scholarly journals On the Dynamic Stability of a Reinforced Concrete Plate, Taking into Account the Material Creep

2018 ◽  
Vol 196 ◽  
pp. 01025
Author(s):  
Elena Kosheleva
Keyword(s):  
Differential Equation ◽  
Reinforced Concrete ◽  
Dynamic Stability ◽  
Critical Frequency ◽  
Dynamic Instability ◽  
Frequency Equation ◽  
Concrete Plate ◽  
Material Creep ◽  
Linear Differential ◽  
Separated Variables

The problem of the dynamic stability of a reinforced concrete plate armoured in two directions parallel to its edges is considered. To describe the viscoelastic properties of concrete, an integral dependence was adopted with an exponential kernel. The use of this dependence led to a linear differential equation of plate vibration. In addition to the creep of concrete, the work of the reinforcement was taken into account. The solution of the differential equation of vibrations of a plate in the form of a series with separated variables is considered, which satisfies the plate fastening conditions. Differential equations are obtained for the time function by the Bubnov-Galerkin method. The task was to find the main areas of dynamic instability. For this, the critical frequency equation was obtained. The influence of the coefficients entering into the equation of critical frequencies on the position of the main regions of dynamic instability is investigated.

scholarly journals STUDY OF SPATIAL PROBLEMS OF DYNAMIC STABILITY OF REINFORCED CONCRETE FRAMES

2021 ◽  
pp. 62-70
Author(s):  
V.М. Fomin ◽  
◽  
І.P. Fomina ◽  
Keyword(s):  
Reinforced Concrete ◽  
Dynamic Stability ◽  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Practical Importance ◽  
Harmful Effect ◽  
Spatial Problem ◽  
Concrete Frames ◽  
Destructive Effect ◽  
Reinforced Concrete Frames

Abstract. The article proposes a method for constructing areas of dynamic instability of reinforced concrete frames in the space of parameters (frequency and amplitude) of seismic and operational dynamic impacts that cause the appearance of longitudinal forces in the bars of structures, which periodically change in time and lead to an unlimited increase in amplitudes of transverse vibrations when the values of these parameters are in the areas of instability. The proposed method is demonstrated by a specific example, which considers the spatial problem of dynamic stability of a П-shaped frame with two concentrated masses located on it, which are under the action of vertical periodic forces. These forces create periodic longitudinal forces in the vertical rods of the frame. Areas of dynamic instability of the frame are constructed. From the point of view of human activity, fluctuations can be both beneficial and harmful. We can observe vibrations of various buildings, structures, bridges, which cause additional stresses and deformations of these structures, have a harmful effect on their safe functioning. Too intense fluctuations lead to serious consequences. This leads to the destruction of individual elements of the structure and, as a result, to accidents. The most destructive effect of vibrations is observed during earthquakes and explosions. The study of vibrations is of great practical importance. This avoids the unwanted effects of fluctuations by limiting their level. Only on the basis of a deep study of various types of vibrations can important practical problems of the dynamics of structures be solved. Solving dynamics problems is a complex problem. In contrast to static calculation, when studying oscillations, one has to take into account an additional factor – time. The dynamic design of structures provides them with bearing capacity under the combined action of static and dynamic loads. A construction will be considered as a system with an infinite number of elementary masses distributed over it with an infinitely large number of dynamic degrees of freedom.

scholarly journals Dynamic Stability of Euler Beams under Axial Unsteady Wind Force

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
You-Qin Huang ◽  
Han-Wen Lu ◽  
Ji-Yang Fu ◽  
Ai-Rong Liu ◽  
Ming Gu
Keyword(s):  
Dynamic Stability ◽  
Dynamic Instability ◽  
Time History ◽  
Wind Load ◽  
Frequency Equation ◽  
Unstable State ◽  
Wind Force ◽  
Eigenvalue Method ◽  
Load Component ◽  
Instability Regions

