Rayleigh-Ritz vibration analysis of Mindlin plates

The Rayleigh-Ritz method is applied to the prediction of the natural frequencies of flexural vibration of square plates having general boundary conditions. The analysis is based on the use of Mindlin plate theory so that the effects of shear deformation and rotary inertia are included. The spatial variations of the plate deflection and the two rotations over the plate middle surface are assumed to be series of products of appropriate Timoshenko beam functions. Results are presented for a number of types of plate and these demonstrate the manner of convergence of the method as the number of terms in the assumed series increases.     

Impedance of infinite Kirchhoff and Mindlin plates with a rigid circular massless plug

Point force impedance expressions have been previously developed for infinite Kirchhoff and Mindlin plates. The present work develops impedance expressions for the more general case of an infinite plate with a circular, massless, rigid plug using both Kirchhoff and Mindlin plate theories. The models have been developed to analyze vibration propagation in buildings. The plate with the rigid plug provides a more reasonable model of the kinematic constraint at the column/floor interface. The models are used to investigate the potential benefits of using thick floors to block the transmission of structure-borne vibration in buildings.     

Relationship of a gauge model of an elasto-plastic medium to the Mindlin theory

We examine the relationship between the simplest gauge model of a material with the Mindlin theory that takes into account microstructure in linear elasticity. We establish a connection between the dynamical equations for the two models. The connection allows us to relate an unknown material constant in the gauge Lagrangian to the inertial properties of the structural elements. We obtain an estimate of the unknown constant and the corresponding characteristic frequency for the dimensions of elements with different structural levels of deformation.Institute of Strength Physics and Materials Research, Russian Academy of Sciences, Siberian Branch. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 44–48, April, 1994.     

Rayleigh-Ritz vibration analysis of rectangular Mindlin plates subjected to membrane stresses

A previously developed analysis of the flexural vibration of isotropic rectangular plates is extended to include the presence of a membrane stress system. The method of analysis is the Rayleigh-Ritz method and Mindlin plate theory is used which takes into account effects which are disregarded in the classical plate theory. As in the aforementioned earlier analysis the spatial variations of the deflection and two rotations over the plate middle surface are based on the use of Timoshenko beam functions. The membrane stress system comprises biaxial direct stress plus in-plane shearing stress and is uniform throughout the plate. Numerical results are presented for a number of types of plate and of applied stress which show the manner of variation of the frequencies of vibration as the intensity of stress changes. This manner of variation is similar in form to that demonstrated elsewhere by analyses based on the use of the classical plate theory but the magnitudes of the present calculated frequencies are considerably reduced for moderately thick plates.     

Axisymmetric vibrations of a circular plate of linearly varying thickness on an elastic foundation according to Mindlin theory

Free axisymmetric vibrations of an elastic circular plate of linearly varying thickness on an elastic foundation have been studied on the basis of shear theory [1,2]. The transverse displacement and local rotation are expressed as an infinite series. The frequencies corresponding to the first two modes of vibrations are obtained for a circular plate with clamped and simply supported edge conditions for various values of the taper constant and the foundation modulus. The results have been compared with those of reference [3].     

Vibration of tapered Mindlin plates in terms of static Timoshenko beam functions

In this paper, the free vibrations of rectangular Mindlin plates with variable thickness in one or two directions are investigated. The thickness variation of the plate is continuous and can be represented by a power function of the rectangular co-ordinates. A wide range of tapered rectangular plates can be described by giving various index values to the power function. Two sets of new admissible functions are developed, respectively, to approximate the flexural displacement and the angle of rotation due to bending of the plate. The eigenfrequency equation is obtained by using the Rayleigh-Ritz method. The complete solutions of displacement and angle of rotation due to bending for a tapered Timoshenko beam (a strip taken from the tapered Mindlin plate in some direction) under a Taylor series of static load have been derived, which are used as the admissible functions of the rectangular Mindlin plates with taper thickness in one or two directions. Unlike conventional admissible functions which are independent of the thickness variation of the plate, the static Timoshenko beam functions presented in this paper are closely connected with the thickness variation of the plate so that higher accuracy and more rapid convergence can be expected. Some numerical results are furnished for both truncated Mindlin plates and sharp-ended Mindlin plates. On the basis of convergence study and comparison with available results in literature, it is shown that the first few eigenfrequencies can be obtained with quite satisfactory accuracy by using only a small number of terms of the static Timoshenko beam functions.     

