LATERAL VIBRATIONS OF BEAMS ON AN ELASTIC BASE AT CHANGING THE SUPPORTING CONDITIONS

2020 ◽  
Vol 91 (5) ◽  
pp. 70-76
Author(s):  
E.V. LEONTIEV ◽  
◽  
Keyword(s):  
Dynamic Behavior ◽  
Elastic Foundation ◽  
Dynamic Problem ◽  
Static Problem ◽  
Elastic Base ◽  
Design Model ◽  
Lateral Vibrations ◽  
Internal Forces ◽  
Vibration Loads ◽  
The Right

The paper considers the system "beam - elastic foundation", in which a beam with free edges was at first on a solid elastic foundation, but when a defect suddenly forms in the foundation under the right side of the beam, part of foundation was removed from design model. As a result of calculations performed by the method of initial parameters, the displacements and internal forces for the static problem are determined. The dynamic problem of determining the forces and displacements was solved, taking into account the three vibration loads F (t) = F sinγt applied at arbitrary points d when the conditions for supporting the right side of the beam on an elastic foundation were changed, the values of the dynamics coefficients were determined. Conditions are formulated that must be taken into account when analyzing the dynamic behavior of a structure under the influence of vibration loads in the case of a change in the conditions of bearing on an elastic foundation.

scholarly journals Geometric nonlinear free vibration of axially functionally graded non-uniform beams supported on elastic foundation

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Hareram Lohar ◽  
Anirban Mitra ◽  
Sarmila Sahoo
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Dynamic Problem ◽  
Free Vibration Analysis ◽  
Static Problem ◽  
Functionally Graded ◽  
Dimensionless Frequency ◽  
Energy Principle ◽  
Eigen Value ◽  
Minimum Potential Energy Principle

AbstractIn the present study non-linear free vibration analysis is performed on a tapered Axially Functionally Graded (AFG) beam resting on an elastic foundation with different boundary conditions. Firstly the static problem is carried out through an iterative scheme using a relaxation parameter and later on the subsequent dynamic problem is solved as a standard eigen value problem. Minimum potential energy principle is used for the formulation of the static problem whereas for the dynamic problem Hamilton’s principle is utilized. The free vibrational frequencies are tabulated for different taper profile, taper parameter and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane.

scholarly journals Development of Calculation Theory for Hinged-Connected Beams on Elastic Base

2020 ◽  
Vol 19 (5) ◽  
pp. 389-394
Author(s):  
O. V. Kozunova
Keyword(s):  
Elastic Foundation ◽  
Mixed Method ◽  
Elastic Base ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Medium Effects ◽  
Normative Documents ◽  
Universal Approach ◽  
Internal Forces ◽  
The Republic

The paper provides a brief review of the literature on the theory and methods of calculating hinged-connected or articulated structures on an elastic base. The author refers to the works of B. G. Korenev, G. Ya. Popov, I. A. Simvulidi, R. V. Serebryany, A. G. Yuriev, in which, using various approaches, studies have been carried out to calculate hinged-connected beams and slabs on an elastic base. From the analysis of  scientific literature on the topic under consideration, it can be concluded that there is no general approach to solving this problem, which is valid for any hinged-connected beams and plates lying on any model of an elastic base under the action of an arbitrary external load.  In addition, a similar problem for this type of engineering calculations is observed in the normative documents. In the Republic of Belarus, a number of industry documents have been used to calculate pavement bearing elements for various highways and track transverse structures, in which road pavements with a load-bearing element and the connection of elements between themselves (hinged or rigid) are considered in an incoherent formulation. The paper proposes a universal approach for calculating hinged-connected beams on an elastic foundation, based on the mixed method of structural mechanics, taking into account the Zhemochkin ratios for functions of the elastic medium effects. The following hypotheses and assumptions are taken into account: only normal stresses act on  the  contact  of  the  beam  with the base, hypotheses  of  the bending  theory are valid  for beams,  hinges  between  the beams are cylindrical, and the distribution of contact stresses along the width of the beams is uniform. As a result of the proposed calculation, the stress-strain state of a system of hinged-connected beams on an elastic foundation has been investigated, namely: distribution of contact stresses under beams, internal forces in the beams and hinged joints, as well as settlements of the elastic foundation under them. The numerical implementation of this approach has been performed using the mathematical package Mathematica 10.4. Examples of calculation are given for different versions of hinged-connected beams and an elastic base: for three hinged-connected beams based on Winkler and seven – on an elastic half-space.