Dynamic instability of beams in complex structures caused by unsteady wind load has occurred more frequently. However, studies on the parametric resonance of beams are generally limited to harmonic loads, while arbitrary dynamic load is rarely involved. The critical frequency equation for simply supported Euler beams with uniform section under arbitrary axial dynamic forces is firstly derived in this paper based on the Mathieu-Hill equation. Dynamic instability regions with high precision are then calculated by a presented eigenvalue method. Further, the dynamically unstable state of beams under the wind force with any mean or fluctuating component is determined by load normalization, and the wind-induced parametric resonant response is computed by the Runge-Kutta approach. Finally, a measured wind load time-history is input into the dynamic system to indicate that the proposed methods are effective. This study presents a new method to determine the wind-induced dynamic stability of Euler beams. The beam would become dynamically unstable provided that the parametric point, denoting the relation between load properties and structural frequency, is located in the instability region, no matter whether the wind load component is large or not.

scholarly journals The appliance of interval calculus in estimation of plate deflection by solving Poisson's bisquared partial differential equation

2008 ◽  
Vol 6 (2) ◽  
pp. 207-220
Author(s):  
Djordje Djordjevic ◽  
Dusan Petkovic ◽  
Darko Zivkovic
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Reinforced Concrete ◽  
Unit Area ◽  
Direct Influence ◽  
Partial Differential ◽  
Simply Supported ◽  
Concrete Plate ◽  
Knowing That ◽  
Plate Deflection

The work analyzed the appliance of interval calculus connected to estimation of elements deflection done by reinforced concrete. The simply supported reinforced concrete plate was taken as an example. The plate was loaded by load per unit area. Knowing that there are several parameters that influence the plate deflection, we showed the calculus where the mentioned parameters were given at a certain interval. The results (the final values of deflection) we also got in the form of intervals so it was possible to follow the direct influence of a change of one or more entering parameters on deflection values by using one model and one caculus.

Experimental Study and Numerical Simulation for Explosion and Phenomena of RC Slabs

2014 ◽  
Vol 501-504 ◽  
pp. 1096-1103
Author(s):  
Hong Xiao Wu ◽  
Hao Zhe Xing ◽  
Zhi Fang Yan
Keyword(s):  
Reinforced Concrete ◽  
Impact Loading ◽  
Loading Condition ◽  
Damage Mechanism ◽  
Failure Characteristics ◽  
Explosion Pressure ◽  
Concrete Plate ◽  
Solid Models ◽  
Calculation Results ◽  
Rc Slabs

The blast impact dynamic experiment of reinforced concrete rectangular plate with simply supported boundary conditions was performed using explosion pressure simulator. With 3-D FEM software LS-DYNA, the separate solid models of concrete and steel were established and 3-D FEM dynamic analysis of the experiment process was carried out. Compared calculation results to experiment results synthetically, the damage mechanism and failure characteristics of reinforced concrete plate under explosion impact loading condition were got and it is also verified that the H-J-C model can approximately simulate the concrete properties well under explosion impact loading condition.

scholarly journals Correctness conditions for high-order differential equations with unbounded coefficients

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kordan N. Ospanov
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Order Linear Differential Equation ◽  
Unbounded Coefficients ◽  
Weighted Norms ◽  
Uniqueness Of The Solution ◽  
Linear Differential

AbstractWe give some sufficient conditions for the existence and uniqueness of the solution of a higher-order linear differential equation with unbounded coefficients in the Hilbert space. We obtain some estimates for the weighted norms of the solution and its derivatives. Using these estimates, we show the conditions for the compactness of some integral operators associated with the resolvent.

Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kusano Takaŝi ◽  
Jelena V. Manojlović
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Continuous Function ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Regular Variation ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Positive Continuous Function ◽  
Linear Differential

AbstractWe study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation(p(t)\lvert x^{\prime}\rvert^{\alpha}\operatorname{sgn}x^{\prime})^{\prime}+q(% t)\lvert x\rvert^{\alpha}\operatorname{sgn}x=0,where q is a continuous function which may take both positive and negative values in any neighborhood of infinity and p is a positive continuous function satisfying one of the conditions\int_{a}^{\infty}\frac{ds}{p(s)^{1/\alpha}}=\infty\quad\text{or}\quad\int_{a}^% {\infty}\frac{ds}{p(s)^{1/\alpha}}<\infty.The asymptotic formulas for generalized regularly varying solutions are established using the Karamata theory of regular variation.

