A new simplified method for anti-symmetric mode in-plane vibrations of frame structures with column cracks

2016 ◽  
Vol 24 (24) ◽  
pp. 5794-5810 ◽  
Author(s):  
Kemal Mazanoglu ◽  
Elif C Kandemir-Mazanoglu
Keyword(s):  
Beam Theory ◽  
Equivalent Model ◽  
Frame Structures ◽  
Symmetric Mode ◽  
Lumped Mass ◽  
Beam Elements ◽  
Local Flexibility ◽  
Mode Vibration ◽  
Frame Systems ◽  
Lumped Masses

This paper is on the natural frequency and mode shape computation of frame structures with column cracks. First, a model of intact frame structures is built to perform vibration analysis. Beam elements are considered as lumped masses and rotational springs at the storey levels of frames. Equivalent model of columns and lumped mass-stiffness effects of beams have been combined to carry out continuous solution for the anti-symmetric mode in-plane vibrations of frames. In addition, frame systems with multiple column cracks are analyzed in terms of anti-symmetric mode vibration characteristics. Cracks are considered as massless rotational springs in compliance with the local flexibility model. Compatibility and continuity conditions are satisfied at crack and storey locations of the equivalent column, modeled using the Euler–Bernoulli beam theory. The proposed method is tested for single-storey single- and multi-bay, H-type and double-storey single-bay frame systems with intact and cracked columns. Results are validated by those given in the current literature and/or obtained by the finite element analyses.

Large Displacement Matrix Analysis of Elastic/Viscoplastic, Plane Frame Structures

1975 ◽  
Vol 97 (4) ◽  
pp. 1238-1244
Author(s):  
Rong Chung Shieh
Keyword(s):  
Beam Theory ◽  
Rate Sensitivity ◽  
Correlation Study ◽  
Large Displacement ◽  
Matrix Analysis ◽  
Frame Structures ◽  
Plastic Behavior ◽  
Lumped Mass ◽  
Experimental Correlation ◽  
Plane Frame

Within the framework of lumped mass/elementary beam theory, a large displacement matrix analysis of elastic/perfectly viscoplastic plane frame structures undergoing primarily flexural deformations and following a constitutive power law is first formulated. A general purpose computer program based on the step-by-step computational procedure in conjunction with the fourth order Runge-Kutta integration technique is then developed. The computerized study is then used in an analytical/experimental correlation study of the dynamic response of a laboratory impact test problem of a mild steel plane frame dropped into a narrow rigid pole obstacle at 20 mph (32.2 km/hr); good analytical and experimental correlation results are obtained up to 2 percent of strain. An example problem of inelastic response of an automobile bumper (beam) subjected to impact loading is also given. Discussion of the results with regard to strain rate sensitivity effects on dynamic plastic behavior and comparison of the “exact” solution with those obtained under certain simplified approximations are made.

Development of an Adjustable Frequency Device for a Test Vehicle Based on Curved Beam Theory

2021 ◽  
Vol 8 ◽  
pp. 5-8
Author(s):  
J. D. Yau ◽  
S. Urushadze
Keyword(s):  
Experimental Studies ◽  
Beam Theory ◽  
Frequency Measurement ◽  
Curved Beam ◽  
Beam Model ◽  
Lumped Mass ◽  
Test Beam ◽  
Test Vehicle ◽  
Instrumented Vehicle ◽  
Thin Beams

In this article, an adjustable frequency device based on curved beam theory is designed to control vertical stiffness of an instrumented vehicle that it can detect dynamic data when moving on a test beam for frequency measurement. The adjustable frequency device consists of a set of two-layer cantilever semi-circular thin-beams to support a lumped mass for vibrations, in which a rotatable U-frame is used to change its subtended angle for adjustment of the supporting stiffness and corresponding vertical frequencies of the vehicle. Based on curved beam theory, an analytical frequency equation of the single-degree-of-freedom test vehicle was derived and applied to mobile frequency measurement of a simple beam. To determine the sectional rigidity of the semi-circular thin-beams, both theoretical and experimental studies were be carried out in the ITAM laboratory of the Academy of Science in Czech. The analytical and experimental results indicated that the present semi-circular beam model with guided ends is applicable to prediction of natural frequencies of the test vehicle considering different supporting stiffness

scholarly journals Lateral-Mode Vibration of Microcantilever-Based Sensors in Viscous Fluids Using Timoshenko Beam Theory

2015 ◽  
Vol 24 (4) ◽  
pp. 848-860 ◽  
Author(s):  
Joshua A. Schultz ◽  
Stephen M. Heinrich ◽  
Fabien Josse ◽  
Isabelle Dufour ◽  
Nicholas J. Nigro ◽  
...  
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Viscous Fluids ◽  
Mode Vibration ◽  
Lateral Mode

Response of Electrostatically Actuated Flexible MEMS Structures to the Onset of Low-Velocity Contact

2009 ◽  
Author(s):  
Bryan Wilcox ◽  
Harry Dankowicz ◽  
Walter Lacarbonara
Keyword(s):  
Steady State ◽  
Contact Region ◽  
Response Amplitude ◽  
Physical Contact ◽  
Model Description ◽  
System Response ◽  
Scaling Effects ◽  
Lumped Mass ◽  
Low Velocity ◽  
Beam Elements

