scholarly journals THE REACTIONS OF THE «BEAM – FOUNDATION» SYSTEM TO THE SUDDEN CHANGE OF THE BOUNDARY CONDITIONS

2018 ◽  
Vol 188 ◽  
pp. 03008 ◽  
Author(s):  
Vladimir A. Gordon ◽  
Olga V. Pilipenko ◽  
Vladimir A. Trifonov
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Dynamic Process ◽  
Sudden Change ◽  
Static Problem ◽  
Forced Vibrations ◽  
Winkler Foundation ◽  
Initial Condition ◽  
Foundation Parameters ◽  
Beam Foundation

The authors constructed a mathematical model of a dynamic process in a loaded beam on the elastic Winkler foundation in a sudden formation of a defect in the form of a change in the boundary conditions. The solution of the static problem of bending of the beam pinched at the ends served as the initial condition for the process of forced vibrations hinged supported at the ends of a beam, which arose after a sudden break in the connections that prevented the rotation of the end sections. The authors determined the dynamic increments of stresses in a beam for various combinations of a beam and foundation parameters.

scholarly journals DYNAMIC EFFECTS IN THE BEAM ON AN ELASTIC FOUNDATION CAUSED BY THE SUDDEN TRANSFORMATION OF SUPPORTING CONDITIONS

2018 ◽  
Vol 14 (4) ◽  
pp. 27-47
Author(s):  
Vladimir I. Travush ◽  
Vladimir A. Gordon ◽  
Vitaly I. Kolchunov ◽  
Yevgeny V. Leontiev
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Dynamic Process ◽  
Static Problem ◽  
Forced Vibrations ◽  
Initial Condition ◽  
Dynamic Effects ◽  
Foundation Parameters

A mathematical model of a dynamic process in a loaded beam on an elastic Winkler base with the sudden formation of a defect in the form of a change in the boundary conditions is constructed. The solution of the static problem of bending of the beam fixed at the ends serves as the initial condition for the process of forced vibrations hinged supported at the ends of the beam, which arose after a sudden break in the bonds that prevented the rotation of the end sections. Dynamic increments of stresses in the beam for various combinations of beam and foundation parameters are determined. determined.

DYNAMIC LOADING OF THE ROD IN CASE OF A SUDDEN CHANGE IN THE STRUCTURE OF THE ELASTIC BASE

2021 ◽  
Vol 2 ◽  
pp. 27-41
Author(s):  
А.А. PODDUBNY ◽  
V.A. GORDON ◽  
T.V. POTURAEVA
Keyword(s):  
Nonlinear System ◽  
Sudden Change ◽  
Physical And Mechanical Properties ◽  
Shear Stiffness ◽  
Static Problem ◽  
Elastic Base ◽  
Forced Vibrations ◽  
Natural Vibrations ◽  
Static State ◽  
Two Parameter

A mathematical model of the dynamic process in the structurally nonlinear system «beam – two-parameter foundation», which arises as a result of a sudden change in the physical and mechanical properties of the foundation, leading to zeroing of its shear stiffness, is constructed in a structurally-nonlinear system «beam – two-parameter foundation» The solution of the static problem of bending of a beam supported on a Pasternak base serves as the initial condition for the problem of forced vibrations of a beam on a Winkler base that arose after the sudden formation of a defect. Solutions to static and dynamic problems are constructed by the method of initial parameters with the use of vectors of states of beam sections and matrices of the influence of initial parameters on the state of arbitrary sections. In the analysis of forced vibrations, the decomposition of the load and deflections of the initial static state into rows according to the forms of natural vibrations of the new state is used.

MODELING OF THE DYNAMIC PROCESS RELEASE OF STUCK DRILLING TOOLS BY HYDRO-PULSE METHOD

2019 ◽  
pp. 94-103
Author(s):  
K. H. Levchyk ◽  
M. V. Shcherbyna
Keyword(s):  
Mathematical Model ◽  
Dynamic Process ◽  
Drilling Fluid ◽  
Pulse Method ◽  
Geometrical Parameters ◽  
Technical Solution ◽  
Rock Layer ◽  
Drilling Tool ◽  
Drilling Tools ◽  
Drill Pipes

A technical solution is proposed for the elimination the grabbing of drilling tool, based on the use of energy due to the circulation of the drilling fluid. The expediency eliminating the grabbing drilling tool using the hydro-impulse method is substantiated. A method of drawing up a mathematical model for the dynamic process of a grabbing string of drill pipes in the case of perturbation of hydro-impulse oscillations in the area of the productive rock layer is developed. The law of longitudinal displacements arising in the trapped string is obtained, which allows choosing the optimal geometrical parameters of the passage channels and the frequency rotational of shutter for these channels. Recommendations for using this method for practical use have been systematized.

Mathematical model of heating a prism with boundary conditions of the 3rd kind

2007 ◽  
Vol 80 (6) ◽  
pp. 1065-1071
Author(s):  
Yu. M. Pleskachevskii ◽  
V. I. Timoshpol’skii ◽  
S. V. Shil’ko ◽  
S. L. Gavrilenko ◽  
S. M. Kabishov
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions

Analytical Buckling Loads of Columns Weakened Simultaneously with Transverse Cracks and Partial Delamination

2019 ◽  
Vol 19 (03) ◽  
pp. 1950027 ◽  
Author(s):  
Igor Planinc ◽  
Simon Schnabl
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Parametric Study ◽  
Transverse Crack ◽  
Transverse Cracks ◽  
Buckling Loads ◽  
Crack Location ◽  
Benchmark Solution ◽  
First Time

