Equilibrium Configurations of Cantilever Beams Subjected to Inclined End Loads

1992 ◽  
Vol 59 (3) ◽  
pp. 572-579 ◽  
Author(s):  
S. Navaee ◽  
R. E. Elling
Keyword(s):  
Cantilever Beam ◽  
Loading Condition ◽  
Multiple Equilibrium ◽  
Cantilever Beams ◽  
Equilibrium Solutions ◽  
Constant Angle ◽  
Equilibrium Configurations ◽  
Inclination Angles ◽  
Beam Parameters

In this study, equilibrium configurations of a cantilever beam subjected to an end load with constant angle of inclination is investigated. It is shown analytically that if the beam is sufficiently flexible, there are multiple equilibrium solutions for a specific beam and loading condition. A method is also presented for the determination of these deflected configurations. The cantilever beam studied in this research is considered to be initially straight and prismatic in addition to being homogeneous, elastic, and isotropic. The procedure outlined in this paper is utilized to show that for each combination of load and beam parameters, there are certain number of equilibrium configurations for a cantilever beam. The ranges of these combinations, along with some examples of the deflected shapes of the beams, are provided for several load inclination angles.

Error analyses of a Multi-Input-Multi-Output cantilever beam test

2021 ◽  
pp. 107754632110337
Author(s):  
Arup Maji ◽  
Fernando Moreu ◽  
James Woodall ◽  
Maimuna Hossain
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Cantilever Beam ◽  
Transfer Functions ◽  
Linear Superposition ◽  
Transfer Function Matrix ◽  
Error Analyses ◽  
Pseudo Inverse ◽  
Function Matrix

Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.

New Methodology for the Determination of the Vertical Center of Gravity of In-Service Semisubmersibles: Proposal and Numerical Assessment

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Ivan N. Porciuncula ◽  
Claudio A. Rodríguez ◽  
Paulo T. T. Esperança
Keyword(s):  
Accurate Determination ◽  
Center Of Gravity ◽  
Practical Implementation ◽  
Numerical Assessment ◽  
Neutral Equilibrium ◽  
Inclination Angles ◽  
Numerical Tools ◽  
The Stability ◽  
Metacentric Height

Along its lifetime, an offshore unit is subjected to several equipment interventions. These modifications may include large conversions in loco that usually are not adequately documented. Hence, the accurate determination of the platform's center of gravity (KG) is not possible. For vessels with low metacentric height (GM), such as semisubmersibles, Classification Societies penalize the platform's KG, inhibiting the installation of new equipment until an accurate measurement of KG is provided, i.e., until an updated inclining test is performed. For an operating semisubmersible, the execution of this type of test is not an alternative because it implies in removing the vessel from its in-service location to sheltered waters. Relatively recently, some methods have been proposed for the estimation of KG for in-service vessels. However, as all of the methods depend on accurate measurements of inclination angles and, eventually, on numerical tools for the simulation of vessel dynamics onboard, they are not straightforward for practical implementation. The objective of the paper is to present a practical methodology for the experimental determination of KG, without the need of accurate measurements of inclinations and/or complex numerical simulations, but based on actual operations that can be performed onboard. Indeed, the proposed methodology relies on the search, identification, and execution of a neutral equilibrium condition where, for instance, KG = KM. The method is exemplified using actual data of a typical semisubmersible. The paper also numerically explores and discusses the stability of the platform under various conditions with unstable initial GM, as well as the effect of mooring and risers.

scholarly journals Large Deflection Model for Multiple, Inline, Interacting Cantilever Beams

2020 ◽  
Vol 88 (4) ◽  
Author(s):  
Austin Bebee ◽  
Christopher J. Stubbs ◽  
Daniel J. Robertson
Keyword(s):  
Mathematical Model ◽  
Flexural Rigidity ◽  
Cantilever Beams ◽  
Model Concept ◽  
Math Model ◽  
Rigid Body Model ◽  
High Throughput Phenotyping ◽  
Stalk Lodging ◽  
The Mathematical Model