Near-grazing, low-velocity contact in vibro-impacting systems has been shown to result in dramatic changes in steady-state system response following rapid transient growth of deviations away from the pre-grazing steady-state response. In low-dimensional example systems such transitions are often associated with large jumps in response amplitude. Coupled with the rapidity of the transient dynamics, this phenomenology supports the design of limit-switch sensors that trigger at the onset of grazing contact. A particularly exciting area of application of such sensors, and one in which their implementation might offer particular advantages, is in the context of microelectromechanical structures. Here, desirable scaling effects, such as increased system frequencies, low damping, batch fabrication, and decreased packaging size, can be leveraged. Fabricating simple beam structures at the microscale is relatively easier than fabricating proof-mass-based lumped-parameter systems with elaborate suspension structures. Consequently, it often becomes necessary to account for the flexibility of participating mechanical members, for example doubly-clamped, silicon-based beam elements. Physical contact further poses modeling challenges, as the flexibility of the beam elements and that of the contact region necessitate a compliant, but very stiff model description. The present work investigates a sequence of reduced-order models for such a doubly-clamped beam, subject to capacitive electrostatic actuation and a low-compliance physical constraint localized at a point along the span of the beam. The objective is to determine whether grazing-induced transitions, characteristic of lumped-mass models, are retained in the flexible structure. Specifically, numerical simulations are employed to quantify the variations in the response amplitude following the onset of contact and to contrast these to a spreading of system energy across mechanical modes.

Modeling and Experimentation of a Ribbed Caudal Fin for Aquatic Robots

2017 ◽  
Author(s):  
Oscar Rios ◽  
Ardavan Amini ◽  
Hidenori Murakami
Keyword(s):  
Large Deformation ◽  
Beam Theory ◽  
Fe Model ◽  
Beam Model ◽  
Caudal Fin ◽  
Nonlinear Beam ◽  
Beam Elements ◽  
Side Walls ◽  
Thin Beams ◽  
Shear Deformable

Presented in this study is a mathematical model and preliminary experimental results of a ribbed caudal fin to be used in an aquatic robot. The ribbed caudal fin is comprised of two thin beams separated by ribbed sectionals as it tapers towards the fin. By oscillating the ribbed caudal fin, the aquatic robot can achieve forward propulsion and maneuver around its environment. The fully enclosed system allows for the aquatic robot to have very little effect on marine life and fully blend into its respective environment. Because of these advantages, there are many applications including surveillance, sensing, and detection. Because the caudal fin actuator has very thin side walls, Kirchhoff-Love’s large deformation beam theory is applicable for the large deformation of the fish-fin actuator. In the model, it is critical to accurately model the curvature of beams. To this end, C1 beam elements for thin beams are developed by specializing the shear-deformable beam elements, developed by the authors, based upon Reissner’s shear-deformable nonlinear beam model. Furthermore, preliminary experiments on the ribbed fin are presented to supplement the FE model.

scholarly journals A non-linear element for analysing elastic frame structures at large deflections

2000 ◽  
Vol 22 (1) ◽  
pp. 19-28
Author(s):  
Nguyen Dinh Kien
Keyword(s):  
Beam Theory ◽  
Frame Structures ◽  
Large Deflections ◽  
Force Vector ◽  
Tangent Stiffness Matrix ◽  
Nodal Force ◽  
Axial Forces ◽  
Non Linear Equation ◽  
Non Linear ◽  
Raphson Method

A non-linear finite element for analyzing elastic frame structures at large deflections is presented. A co-rotational technique combined with Classical beam theory with the inclusion of the effect of axial forces is adopted. The element nodal force vector is derived from the strain energy of the element. The element tangent stiffness matrix is obtained by differentiating the nodal force vector, with respect to the degree of freedom (d.o.f.). The obtained formulations have a simple and compact mathematical forms which are easy to implement into a computer program. An incremental interactive technique based on Newton-Raphson method is adopted to solve the non-linear equation and to trace the equilibrium paths of the structures. Numerical examples are presented to show the accuracy and efficiency of the proposed formulations.

scholarly journals Natural Frequencies and Mode Shapes of Drill Pipe in Subsea Xmas Tree Installation

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Wensheng Xiao ◽  
Haozhi Qin ◽  
Jian Liu ◽  
Qi Liu ◽  
Junguo Cui ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Drill Pipe ◽  
Beam Theory ◽  
Transformation Method ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Order Partial Differential Equation ◽  
Lumped Mass ◽  
Acceleration Sensors

In this study, experimental and numerical investigations on the vibration characteristics of a drill pipe during the lowering of a subsea Xmas tree were presented. A fourth-order partial differential equation with variable coefficients was established based on Euler–Bernoulli beam theory. The natural frequencies and mode shapes are obtained by using the differential transformation method. Four drill pipe models of different sizes were used in the experiments which were measured using piezoelectric acceleration sensors and fiber Bragg grating sensors, respectively. The factors that affect the natural frequencies and mode shapes, such as length, diameter, lumped mass, and boundary conditions, were analyzed. The results show that all factors have remarkable effects on the natural frequency, but changes in the length and diameter of the pipe have little effect on the mode shapes; the main factors affecting the mode shape are the boundary conditions and lumped mass. The results of the numerical calculation were validated by a comparison with the experimental results and showed good agreement.

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