This paper focuses on development of a new mathematical model and its analytical solution for buckling analysis of elastic columns weakened simultaneously with transverse open cracks and partial longitudinal delamination. Consequently, the analytical solution for buckling loads is derived for the first time. The critical buckling loads are calculated using the proposed analytical model. A parametric study is performed to investigate the effects of transverse crack location and magnitude, length and degree of partial longitudinal delamination, and different boundary conditions on critical buckling loads of weakened columns. It is shown that the critical buckling loads of weakened columns can be greatly affected by all the analyzed parameters. Finally, the presented results can be used as a benchmark solution.

scholarly journals Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect

Nanomaterials ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 3066
Author(s):  
Amin Alibakhshi ◽  
Shahriar Dastjerdi ◽  
Mohammad Malikan ◽  
Victor A. Eremeyev
Keyword(s):  
Size Effect ◽  
Boundary Conditions ◽  
Frequency Response ◽  
Multiple Scales ◽  
Forced Vibrations ◽  
Response Force ◽  
Nonlinear Frequency ◽  
Large Rotation ◽  
Free And Forced Vibrations ◽  
Stiffening Effect

In recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the influence of the size effect and large rotation for such a beam that is important for the large deformation was not addressed. This paper attempts to explore the free and forced vibrations of a micro/nanobeam made of a hyperelastic material incorporating strain-stiffening, size effect, and moderate rotation. The beam is modelled based on the Euler–Bernoulli beam theory, and strains are obtained via an extended von Kármán theory. Boundary conditions and governing equations are derived by way of Hamilton’s principle. The multiple scales method is applied to obtain the frequency response equation, and Hamilton’s technique is utilized to obtain the free undamped nonlinear frequency. The influence of important system parameters such as the stiffening parameter, damping coefficient, length of the beam, length-scale parameter, and forcing amplitude on the frequency response, force response, and nonlinear frequency is analyzed. Results show that the hyperelastic microbeam shows a nonlinear hardening behavior, which this type of nonlinearity gets stronger by increasing the strain-stiffening effect. Conversely, as the strain-stiffening effect is decreased, the nonlinear frequency is decreased accordingly. The evidence from this study suggests that incorporating strain-stiffening in hyperelastic beams could improve their vibrational performance. The model proposed in this paper is mathematically simple and can be utilized for other kinds of micro/nanobeams with different boundary conditions.

scholarly journals The Krylov problem in the case of a beam on Vlasov inertial foundation

2018 ◽  
Vol 19 (6) ◽  
pp. 728-736
Author(s):  
Wacław Szcześniak ◽  
Magdalena Ataman
Keyword(s):  
Closed Form ◽  
Compressive Force ◽  
Elastic Beam ◽  
Forced Vibrations ◽  
Critical Force ◽  
Winkler Foundation ◽  
Static Deflection ◽  
Numerical Examples ◽  
Moving Force ◽  
Axial Forces

The paper deals with vibrations of the elastic beam caused by the moving force traveling with uniform speed. The function defining the pure forced vibrations (aperiodic vibrations) is presented in a closed form. Dynamic deflection of the beam caused by moving force is compared with the static deflection of the beam subjected to the force , and compressed by axial forces . Comparing equations (9) and (13), it can be concluded that the effect on the deflection of the speed of the moving force is the same as that of an additional compressive force . Selected problems of stability of the beam on the Winkler foundation and on the Vlasov inertial foundation are discussed. One can see that the critical force of the beam on Vlasov foundation is greater than in the case of Winkler's foundation. Numerical examples are presented in the paper

scholarly journals Influence of Nano-Fluid Lubrication On Single Porous-Layered Journal Bearing: A Hypothetical Approach

2021 ◽  
Author(s):  
BIPLAB BHATTACHARJEE ◽  
PRASUN CHAKRABORTI ◽  
KISHAN CHOUDHURY
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Micropolar Fluid ◽  
Journal Bearing ◽  
Performance Characteristics ◽  
Published Data ◽  
Nano Fluid ◽  
Nano Lubricant ◽  
Output Characteristics ◽  
Modified Darcy’S Law

Abstract In this article a mathematical model of single layered nano-fluid lubricated PJB (porous journal bearing) has been formulated. The nano-lubricant's impact on the efficiency of said journal bearing has been studied using modified Darcy's law and boundary conditions. The different nanoparticles often used as an additive in industrial lubricating oils improve their viscosity significantly. The brief description of dimensionless performance characteristics of the investigated bearing was obtained by the use of the nano-lubricant's modified Krieger-Dougherty viscosity model. The observations revealed that the output characteristics are substantially improved by using nano-lubricant. The present study was validated by comparing the findings of recently published data with micropolar fluid and was found to be completely compatible since data with nano-lubricant are still unavailable.

scholarly journals Lamb waves in multilayered media: 3D and 6D formalisms

2019 ◽  
Vol 97 ◽  
pp. 03003
Author(s):  
Anna Avershyeva ◽  
Sergey Kuznetsov
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Fundamental Matrix ◽  
Elastic Anisotropy ◽  
Lamb Waves ◽  
Stratified Media ◽  
Multilayered Media ◽  
Different Types ◽  
Secular Equations ◽  
Fundamental Matrices

A mathematical model for analyzing Lamb waves propagating in stratified media with arbitrary elastic anisotropy is worked out. The model incorporates a combined Fundamental Matrix (FM) and Modified Transfer Matrix (MTM) methods. Multilayered unbounded plates with different types of boundary conditions imposed on the outer surfaces are considered. Closed form fundamental matrices and secular equations for dispersion relations are derived.

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