Deformation and Moments in Elastically Restrained Circular Plates Under Arbitrary Load or Linear Thermal Gradient

Effect of transverse velocity and temperature gradients on sound attenuation in two-dimensional ducts

In general, internal cells are required to solve deformation of thin plate with arbitrary distributed load using conventional boundary element methods (BEM). However, in this case, the merit of BEM, which is the easy preparation of data, is lost. In this paper, it is shown that deformation analysis of thin plate with arbitrary distributed load can be solved without the use of internal cells by using the triple-reciprocity boundary element method. Distribution of arbitrary load is interpolated using boundary integral equations. The problem of thin plate according to Kirchhoff's theory is formulated by means of two coupled Poisson equations to be expressed in integral form using the second theorem of Green in the classical way. A new computer program was developed and applied to several example problems.

Discontinuity solutions to plate and beam problems

As a result of the nonlinear effect, acoustic streaming has been widely used for increasing the transport coefficient or driving a rotor, for example, in resonant cavities and non-contact ultrasonic motors. It has been demonstrated by experiments that a temperature gradient transverse to the wave propagating direction can significantly increase the velocity of the streaming flows in resonant cavities. To check whether the transverse temperature gradient can also increase the working velocity of acoustic streaming-driven motors, we investigate this issue by numerically solving the hydrodynamic equations. It is found that the velocity of the rotor only weakly depends on the transverse temperature gradient, e.g., even with a temperature difference of 40°C between the rotor and the stator, the velocity increases only ∼8.8%.

Purpose. This study aims to improve the accuracy of methods for determining fin efficiency. Its goal is to derive calculation relationships for finning coefficients that account for transverse temperature non-uniformity within the fin cross-section. Design / Method / Approach. The article presents the reduction of the heat conduction equation for a fin to a dimensionless form, based on dimensional analysis of the variables involved. Further development relies on analyzing the results of numerical simulations and their subsequent generalization. To this end, the gradient descent method is applied, minimizing the quadratic error function. Findings. A criterial dependence has been formulated to complement the derived heat conduction equation. Test calculations and comparisons with numerical simulations in Ansys Fluent confirm an improvement in calculation accuracy when using the proposed equation. Theoretical Implications. This paper addresses factors previously neglected in the analysis of heat transfer in fins. The results of the study thus complement existing approaches to determining finning coefficients. Practical Implications. The derived criterial relationship will enhance the accuracy of heat transfer calculations in the chambers and gas generators of liquid rocket engines. Originality / Value. The paper introduces an original criterial relationship that accounts for temperature non-uniformity across the fin cross-section. Incorporating this factor improves calculation accuracy, highlighting the practical value of the developed equation. Research Limitations / Future Research. This study focuses on rectangular fins; therefore, the proposed model is not applicable to fins with variable thickness in the ducts of liquid propellant rocket engines (LPREs). Developing a fin model without these limitations will be the objective of future research on this topic. Article Type. Applied Research. PURL: https://purl.org/cims/4.299

The linear stability of combined evaporating liquid—vapor-gas mixture flow is investigated under conditions of inhomogeneous heating within the framework of the conjugate problem. The exact solution of the Navier-Stokes equations in the Boussinesq approximation is used to describe the two-layer flow. The solution takes into account the influence of both nonzero streamwise and transverse temperature gradients and the direct and inverse thermal diffusion effects in the vapor-gas layer and on the phase interface. The influence of the applied external thermal load on the main flow parameters, their structure, the volume vapor content, the mass evaporation rate, and the stability is studied for systems with various liquid-layer thicknesses. The typical forms of characteristic perturbations are distinguished and the critical loads that lead to loss of stability at small transverse temperature drops are determined.

Detail dynamic characteristics analysis of buck-type PET under general load condition was accomplished and the study showed that: under general inductive load condition, the open-loop system is marginally stable and serious output voltage oscillation can be provoked by any random disturbance upon input voltage, control signal or output current. Therefore, in order to ensure the out power quality, we must find out a suitable close-loop regulator. In this paper, we employed the classical PID control algorithm to instantaneously control output voltage following the pre-setting signal. The close-loop system was stable and had good dynamic response characteristic. In addition, during one switching period, the line-frequency input/output voltage and output impedance were treated as constants, and a parameter-/spl gamma/, which is related to load feature, was introduced to simplify the modeling and analyzing process, it is a valid method for small-signal modeling and system dynamic analysis of the PET.