Abstract Numerous natural and synthetic systems can be modeled as clusters of interacting cantilever beams. However, a closed-form mathematical model capable of representing the mechanics of multiple interacting cantilever beams undergoing large deflections has yet to be presented. In this work, a pioneering mathematical model of the force–deflection response of multiple, inline, interacting (i.e., contacting) cantilever beams is presented. The math model enables the determination of the force–deflection response of a system of interacting cantilever beams and is predicated upon the “Pseudo Rigid Body Model” concept. The model was validated through data triangulation experiments which included both physical and computational studies. An analysis of the mathematical model indicates it is most accurate with deflections less than 50 deg. In the future, the model may be used in high throughput phenotyping applications for investigating stalk lodging and estimating the flexural rigidity of crop stems. The model can also be used to gain intuition and aid in the design of synthetic systems composed of multiple cantilever beams.

scholarly journals Determination of reduced mass and stiffness of flexural vibrating cantilever beam

2018 ◽  
Vol 6 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Tamerlan Omarov ◽  
Kuralay Tulegenova ◽  
Yerulan Bekenov ◽  
Gulnara Abdraimova ◽  
Algazy Zhauyt ◽  
...  
Keyword(s):  
Cantilever Beam

The Structural Properties Research of Piezoelectric Cantilever Beam Based on Vehicular Environment

2014 ◽  
Vol 525 ◽  
pp. 342-345
Author(s):  
Yan Zhao ◽  
Shan Shan Liu ◽  
Yu Feng Li
Keyword(s):  
Cantilever Beam ◽  
Simulation Analysis ◽  
Low Frequency ◽  
Electrical Energy ◽  
Body Vibration ◽  
Low Frequency Vibration ◽  
Generating Capacity ◽  
Nature Frequency ◽  
Beam Parameters ◽  
Vibration Simulation

The piezoelectric power generating device can convert the vibration energy into electrical energy in vehicular environment. So it can provide energy for electronic components. Firstly, the mathematical model of road-vehicles-piezoelectric device coupled vibration was established under the random road excitation. Then vibration simulation analysis of the established model was made. The acceleration and spectrum of the vehicles body and its connection with the suspension were researched under B-class. The car body vibration is low-frequency vibration. Further studies shows that expanding the speed range and changing the roads level almost have no effect on the natural frequency of vehicles body vibration. Secondly, in order to make the maximum generating capacity, the influences of cantilever beam parameters have on its nature frequency were researched. The research results provide basis for parameters design in cantilever beam.

scholarly journals Calibration of Design Buckling Curves for Lateral-Torsional Buckling of Cantilever Beams Made of Glass—Experimental and Numerical Investigations

2019 ◽  
Vol 9 (16) ◽  
pp. 3432
Author(s):  
Ralph Timmers ◽  
Tobias Neulichedl
Keyword(s):  
Cantilever Beam ◽  
Cantilever Beams ◽  
Testing Device ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Numerical Investigations ◽  
Buckling Behavior ◽  
Load Carrying ◽  
Special Case ◽  
Important System

Using glass as a primary load-carrying element is becoming more and more popular in architecture. Probably the most used application is the single-span girder, but another important system is the cantilever beam, which is widely used, e.g., as a canopy in front of an entrance. Research on the lateral-torsional buckling behavior of glass beams has been typically performed on single-span girders. As a consequence, the design buckling curves provided in literature are usually too conservative for the widely used case of a cantilever beam, which is also related to the loading situation. Therefore, experimental and numerical investigations have been performed for this special case. Based on the obtained results, design buckling curves have been developed and resulted in being more economical than the curves already given in the literature. Among others, information on the shape and size of the real imperfections, a testing device for cantilever beams, and experimentally and numerically obtained load-deflection curves are additional outcomes of the investigations presented here.

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