On the Mechanism of Bandgap Formation in Beams With Periodic Arrangement of Beam-Like Resonators

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Ó. Serrano ◽  
R. Zaera ◽  
J. Fernández-Sáez
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Band Structure ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Numerical Procedure ◽  
The Finite Element Method ◽  
Horizontal Beam ◽  
Bloch’S Theorem ◽  
Periodic Arrangement

Abstract Metastructures made of spring-mass resonators present a bandgap at the natural frequency of the resonator. This rule cannot be generalized for more complex resonators. This work analyzes the case of a metastructure composed of a periodic arrangement of vertical beams rigidly joined to a horizontal beam. The vertical beams work as resonators, and their natural frequencies play a strong role on the band structure of the whole system, however, different than the case with spring-mass resonators. Since this metastructure can be considered a lattice, Bloch’s theorem is applied to the unit cell and a numerical procedure based on the finite element method permits to obtain the dispersion curves. Illustrative results show the influence of the natural frequencies of the horizontal and vertical beams on the band structure.

Natural Frequencies of Rectangular Membrane With Boundary Perturbation

1995 ◽  
Vol 1 (2) ◽  
pp. 139-144 ◽  
Author(s):  
Jamal A. Masad
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Perturbation Approach ◽  
Boundary Perturbation ◽  
The Finite Element Method ◽  
Analytic Expression ◽  
Element Method

A perturbation approach, coupled with the adjoint concept, is used to derive an analytic expression for the natural frequencies of a nearly rectangular membrane. The method is applied for a rectangular membrane with a semicircle at one of the boundaries. The fundamental natural frequency results for this configuration are presented and compared with results from a finite-element method and results from an approximate Galerkin method. The agreement between the fundamental natural frequencies calculated with the perturbation approach and those calculated with the finite-element method improves as the radius of the semicircle decreases and as the semicircle location becomes more eccentric.

Influence Analysis of Hull Deformation on Dynamic Behavior of Propulsion Shafting

2014 ◽  
Vol 904 ◽  
pp. 432-436
Author(s):  
Feng Bao An ◽  
Ping Yang ◽  
Xin Ping Yan ◽  
Ming Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequency ◽  
Dynamic Behavior ◽  
Natural Frequencies ◽  
Container Ship ◽  
Structure Model ◽  
The Finite Element Method ◽  
Ship Structure ◽  
Ship Propulsion

The aim of this paper is to study the influence of hull deformation on dynamic behavior of ship propulsion shafting. Taking an 8530TEU container ship as an objective and using the finite element method, a global ship structure model is built up to evaluate the hull deformations under typical loading cases. Then the hull bottom-propulsion shafting integrated model is adopted to analyze the effect of hull deformation on shafting natural frequency under dry and wet mode. The results show that the natural frequencies of the shafting will increase due to the effect of hull deformation. Consequently, it is necessary to consider the effect of ship deformation when dealing with the dynamic behavior of ship propulsion shafting.

scholarly journals Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Juliano dos Santos Becho ◽  
Marcelo Greco
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rheological Model ◽  
Iterative Process ◽  
Numerical Procedure ◽  
Viscoelastic Behavior ◽  
Retardation Time ◽  
The Finite Element Method ◽  
Divergence Problem ◽  
Element Method

A numerical procedure is presented to avoid the divergence problem during the iterative process in viscoelastic analyses. This problem is observed when the positional formulation of the finite element method is adopted in association with the finite difference method. To do this, the nonlinear positional formulation is presented considering plane frame elements with Bernoulli–Euler kinematics and viscoelastic behavior. The considered geometrical nonlinearity refers to the structural equilibrium analysis in the deformed position using the Newton–Raphson iterative method. However, the considered physical nonlinearity refers to the description of the viscoelastic behavior through the adoption of the stress-strain relation based on the Kelvin–Voigt rheological model. After the presentation of the formulation, a detailed analysis of the divergence problem in the iterative process is performed. Then, an original numerical procedure is presented to avoid the divergence problem based on the retardation time of the adopted rheological model and the penalization of the nodal position correction vector. Based on the developments and the obtained results, it is possible to conclude that the presented formulation is consistent and that the proposed procedure allows for obtaining the equilibrium positions for any time step value adopted without presenting divergence problems during the iterative process and without changing the analysis of the final results.

scholarly journals Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method

2021 ◽  
Vol 13 (11) ◽  
pp. 168781402110609
Author(s):  
Hossein Talebi Rostami ◽  
Maryam Fallah Najafabadi ◽  
Davood Domiri Ganji
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Variable Properties ◽  
The Third ◽  
Koch Snowflake

This study analyzed a Timoshenko beam with Koch snowflake cross-section in different boundary conditions and for variable properties. The equation of motion was solved by the finite element method and verified by Solidworks simulation in a way that the maximum error was about 2.9% for natural frequencies. Displacement and natural frequency for each case presented and compared to other cases. Significant research achievements illustrate that if we change the Koch snowflake cross-section of the beam from the first iteration to the second, the area and moment of inertia will increase, and we have a 5.2% rise in the first natural frequency. Similarly, by changing the cross-section from the second iteration to the third, a 10.2% growth is observed. Also, the hollow cross-section is considered, which can enlarge the natural frequency by about 26.37% compared to a solid one. Moreover, all the clamped-clamped, hinged-hinged, clamped-free, and free-free boundary conditions have the highest natural frequency for the Timoshenko beam with the third iteration of the Koch snowflake cross-section in solid mode. Finally, examining important physical parameters demonstrates that variable density from a minimum value to the standard value along the beam increases the natural frequencies, while variable elastic modulus decreases it.

