scholarly journals Confinement of Vibrations in Variable-Geometry Nonlinear Flexible Beam

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
W. Gafsi ◽  
F. Najar ◽  
S. Choura ◽  
S. El-Borgi
Keyword(s):  
Passive Control ◽  
Inverse Eigenvalue Problem ◽  
Beam Dynamics ◽  
Mode Shapes ◽  
Physical Parameters ◽  
Geometrical Parameters ◽  
Flexible Beam ◽  
Beam Model ◽  
Nonlinear Frequency ◽  
Nonlinear Beam

In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differential equation that describes the beam dynamics. The nonlinear frequency response curves of the beam are approximated using the differential quadrature method and the finite difference method. We confirm that using the linear model, the strategy of vibration confinement remains valid for the nonlinear beam.

Natural Frequencies and Mode Shapes of Slacked Carbon Nanotube NEMS Resonators

2010 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammed I. Younis
Keyword(s):  
Natural Frequencies ◽  
Electrostatic Force ◽  
Static Solution ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Physical Parameters ◽  
Beam Model ◽  
Order Model ◽  
Research Attention ◽  
Reduced Order

Estimating accurately the natural frequencies of electrically actuated carbon nanotubes (CNTs) has been the center of research attention over the past few years. Despite this important topic, a robust knowledge is still missing to understand the role of various physical parameters that affect the natural frequencies, such as the stretching of doubly-clamped CNTs, the DC electrostatic force, and the curvature of CNTs with slacks. In this investigation, we use a 2D nonlinear curved beam model (arch) to simulate the coupled in-plane and the out-of-plane motions of a CNT with curvature (slack). We calculate the variation of its natural frequencies and mode-shapes with the level of slack and the DC electrostatic load. Toward this, we derive a reduced-order model using a multi-mode Galerkin procedure based on the mode shapes of the straight unactuated CNT. We calculate the natural frequencies of the slacked CNT for a given voltage by substituting the static solution into the Jacobian of the reduced-order-model and then finding the corresponding eigenvalues. We show various scenarios of mode crossing and mode veering as the levels of slack and DC load are varied.

Flexural Vibration of Prestressed Concrete Bridges with Corrugated Steel Webs

2017 ◽  
Vol 17 (02) ◽  
pp. 1750023 ◽  
Author(s):  
Xia-Chun Chen ◽  
Zhen-Hu Li ◽  
Francis T. K. Au ◽  
Rui-Juan Jiang
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Prestressed Concrete ◽  
Natural Frequencies ◽  
Sandwich Beam ◽  
Flexural Vibration ◽  
Concrete Bridges ◽  
Mode Shapes ◽  
Beam Model ◽  
Prestressed Concrete Bridges

Prestressed concrete bridges with corrugated steel webs have emerged as a new form of steel-concrete composite bridges with remarkable advantages compared with the traditional ones. However, the assumption that plane sections remain plane may no longer be valid for such bridges due to the different behavior of the constituents. The sandwich beam theory is extended to predict the flexural vibration behavior of this type of bridges considering the presence of diaphragms, external prestressing tendons and interaction between the web shear deformation and flange local bending. To this end, a [Formula: see text] beam finite element is formulated. The proposed theory and finite element model are verified both numerically and experimentally. A comparison between the analyses based on the sandwich beam model and on the classical Euler–Bernoulli and Timoshenko models reveals the following findings. First of all, the extended sandwich beam model is applicable to the flexural vibration analysis of the bridges considered. By letting [Formula: see text] denote the square root of the ratio of equivalent shear rigidity to the flange local flexural rigidity, and L the span length, the combined parameter [Formula: see text] appears to be more suitable for considering the diaphragm effect and the interaction between the shear deformation and flange local bending. The diaphragms have significant effect on the flexural natural frequencies and mode shapes only when the [Formula: see text] value of the bridge falls below a certain limit. For a bridge with an [Formula: see text] value over a certain limit, the flexural natural frequencies and mode shapes obtained from the sandwich beam model and the classical Euler–Bernoulli and Timoshenko models tend to be the same. In such cases, either of the classical beam theories may be used.

