RELATIONSHIP OF MAXIMUM DEFLECTIONS AND NATURAL FREQUENCIES VIBRATIONS OF ISOTROPIC CIRCULAR PLATES WITH INHOMOGENEOUS RESISTANCE CONDITIONS ON THE OUTER AND INNER CONTOUR

The relationship between the maximum deflections from a static uniformly distributed load W0 and the fundamental frequency of natural transverse vibrations of a round isotropic plate of linearly variable thickness with thickening to the edge under homogeneous conditions of support along the outer contour, depending on the ratio of the thickness of the plate in the center to the thickness along the edge, is considered. According to the results of the study, graphs of the dependence of the maximum deflection and the frequency of natural vibrations of the plate on the ratio t1 / t2 are constructed. It is shown that for round plates of linearly variable thickness at t1/t2<1.1 coefficient K with an accuracy of 5.9% coincides with the analytical coefficient for round plates of constant thickness. Numerical studies shows that when the ratio of the thicknesses on the contour and in the center is equal to two, the difference in the coefficient K, which depends on the relationship between the static and dynamic characteristics of the platinum, is about 25% for hinged support along the contour and up to 37% for rigid support. This indicates a more significant effect of uneven mass distribution for such boundary conditions.

TRANSVERSE BENDING AND FREE VIBRATIONS OF ELASTIC ISOTROPIC PLATES IN THE FORM OF ISOSCELES TRIANGLES

This paper considers elastic isotropic plates in the form of isosceles triangles with combined boundary conditions (a combination of hinged support and rigid restraint conditions along the sides of the contour). Calculations were performed using FEM to determine the integral physical characteristics in the considered problems F (the maximum deflection of uniformly loaded plates w0 and the fundamental frequency of oscillations in the unloaded state ω). On the basis of the obtained numerical results, approximating functions have been constructed: "maximum deflection - form factor of plates", "basic frequency of oscillations - form factor of plates", the structure of which corresponds to the structure of similar formulas obtained when presenting known exact solutions in the corresponding problems of technical theory of plates in isoperimetric form. Based on the properties of the form factor of plates, these approximating functions limit the whole set of considered integral physical quantities and therefore can be used as reference solutions for the calculation of triangular plates of arbitrary form applying the method of interpolation by form factor (MIFF). We consider an example of calculation of a plate in the form of a rectangular triangle with hinged support of the sides.

THE SUPPORT BONDS RIGIDITY INFLUENCES ON THE CARRYING CAPACITY REDUCTION OF THE SHALLOW SHELLS ON A RECTANGULAR PLAN

Geometric nonlinearity shallow shells on a square and rectangular plan with constant and variable thickness are considered. Loss of stability of a structure due to a decrease in the rigidity of one of the support (transition from fixed support to hinged support) is considered. The Bubnov-Galerkin method is used to solve differential equations of shallow geometrically nonlinear shells. The Vlasov's beam functions are used for approximating. The use of dimensionless quantities makes it possible to repeat the calculations and obtain similar dependences. The graphs are given that make it possible to assess the reduction in the critical load in the shell at each stage of reducing the rigidity of the support and to predict the further behavior of the structure. Regularities of changes in internal forces for various types of structure support are shown. Conclusions are made about the necessary design solutions to prevent the progressive collapse of the shell due to a decrease in the rigidity of one of the supports.

Vibrations and Stability of a Plate in Supersonic Flow Subjected to a Follower Force, and Having a Hinged External Support and a Resilient Attenuation Internal Support

The vibrations and stability of a plate having a finite length were considered in a flat supersonic flow, having adopted an assumption that one of the edges of the plate has a hinged support, and the other edge is free. Another support was located in an internal point of the plate and featured resilient attenuation properties. A compressive force, called the follower force, was applied within the plane of the plate in a direction tangent to the deformed surface of the plate. This way, a superficial system was forced in which two independent physical factors occurred and caused its self-excitation. Therefore the superficial system could be termed a ‘double self-excited system’. The solution of the equations of motion for the system was derived with a Laplace transformation.

Theoretical Analysis and Modeling Fora Piezoelectric Bimorph Actuator with Overhanging

The characteristics of a piezoelectric bimorph that fixed in one end (cantilever structure) have been well studied. The displacement of deformation and the force applying to the load are usually not easy to be both satisfied for many specific applications. In this paper, a new structure of a piezoelectric bimorphusing a hinged support and a pinned support (overhanging structure) has been analyzed and modeled to give flexibility in designing such a device to meet requirements of both the displacement and the force.

Seismic Response Analysis of Dendritic Column in the Folded Plate Grid Frame

Firstly, we described the basic situation of dendritic structure. Then studied the elastoplastic time-procedure analysis of the dendriform-column, and researched in dynamic performance of structure under seldom occurred earthquake. Finally, we presented the performance difference comparison in the hinged support and fixed support conditions, and the corresponding analysis for folded plate grid frame structure. All these experiences will promote the application of dendriform-column in folded plate grid frame structure on the design and research work.

Effective Prestressing Force Testing Method of External Prestressed Bridge Based on Frequency Method

A practical project is taken for the example to analyze the application of frequency method in the effective prestress test of external prestressed bridge. In the process of solving the dynamic differential equation of tension cable, the effects of boundary conditions on the natural frequencies of external prestressed tendons are analyzed. The analysis results show that the fundamental frequency of the prestressed tendons under fixed boundary condition is higher than that under hinged-support support boundary condition, and the relative variance decreases with the increase of tensioning force. With the same tensioning force, the relative variance decreases with the increase of cable length. In the practical test, only the upper and lower bound limits can be obtained according to the measured prestressed tendon frequencies, while the real effective prestress values are between them. For external prestressed tendons, a kind of short tension cable, the frequency method can produce certain error in calculating the effective prestress.

The Response of the Bi-Directional Beam String Structure under Vertical Seismic Considering Supporting Frame

This paper using time time-procedure analysis method to analyze seismic response on a 80 m × 80 m bidirectional beam string structure model. Under vertical seismic action, we respectively compared to the seismic performance under the structure have or no supporting frame and have the same supporting frame but different support conditions. Under vertical seismic action, the axial force of brace is almost the same considering or unconsidering the supporting frame, while the upper beam vertical displacement is increased and the surrounding of the roof even increased several times considering supporting frame; the boundary conditions for the sliding hinge support bidirectional beam string structure which under vertical seismic ( middle seismic ) action the brace axial force and winding beam vertical displacement are nearly same with the fixed hinged support, while the horizontal displacement of the winding beam is larger than the fixed hinged support; the change of support conditions affect the order of the various modes of the structure but no affect the structural vibration modes.

Experimental Study on Eccentric Compression Behavior of Timber Columns with Longitudinal Cracks Strengthened by CFRP Sheets

This paper presents a study on reinforcement of timber columns with longitudinal cracks strengthened by CFRP sheets under eccentric compression. An experimental program using special eccentric compression hinged-support was proposed to identify the failure modes and to investigate the recovery in load carrying capacity. Different combinations of eccentric distance and directions of the eccentric plane related to that of the crack plane were considered. This test can provide detailed experimental data for the application of CFRP strengthening on timber columns under eccentric compression which is an efficient method to maintain the original historical structure.