Impact of blast and mechanical loads on the shear deformable stiffened sandwich plate with an auxetic core layer in thermal environment

2021 ◽  
pp. 109963622110219
Author(s):  
Vu Thi Thuy Anh ◽  
Vu Dinh Quang ◽  
Nguyen Dinh Duc ◽  
Pham Ngoc Thinh
Keyword(s):  
Dynamic Behavior ◽  
Elastic Foundation ◽  
Nonlinear Dynamic ◽  
Sandwich Plate ◽  
Thermal Environment ◽  
Core Layer ◽  
Mechanical Loads ◽  
Environment Temperature ◽  
Nonlinear Dynamic Behavior ◽  
Fgm Layer

By using the first order shear deformation theory (FSTD), this paper presents the results of the nonlinear dynamic behavior and natural frequencies of sandwich plate supported by elastic foundations in thermal environment and subjected to mechanical load and blast loading. This work takes advantage of the sandwich plate configuration with three layers: graphene platelet –reinforced composite (GPL) layer – auxetic layer – FGM layer, to analyze the dynamic and vibration problem, in which the auxetic core layer has a negative Poisson's ratios and the FGM layer is reinforced by stiffeners made of full metal or full ceramic depending on a situation of stiffeners at the metal-rich or ceramic-rich side of the plate respectively. Corresponding to the combination of material layers, the mechanical quantities of the problem are processed and calculated to suit the structure and reinforcement conditions. Numerical results are provided to explore the influences of geometrical parameters, elastic foundation parameters, GPL volume fraction, blast and mechanical loads on the nonlinear dynamic behavior and vibration of sandwich plate resting on elastic foundation and in thermal environment. In addition, the study is not only assumed that the material properties depend on environment temperature variation, but also considered the thermal stresses in the stiffeners, as well as considered the effect of imperfections in the original shape of the structure.

Anchorages of stirrups under transverse tension in concrete - development of a design model

2019 ◽  
Author(s):  
Mirhat Medziti ◽  
Daia Zwicky
Keyword(s):  
Crack Width ◽  
Concrete Beams ◽  
Tensile Force ◽  
Concrete Structures ◽  
Experimental Tests ◽  
Reinforced Concrete Beams ◽  
Design Model ◽  
Hook Effect ◽  
Internal Forces ◽  
Negative Bending

<p>According to Swiss code SIA 262 "Concrete structures", stirrups of reinforced concrete beams must "surround the tensile longitudinal reinforcement" and must "be anchored to mobilize the static height of internal forces". For existing concrete structures, Swiss code SIA 269/2 provides stirrup detailing requirements while limiting these directives for stirrup anchorage to the compression zone. In zones of negative bending, these requirements are often not satisfied for execution reasons. This question is addressed in a largely experimental Ra&amp;D project. Anchorage tests were performed and analyzed, with a total of 144 tests on 9 concrete beams. These underwent a longitudinal tensile force up to 1’000 kN to simulate transverse cracking at stirrup anchorages in negative flexure zones. The study parameters are crack width (0, 0.4 and 0.9 mm), stirrup diameter (10 and 14 mm), bar ribbing (smooth and ribbed) and hook angle (90°, 135°, 180° and straight bars). A design model based on the "tension chord model" (TCM) developed at ETH Zurich is proposed. This simple and practical design model has proved ist effectiveness to consider bond effects. Reduction factors for bar diameter (k<sub>Ø</sub>), relative bar ribbing (k<sub>fR</sub>), hook effect (k<sub>θ</sub>) and crack width (k<sub>w</sub>) were taken into account for calibration. Results of analytical calculations are coherent with experimental tests.</p>

scholarly journals Dynamic Behavior of Geared Rotors

1997 ◽  
Author(s):  
T. N. Shiau ◽  
J. S. Rao ◽  
J. R. Chang ◽  
Siu-Tong Choi
Keyword(s):  
Dynamic Behavior ◽  
Chaotic Behavior ◽  
Squeeze Film ◽  
Rotor Systems ◽  
Lateral Vibrations ◽  
Squeeze Film Dampers ◽  
Torsional Excitation ◽  
Route To Chaos

This paper is concerned with the dynamic behavior of geared rotor systems supported by squeeze film dampers, wherein coupled bending torsion vibrations occur. Considering the imbalance forces and gravity, it is shown that geared rotors exhibit chaotic behavior due to non linearity of damper forces. The route to chaos in such systems is established. In geared rotor systems, it is shown that torsional excitation can induce lateral vibrations. It is shown that squeeze film dampers can suppress large amplitudes of whirl arising out of torsional excitation.

scholarly journals NON-RIGID KINEMATIC EXCITATION FOR MULTIPLY-SUPPORTED SYSTEM WITH HOMOGENEOUS DAMPING

2018 ◽  
Vol 14 (4) ◽  
pp. 152-157
Author(s):  
Alexander G. Tyapin
Keyword(s):  
Mass Matrix ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Internal Damping ◽  
Static Response ◽  
Kinematic Excitation ◽  
Hand Part ◽  
Internal Forces ◽  
The Right ◽  
Damping Model