An Approach to Approximate the Full Strain Field of Turbofan Blades During Operation

2018 ◽  
Author(s):  
Gen Fu ◽  
Alexandrina Untaroiu ◽  
Walter O’Brien
Keyword(s):  
Numerical Model ◽  
Cantilever Beam ◽  
Strain Field ◽  
Measured Data ◽  
Mode Shapes ◽  
Beam Model ◽  
Reference Solution ◽  
Full Field ◽  
Field Response ◽  
Critical Locations

The measurement of the aeromechanical response of the fan blades is important to quantifying their integrity. The accurate knowledge of the response at critical locations of the structure is crucial when assessing the structural condition. A reliable and low cost measuring technique is necessary. Currently, sensors can only provide the measured data at several discrete points. A significant number of sensors may be required to fully characterize the aeromechanical response of the blades. However, the amount of instrumentation that can be placed on the structure is limited due to data acquisition system limitations, instrumentation accessibility, and the effect of the instrumentation on the measured response. From a practical stand point, it is not possible to place sensors at all the critical locations for different excitations. Therefore, development of an approach that derives the full strain field response based on a limited set of measured data is required. In this study, the traditional model reduction method is used to expand the full strain field response of the structure by using a set of discrete measured data. Two computational models are developed and used to verify the expansion approach. The solution of the numerical model is chosen as the reference solution. In addition, the numerical model also provides the mode shapes of the structure. In the expansion approach, this information is used to develop the algorithm. First, a cantilever beam model is created. The influences of the sensor location, number of sensors and the number of modes included are analyzed using this cantilever beam model. The expanded full field response data is compared with the reference solution to evaluate the expansion procedure. The rotor 67 blade model is then used to test the expansion method. The results show that the expanded full field data is in good agreement with the calculated data. The expansion algorithm can be used for the full field strain by using the limited sets of strain data.

scholarly journals A Multiobjective Perspective to Optimal Sensor Placement by Using a Decomposition-Based Evolutionary Algorithm in Structural Health Monitoring

2020 ◽  
Vol 10 (21) ◽  
pp. 7710
Author(s):  
Tsung-Yueh Lin ◽  
Jin Tao ◽  
Hsin-Haou Huang
Keyword(s):  
Structural Health Monitoring ◽  
Evolutionary Algorithm ◽  
Health Monitoring ◽  
Sensor Placement ◽  
Frame Structure ◽  
Mode Shapes ◽  
Beam Model ◽  
Optimal Sensor Placement ◽  
Modal Assurance Criterion ◽  
Structural Health

The objective of optimal sensor placement in a dynamic system is to obtain a sensor layout that provides as much information as possible for structural health monitoring (SHM). Whereas most studies use only one modal assurance criterion for SHM, this work considers two additional metrics, signal redundancy and noise ratio, combining into three optimization objectives: Linear independence of mode shapes, dynamic information redundancy, and vibration response signal strength. A modified multiobjective evolutionary algorithm was combined with particle swarm optimization to explore the optimal solution sets. In the final determination, a multiobjective decision-making (MODM) strategy based on distance measurement was used to optimize the aforementioned objectives. We applied it to a reduced finite-element beam model of a reference building and compared it with other selection methods. The results indicated that MODM suitably balanced the objective functions and outperformed the compared methods. We further constructed a three-story frame structure for experimentally validating the effectiveness of the proposed algorithm. The results indicated that complete structural modal information can be effectively obtained by applying the MODM approach to identify sensor locations.

scholarly journals Phononic Band Gap and Free Vibration Analysis of Fluid-Conveying Pipes with Periodically Varying Cross-Section

2021 ◽  
Vol 11 (21) ◽  
pp. 10485
Author(s):  
Hao Yu ◽  
Feng Liang ◽  
Yu Qian ◽  
Jun-Jie Gong ◽  
Yao Chen ◽  
...  
Keyword(s):  
Free Vibration ◽  
Band Gap ◽  
Cross Section ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Critical Parameters ◽  
Mode Shapes ◽  
Beam Model ◽  
The Impact ◽  
Fluid Conveying Pipes