The effects of a transverse temperature gradient in reversively switched-on dynistors have been studied. Taking into account these effects is important for high-voltage frequency dynistor assemblies because of the problems of a distributed cooling of the devices. A simulation description is given for the spatial dynamics of charges and heat in dynistor chips in switching of repeated current pulses. An estimation method is suggested for calculating the maximum repetition frequency coordinated with the heatsink heatsink cooling power.

The article discusses a calculation procedure for determining deformations and load distribution in round-profiled threads under general load conditions. It is shown that on manufacturing of threaded parts with different classes of accuracy owing to a small theoretical linear contact between screw and nut threads the real contact can be moved up to rounded portions of the thread crests. In this case the contact and bending deformations of the threads will have a great influence on the screw durability. The equations for calculation both these deformations and the deformations from thread shearing are given. The load distribution in screw drive with the round-profiled thread is shown in comparison with the load distribution in the widely used screw-drive with the trapezoidal thread. The law of change of the load value on the most loaded thread depending on a screw diameter and a number of the working threads are given as well. A comparative analysis for guarantee the equal durability of the thread and the screw shank is carried out

A numerical method for the topological design of periodic continuous domains under general loading is presented. Both the analysis and the design are defined over a single cell. Confining the analysis to the repetitive unit is obtained by the representative cell method which by means of the discrete Fourier transform reduces the original problem to a boundary value problem defined over one module, the representative cell. The repeating module is then meshed into a dense grid of finite elements and solved by finite element analysis. The technique is combined with topology optimization of infinite spatially periodic structures under arbitrary static loading. Minimum compliance structures under a constant volume of material are obtained by using the densities of material as design variables and by satisfying a classical optimality criterion which is generalized to encompass periodic structures. The method is illustrated with the design of an infinite strip possessing 1D translational symmetry and a cyclic structure under a tangential point force. A parametric study presents the evolution of the solution as a function of the aspect ratio of the representative cell.

Circular plates are important structural elements in modern engineering structures. In this paper a computationally efficient and accurate numerical model is presented for the study of free vibration and bending behavior of thick circular plates based on Mindlin plate theory. The approach developed is based on the discrete singular convolution method and the use of regularized Shannon's delta kernel. Frequency parameters, deflections and bending moments are obtained for different geometric parameters of the circular plate. Comparisons are made with existing numerical and analytical solutions in the literature. It is found that the DSC method yields accurate results for the free vibration and bending problems of thick circular plates. Copyright © 2008 John Wiley & Sons, Ltd.

A homotopy analysis solution to large deformation of beams under static arbitrary distributed load

Bending problem of rectangular plates of unidirectional nonhomogeneity and variable thickness with two opposite edges simply supported under arbitrary distributed loads

Applications of tuned mass damper (TMD) systems for bridge structures are observed for mitigation of problem related to excessive vibration induced by either wind loading or vehicle loading, where dominant modes usually in one direction (commonly vertical) are taken into account. Considering modes dominant in one direction may not be considered as a robust practice while any bridge structure is having dominant modes along both the transverse and vertical directions and the same bridge structure is subjected to loading along both the directions. In the present study, an approach for simultaneous control of major horizontal, vertical and torsional modes is presented targeting robust vibration control under general loading condition. A strategy using modal frequency response function (FRF) is proposed based on the traditional mode-wise control approach. The proposed modal FRF based approach is applied to an existing important large truss bridge (Saraighat Bridge) to carry out an analytical design of TMD system considering general loading conditions. The designed TMD system is found to demonstrate good performance under various white-noise based general loading conditions.

The impact of shallow tunnel construction on the surrounding environment is often considered as a symmetric half-plane problem with circular holes. In this research, the analytical solutions of the ground stresses and displacements of a shallow circular tunnel in an elastic half-plane under arbitrary distributed loads on ground surface were derived, based on the complex variable method. Then, an application was implemented to analyze the potential plastic zone induced by shallow tunneling adjacent to the ground surface structures. The verification of the results obtained from the proposed analytical prediction model was carried out using the numerical simulations. Additionally, the influences of different boundary condition (different magnitudes and ranges of arbitrary distributed loads and different symmetric boundary conditions of the tunnel perimeter) on the distribution characteristics of the potential plastic zones were analyzed. In general, the results showed that the larger the pile loads and the closer the relative position between the tunnel and distributed loads, the more distinct the coalesced trends of the potential plastic zones around the tunnel and the potential plastic zones around the distributed loads.