strain fields at crack tip in Reissner's shell. (4) The calculations of the stress intensity factors and bulging coefficients in finite size spherical shells. (5) The stress-strain fields along crack tip in three dimensional body with surface crack. (6) The calculation of stress intensity factors in a plate with surface crack.

A unified law of motion of lithospheric plates and the driving mechanism

From observed data on lithospheric plates, a unified empirical law for plate motion,valid for continental as well as oceanic plates, is obtained in the following form: The speedof plate motion U depends linearly on a geometric parameter T_d, ratio of the sum of effectiveridge length and trench arc length to the sum of area of continental part of plate and total areaof cold sinking slab. Based on this unified law, a simple mechanical analysis shows that, themain driving forces for lithospheric plates come from push along the mid-ocean ridge andpull by the cold sinking slab, while the main drag forces consist of the viscous traction beneaththe continental part of plate and over both faces of the sinking slab. Moreover, the specific-push along ridge and pull by slab are found to be of equal magnitude.

Cone Effect in Astronomical Adaptive Optics System Investigated by a Pure Numerical Simulation

It is well-known that cone effect or focus anisoplanatism is produced by the limited distance of a laser guide star (LGS) which is created within the Earth atmosphere and consequently located at a finite distance from the observer. In this paper, the cone effect of the LGS for different vertical profiles of the refractive index structure constant Cn2 is numerically investigated by using a revised computer program of atmospheric propagation of optical wave and an adaptive optics (AO) system including dynamic control process. According to the practice, the overall tilt for the tilt-correction mirror is obtained from a natural star and the aberrated wavefront for phase correction of the deformable mirror is obtained from a LGS in our numerical simulation. It is surprisingly found that the effect of altitude of the LGS on the AO phase compensation effectiveness by using the commonly-available vertical profiles of Cn2 and the lateral wind speed in the atmosphere is relatively weak, and the cone effect for some Cn2 profiles is even negligible. It is found that the cone effect does not have obvious relationship with the turbulence strength, however, it depends on the vertical distribution profile of Cn 2 apparently. On the other hand, the cone effect depends on the vertical distribution of the lateral wind speed as well. In comparison to a longer wavelength, the cone effect becomes more obvious in the case of a shorter wavelength. In all cases concerned in this paper, an AO system by using a sodium guide star has almost same phase compensation effectiveness as that by using the astronomical target itself as a beacon. Effect of dynamic control process in an AO system on the cone effect is studied in this paper for the first time within our knowledge.

Self-instability and bending behaviors of nano plates

This paper aims at investigating the size-dependent self-buckling and bending behaviors of nano plates through incorporating surface elasticity into the elasticity with residual stress fields. In the absence of external loading, positive surface tension induces a compressive residual stress field in the bulk of the nano plate and there may be self-equilibrium states corresponding to the plate self-buckling. The self-instability of nano plates is investigated and the critical self-instability size of simply supported rectangular nano plates is determined. In addition, the residual stress field in the bulk of the nano plate is usually neglected in the existing literatures, where the elastic response of the bulk is often described by the classical Hooke’s law. The present paper considered the effect of the residual stress in the bulk induced by surface tension and adopted the elasticity with residual stress fields to study the bending behaviors of nano plates without buckling. The present results show that the surface effects only modify the coefficients in corresponding equations of the classical Kirchhoff plate theory.

Pure-phase plates for super-Gaussian focal-plane irradiance profile generations of extremely high order

A set of recursive formulas for diffractive optical plates design is described. The pure-phase plates simulated by this method homogeneously concentrate more than 96% of the incident laser energy in the desired focal-plane region. The intensity focal-plane profile fits a lath-order super-Gaussian function and has a nearly perfect flat top. Its fit to the required profile measured in the mean square error is 3.576 x 10(-3). (C) 1996 Optical Society of America