scholarly journals Hyperbolastic Models from a Stochastic Differential Equation Point of View

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1835
Author(s):  
Antonio Barrera ◽  
Patricia Román-Román ◽  
Francisco Torres-Ruiz
Keyword(s):  
Differential Equation ◽  
Simulated Data ◽  
Real Data ◽  
Point Of View ◽  
Likelihood Method ◽  
Numerical Resolution ◽  
The Family ◽  
The Common ◽  
Linear Differential ◽  
Mean Function

A joint and unified vision of stochastic diffusion models associated with the family of hyperbolastic curves is presented. The motivation behind this approach stems from the fact that all hyperbolastic curves verify a linear differential equation of the Malthusian type. By virtue of this, and by adding a multiplicative noise to said ordinary differential equation, a diffusion process may be associated with each curve whose mean function is said curve. The inference in the resulting processes is presented jointly, as well as the strategies developed to obtain the initial solutions necessary for the numerical resolution of the system of equations resulting from the application of the maximum likelihood method. The common perspective presented is especially useful for the implementation of the necessary procedures for fitting the models to real data. Some examples based on simulated data support the suitability of the development described in the present paper.

scholarly journals Steady Motion of Ice Sheets

1980 ◽  
Vol 25 (92) ◽  
pp. 229-246 ◽  
Author(s):  
L. W. Morland ◽  
I. R. Johnson
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Power Law ◽  
Perturbation Expansion ◽  
Ice Sheet ◽  
Leading Order ◽  
Plane Flow ◽  
General Law ◽  
Non Linear ◽  
Linear Differential

AbstractSteady plane flow under gravity of a symmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding according to a shear-traction-velocity power law, is treated. The surface accumulation is taken to depend on height, and the drainage and sliding coefficient also depend on the height of overlying ice. The ice is described as a general non-linearly viscous incompressible fluid, with illustrations presented for Glen’s power law, the polynomial law of Colbeck and Evans, and a Newtonian fluid. Uniform temperature is assumed so that effects of a realistic temperature distribution on the ice response are not taken into account. In dimensionless variables a small paramter ν occurs, but the ν = 0 solution corresponds to an unbounded sheet of uniform depth. To obtain a bounded sheet, a horizontal coordinate scaling by a small factor ε(ν) is required, so that the aspect ratio ε of a steady ice sheet is determined by the ice properties, accumulation magnitude, and the magnitude of the central thickness. A perturbation expansion in ε gives simple leading-order terms for the stress and velocity components, and generates a first order non-linear differential equation for the free-surface slope, which is then integrated to determine the profile. The non-linear differential equation can be solved explicitly for a linear sliding law in the Newtonian case. For the general law it is shown that the leading-order approximation is valid both at the margin and in the central zone provided that the power and coefficient in the sliding law satisfy certain restrictions.

scholarly journals New Bi-modular Material Approach to Buckling Problem of Reinforced Concrete Columns

2016 ◽  
Vol 6 (1) ◽  
pp. 19 ◽  
Author(s):  
Ahmad Salah Edeen Nassef ◽  
Mohammed A. Dahim
Keyword(s):  
Differential Equation ◽  
Reinforced Concrete ◽  
Differential Equations ◽  
Concrete Columns ◽  
Neutral Axis ◽  
Reinforced Concrete Columns ◽  
New Approach ◽  
Codes Of Practice ◽  
Governing Differential Equation ◽  
Transverse Deflection

<p class="1Body">This paper was investigating the buckling problem of reinforced concrete columns considering the reinforced concrete as bi – modular material. Governing differential equations was driven. The relation between the non-dimensional transverse deflection and non-dimensional distance between centroid axis and the neutral axis "eccentricity" was drawn to enable the solution of the governing differential equation. The new approach was verified with different experimental results and different codes of practice.<strong></strong></p>

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