Phononic crystals (PCs) are a novel class of artificial periodic structure, and their band gap (BG) attributes provide a new technical approach for vibration reduction in piping systems. In this paper, the vibration suppression performance and natural properties of fluid-conveying pipes with periodically varying cross-section are investigated. The flexural wave equation of substructure pipes is established based on the classical beam model and traveling wave property. The spectral element method (SEM) is developed for semi-analytical solutions, the accuracy of which is confirmed by comparison with the available literature and the widely used transfer matrix method (TMM). The BG distribution and frequency response of the periodic pipe are attained, and the natural frequencies and mode shapes are also obtained. The effects of some critical parameters are discussed. It is revealed that the BG of the present pipe system is fundamentally induced by the geometrical difference of the substructure cross-section, and it is also related to the substructure length and fluid–structure interaction (FSI). The number of cells does not contribute to the BG region, while it has significant effects on the amplitude attenuation, higher order natural frequencies and mode shapes. The impact of FSI is more evident for the pipes with smaller numbers of cells. Moreover, compared with the conventional TMM, the present SEM is demonstrated more effective for comprehensive analysis of BG characteristics and free vibration of PC dynamical structures.

scholarly journals The Effect of Inner Reinforcing Cores on Natural Frequencies of the Lathe Tool Body

2013 ◽  
Vol 21 (Special-Issue) ◽  
pp. 186-192 ◽  
Author(s):  
Ladislav Rolník ◽  
Milan Naď
Keyword(s):  
Material Properties ◽  
Machine Tools ◽  
Structural Modification ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Geometrical Parameters ◽  
Structural Modifications ◽  
Modal Properties ◽  
Machine Productivity ◽  
Lathe Tool

Abstract The contribution is mainly focused on research and development of structural modification of machine tools, lathes in particular. The main aim of the modification is to change the modal properties (mode shapes, natural frequencies) of the lathe tool. The main objective of the contribution will be to formulate, mathematical analyse and evaluate the proposed methods and procedures for structural modifications of the tool, represented by beam body. A modification of modal properties by insertion of beam cores into beam body is studied in this paper. In this paper, the effect of material properties and geometrical parameters of reinforcing cores on natural frequencies of beam body is presented. The implementation will bring benefit on machine productivity, decreasing the machine tool wear and in many cases it will lead to better conditions in the cutting process.

scholarly journals Application of the Generalized Nonlinear Constitutive Law in 2D Shear Flexible Beam Structures

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Reference Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Flexible Beam ◽  
Beam Model ◽  
Beam Structures ◽  
Nodal Displacements ◽  
Nonlinear Constitutive Law

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

Piezoelectric energy harvesting from highly flexible cantilever beam

2018 ◽  
Vol 233 (1) ◽  
pp. 71-92
Author(s):  
Sam Fallahpasand ◽  
Morteza Dardel
Keyword(s):  
Energy Harvesting ◽  
Cantilever Beam ◽  
External Source ◽  
Flexible Beam ◽  
Chaotic Oscillations ◽  
Nonlinear Beam ◽  
Piezoelectric Energy ◽  
Highly Nonlinear ◽  
Strain Model

In many studies, linear or small deflections according to Von Karman strain model are used for energy harvesting of beam’s structures. Analyses of these types are not reliable when deformations become large. In this work, an integro-differential equation of highly flexible cantilever beam with a piezoelectric layer is presented. The harvester is composed of a thin flexible beam with attached piezoceramic which undergoes large deformations. Periodic and chaotic oscillations and their effects on the quality of harvesting energy procedure are investigated. The obtained results showed that chaotic oscillations improve energy harvesting. This means that large deflections in high-flexible electromechanical systems let harvester to gather more energy from the external source in a much wider frequency domain. Fast Fourier transform shows the emerging lots of resonance peaks in the chaotic region, which give cascade of resonances for this highly nonlinear beam. Moreover, it is discussed how this mechanism and its frequency characteristics enhances the quality and quantity of energy harvesting. The present study show how increasing the flexibility of structure can lead to high deflection and obtaining broadband energy harvesting with better energy harvesting characteristics.

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