Jumping Platonic Solids on a Vibrating Plate

The mechanical excitation of solid bodies by a vibrating plate is not only an interesting fundamental problem, but also has relevance in many mechanical systems, for example, in the preparation of granular gases in microgravity. Herein, the energy input by an oscillating plate is numerically investigated as a function of the excitation parameters for selected Platonic solids and their behavior compared to that of a jumping sphere. The most important additional features, not relevant for spheres, are the excitation of body rotations and a permanent energy exchange between the rotational and translational degrees of freedom during the collisions with the plate. The distribution of kinetic energies is analyzed by a numerical simulation of the dynamics, using structures which emulate the mechanical behavior of regular polyhedra.     

水中薄片激光打孔反常现象的分析

 在其它条件相同的情况下，水中激光在金属薄片上的打孔效率远高于空气中的打孔效率。采用自行研制的基于光偏转原理的力学传感器，分别测量了激光在空气和水中烧蚀薄片时薄片表面所受的力。实验结果表明，激光在空气中烧蚀薄片时，靶材仅受到烧蚀力的作用，而在水中打靶时，靶受到烧蚀力和两次射流冲力等综合作用，且水中的三次冲力在幅值和持续时间均远大于空气中靶材所受的冲力，并用扫描电子显微镜观察了孔的形貌，进而分析了水下激光打孔效率远高于空气中打孔效率的机制。     

Free vibration of size-dependent Mindlin microplates based on the modified couple stress theory

This paper develops a Mindlin microplate model based on the modified couple stress theory for the free vibration analysis of microplates. This non-classical plate model contains an internal material length scale parameter related to the material microstructures and is capable of interpreting the size effect that the classical Mindlin plate model is unable to describe. The higher-order governing equations of motion and boundary conditions are derived using the Hamilton principle. The p-version Ritz method is employed to determine the natural frequencies of the microplate with different boundary conditions. A detailed parametric study is conducted to study the influences of the length scale parameter, side-to-thickness ratio and aspect ratio on the free vibration characteristics of the microplate. It is found that the size effect is significant when the thickness of microplate is close to the material length scale parameter.     

Stress-Strain State of Elastic Plate with a Crack

Russian Physics Journal - The paper considers an infinite plate with a crack in the form of a narrow hole with a certain curvature at the tip of the crack. The stress-strain state parameters of...     

A Zone Plate as a Tunable Terahertz Filter

A broadband tunable terahertz filter based on a zone plate is demonstrated in our terahertz time domain spec- trometer. The central bandpass frequency covers the whole spectral range of the terahertz wave emitted from a ZnTe emitter, from 0.5 THz to 2.5 THz, and can be tuned continuously by simply moving the zone plate along the terahertz beam path. The peak transmission is about 40% and the bandwidth varies from 0.16 THz to 0.25 THz at different bandpass frequencies when the aperture size is kept constant.     

Features of Hypersonic Flow Past a Yawed Plate

Doklady Physics - Flow past a yawed plate in the strong interaction mode is considered in the case when the pressure at its trailing edge varies along the transverse coordinate instead of being...     

Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method

A study of the free vibration of Timoshenko beams and axisymmetric Mindlin plates is presented. The analysis is based on the Chebyshev pseudospectral method, which has been widely used in the solution of fluid mechanics problems. Clamped, simply supported, free and sliding boundary conditions of Timoshenko beams are treated, and numerical results are presented for different thickness-to-length ratios. Eigenvalues of the axisymmetric vibration of Mindlin plates with clamped, simply supported and free boundary conditions are presented for various thickness-to-radius ratios.     

Switching between the Functions of Half-Wave Plate and Quarter-Wave Plate Simply by Using a Vanadium Dioxide Film in a Terahertz Metamaterial

We propose a switchable THz metamaterial that can be switched between two functions of half-wave plate and quarter-wave plate.The two switchable functions can be simply achieved by inserting a VO_2 film in the metamaterial design.Finite-difference time-domain(FDTD) simulation results show that the proposed metamaterial can convert x-polarized incident wave to y-polarized reflected wave when VO_2 is at metal phase,and convert x-polarized wave to circularly polarized wave when VO_2 is at insulator phase.The metamaterial performs well in the two functions,i.e.,the same broad working frequency band and near perfect polarization conversion.The switching effect originates from the switchable Fabry-Perot cavity length induced by the phase change of VO_2.We believe that our findings provide a reference in designing switchable metamaterials.     

Radius Measurement of a Concave Mirror by a Zone Plate Interferometer

A new technique to measure the radius of a concave mirror is proposed, in which the radius is calculated from the difference of the two interferograms obtained before and after shifting the sample perpendicular to or along the optical axis. By comparison of these two shifting directions, it is shown that since the amount of shift can be measured accurately and the result is insensitive to the tilt during the shifting, better accuracy can be obtained by shifting the sample along the optical axis.Presented at the International Commission of Optics Topical Meeting, Kyoto, 1994.     

波带片用作电视系统测试卡

波带片具有二元线性变化的空间频率,所以它可以用于快速评价电视系统的频率特性。