scholarly journals COMPARISON OF SAW BLADE NATURAL FREQUENCIES AND CRITICAL SPEEDS USING CSAW AND FINITE ELEMENT ANALYSIS

2011 ◽  
Author(s):  
J. Poirier ◽  
P. Radziszewski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Saw Blade ◽  
Circular Saws ◽  
The Finite Element Model ◽  
Element Method

The natural frequencies of circular saws limit the operating speeds of the saws. Current industry methods of increasing natural frequency include pretensioning, where plastic deformation is induced into the saw. To better model the saw, the finite element model is compared to current software for steel saws; C-SAW, a software program that calculates frequencies for stiffened circular saws. Using C-SAW and the finite element method the results are compared and the finite element method is validated for steel saws.

scholarly journals MODAL ANALYSIS OF REINFORCED CONCRETE AND FIBER CONCRETE BEAMS

2021 ◽  
Vol 3 (1) ◽  
pp. 95-105
Author(s):  
T. Makovkina ◽  
◽  
M. Surianinov ◽  
O. Chuchmai ◽  
◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reinforced Concrete ◽  
Computer Modeling ◽  
Natural Frequencies ◽  
Concrete Beams ◽  
The Finite Element Method ◽  
Fiber Concrete ◽  
Experimental Researches ◽  
Element Method

Analytical, experimental and numerical results of determination of natural frequencies and forms of oscillations of reinforced concrete and fiber concrete beams are given. Modern analytical, numerical and experimental methods of studying the dynamics of reinforced concrete and fiber concrete beams are analyzed. The problem of determining the natural frequencies and forms of oscillations of reinforced concrete and fiber concrete beams at the initial modulus of elasticity and taking into account the nonlinear diagram of deformation of materials is solved analytically. Computer modeling of the considered constructions in four software complexes is done and the technique of their modal analysis on the basis of the finite element method is developed. Experimental researches of free oscillations of the considered designs and the comparative analysis of all received results are carried out. It is established that all involved complexes determine the imaginary frequency and imaginary form of oscillations. The frequency spectrum calculated by the finite element method is approximately 4% lower than that calculated analytically; the results of the calculation in SOFiSTiK differ by 2% from the results obtained in the PC LIRA; the discrepancy with the experimental data reaches 20%, and all frequencies calculated experimentally, greater than the frequencies calculated analytically or by the finite element method. This rather significant discrepancy is explained, according to the authors, by the incorrectness of the used dynamic model of the reinforced beam. The classical dynamics of structures is known to be based on the theory of linear differential equations, and the oscillations of structures are considered in relation to the unstressed initial state. It is obvious that in the study of free and forced oscillations of reinforced concrete building structures such an approach is unsuitable because they are physically nonlinear systems. The concept of determining the nonlinear terms of these equations is practically not studied. Numerous experimental researches and computer modeling for the purpose of qualitative and quantitative detection of all factors influencing a spectrum of natural frequencies of fluctuations are necessary here.

A Maxwell's Second Equation Approach to the Finite Element Method Applied to Magnetic Field Determination

1987 ◽  
Vol 24 (3) ◽  
pp. 259-272 ◽  
Author(s):  
José Roberto Cardoso
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Undergraduate Students ◽  
Engineering Students ◽  
Numerical Procedure ◽  
The Finite Element Method ◽  
Cad Cam ◽  
New Formulation ◽  
The Galerkin Method ◽  
Element Method

The burst of modern computing systems like CAD/CAM has given rise to the use of the finite element method (FEM), which is, at present, the most used numerical procedure in the determination of fields in continuous media. Undergraduate students find difficulty in understanding the usual way of demonstrating FEM by variational analysis or the Galerkin method. This paper introduces a new formulation of FEM, based on a direct application of Maxwell's second equation, which can be easily understood by undergraduate engineering students.

Parallelogrammic elements in the solution of rhombic cantilever plate problems

1966 ◽  
Vol 1 (3) ◽  
pp. 223-230 ◽  
Author(s):  
D. J. Dawe
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequencies ◽  
Cantilever Plate ◽  
Plate Element ◽  
The Finite Element Method ◽  
Skew Angle ◽  
Distributed Load ◽  
Uniformly Distributed Load ◽  
Element Method

The finite element method is applied to the calculation of the deflection under a uniformly distributed load and the natural frequencies of the rhombic cantilever plate. This has required the derivation of stiffness and inertia matrices for a plate element of parallelogrammic planform. Although, in common with the work of past investigators, the accuracy of the results decreases with increase in skew angle it is shown that the method is adequate for angles up to about 45°.

The Vibration Characteristics Analysis of Ship Foundation Based on the Arrangement of Isolators

2011 ◽  
Vol 55-57 ◽  
pp. 2202-2205
Author(s):  
Yu Wang ◽  
Xing Lin Chen ◽  
Guang Min Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequency ◽  
Vibration Characteristics ◽  
Force Characteristic ◽  
The Finite Element Method ◽  
Foundation Vibration ◽  
Characteristics Analysis ◽  
Excitation Force ◽  
General Connection

Contrary to the general connection style, the vibration characteristics of the ship foundation vibration is researched under the arrangement style of isolators acted on it. And the influence of the parameters of rigidity and damp to the excitation force characteristic is studied too. Based on the real ship data and the finite element method, the study is shown that the excitation force from the device to the foundation is not only related to the rigidity, damp of isolators and the natural frequency of device-isolator-foundation system but also the related to arrangement style of isolator. When the excited frequency is lower it had little effect on the vibration characteristics relatively. However that the frequency is higher, it had significant effect on the vibration.

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