This paper continues the discussion of linear equations of motion. The author considers non-rigid kinematic excitation for multiply-supported system leading to the deformations in quasi-static response. It turns out that in the equation of motion written down for relative displacements (relative displacements are defined as absolute displacements minus quasi-static response) the contribution of the internal damping to the load in some cases may be zero (like it was for rigid kinematical excitation). For this effect the system under consideration must have homogeneous damping. It is the often case, though not always. Zero contribution of the internal damping to the load is different in origin for rigid and non-rigid kinematic excitation: in the former case nodal loads in the quasi-static response are zero for each element; in the latter case nodal loads in elements are non-zero, but in each node they are balanced giving zero resulting nodal loads. Thus, damping in the quasi-static response does not impact relative motion, but impacts the resulting internal forces. The implementation of the Rayleigh damping model for the right-hand part of the equation leads to the error (like for rigid kinematic excitation), as damping in the Rayleigh model is not really “internal”: due to the participation of mass matrix it works on rigid displacements, which is impossible for internal damping

Study on Effects of Metro Tunnel Enlarged from Air Defense Tunnel on Adjacent Piles and Control Measures

2012 ◽  
Vol 204-208 ◽  
pp. 1518-1526
Author(s):  
Xi Ping Yao ◽  
Quan Mei Gong ◽  
Jian Jia ◽  
Chen Shen
Keyword(s):  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Control Measures ◽  
Control Effect ◽  
Air Defense ◽  
Single Side ◽  
Internal Forces ◽  
Metro Tunnel ◽  
The Right ◽  
Reinforcement Measures

Based on project in which the existing air defense tunnel was enlarged to build a metro tunnel adjacent to bridge piles in Harbin, the 3-D numerical simulation using FEM was conducted to analyze the internal forces and deformations of piles. The results show that the internal forces and deformations on the right side are larger than those on the left after the enlarged excavation on a single side on sidewalls. The maximum value as well as its position differs according to the distance between the pile and tunnel. After the enlarged excavation on the invert, the increase in the horizontal displacement is smaller than that after the excavation on the sidewall. As to the vertical displacement and axial force, the increase is prominent and the increasing value is larger than the excavation on the sidewall. After the reinforcement measures of advanced pre-supporting and radial grouting are used, According the results, the internal forces and deformations of piles decreases after measures were taken. Compared with measured data on site, the control effect is good.

scholarly journals Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation

2016 ◽  
Vol 9 ◽  
pp. 9-25 ◽  
Author(s):  
Hareram Lohar ◽  
Anirban Mitra ◽  
Sarmila Sahoo
Keyword(s):  
Elastic Foundation ◽  
Static Problem ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Dimensionless Frequency ◽  
Energy Principle ◽  
Various Boundary Conditions ◽  
Non Linear ◽  
Beams On Elastic Foundation ◽  
Minimum Potential Energy Principle

A displacement based semi-analytical method is utilized to study non-linear free vibration and mode shapes of an exponential tapered axially functionally graded (AFG) beam resting on an elastic foundation. In the present study geometric nonlinearity induced through large displacement is taken care of by non-linear strain-displacement relations. The beam is considered to be slender to neglect the rotary inertia and shear deformation effects. In the present paper at first the static problem is solved through an iterative scheme using a relaxation parameter and later on the subsequent dynamic analysis is carried out as a standard eigen value problem. Energy principles are used for the formulation of both the problems. The static problem is solved by using minimum potential energy principle whereas in case of dynamic problem Hamilton’s principle is employed. The free vibrational frequencies are tabulated for exponential taper profile subject to various boundary conditions and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane and in some particular case the mode shape results are furnished.

scholarly journals Models and Techniques of Automatic Humidity Temperature setting on Oyster Mushrooms using Digital Skylite

2019 ◽  
Vol 12 (6) ◽  
pp. 71-75
Author(s):  
Ananto ◽  
Nofrita Sandi ◽  
I Ketut Budaraga
Keyword(s):  
Current Source ◽  
Design Model ◽  
Oyster Mushroom ◽  
Maximum Temperature ◽  
Mushroom Cultivation ◽  
Temperature Regulator ◽  
Automatic Temperature ◽  
Maintenance Techniques ◽  
Oyster Mushrooms ◽  
The Right

Oyster mushroom cultivation in areas that have high temperatures requires special maintenance techniques. The development of technology now makes it easy to carry out maintenance treatments for oyster mushrooms. Not even a few can regulate temperature and humidity automatically in the cultivation room. With an automatic temperature regulator can facilitate maintenance and minimize the failure of oyster mushroom production. However, the humidity temperature setting is not perfect enough if there are no models and adjusting techniques. The model that will be made by using Digital Skylite which is connected to the current source, Digital Skylite functions as an automatic timer. The purpose of this research is to get the right tool design model using Digital Skylite and to see the correct length of time in the Digital Skylite settings. The method used in data collection in this study is Direct Observation (Observation), Observation is carried out by examining and observing the object under study directly. The results of the study were to obtain a maximum temperature regulation design model.

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