Bandgaps and vibration isolation of local resonance sandwich-like plate with simply supported overhanging beam

AbstractThe concept of local resonance phononic crystals proposed in recent years provides a new chance for theoretical and technical breakthroughs in the structural vibration reduction. In this paper, a novel sandwich-like plate model with local resonator to acquire specific low-frequency bandgaps is proposed. The core layer of the present local resonator is composed by the simply supported overhanging beam, linear spring and mass block, and well connected with the upper and lower surface panels. The simply supported overhanging beam is free at right end, and an additional linear spring is added at the left end. The wave equation is established based on the Hamilton principle, and the bending wave bandgap is further obtained. The theoretical results are verified by the COMSOL finite element software. The bandgaps and vibration characteristics of the local resonance sandwich-like plate are studied in detail. The factors which could have effects on the bandgap characteristics, such as the structural damping, mass of vibrator, position of vibrator, bending stiffness of the beam, and the boundary conditions of the sandwich-like plates, are analyzed. The result shows that the stopband is determined by the natural frequency of the resonator, the mass ratio of the resonator, and the surface panel. It shows that the width of bandgap is greatly affected by the damping ratio of the resonator. Finally, it can also be found that the boundary conditions can affect the isolation efficiency.

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Dynamic Instability Analysis and Design Charts of Curved Panels with Linearly Varying Periodic In-Plane Load

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455421501303 ◽

2021 ◽

pp. 2150130

Author(s):

G. Patel ◽

A. N. Nayak ◽

A. K. L. Srivastava

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Dynamic Instability ◽

Excitation Frequency ◽

Instability Region ◽

Concentrated Load ◽

Simply Supported ◽

Finite Element Software ◽

Design Charts ◽

Curved Panels

The present paper reports an extensive study on dynamic instability characteristics of curved panels under linearly varying in-plane periodic loading employing finite element formulation with a quadratic isoparametric eight nodded element. At first, the influences of three types of linearly varying in-plane periodic edge loads (triangular, trapezoidal and uniform loads), three types of curved panels (cylindrical, spherical and hyperbolic) and six boundary conditions on excitation frequency and instability region are investigated. Further, the effects of varied parameters, such as shallowness parameter, span to thickness ratio, aspect ratio, and Poisson’s ratio, on the dynamic instability characteristics of curved panels with clamped–clamped–clamped–clamped (CCCC) and simply supported-free-simply supported-free (SFSF) boundary conditions under triangular load are studied. It is found that the above parameters influence significantly on the excitation frequency, at which the dynamic instability initiates, and the width of dynamic instability region (DIR). In addition, a comparative study is also made to find the influences of the various in-plane periodic loads, such as uniform, triangular, parabolic, patch and concentrated load, on the dynamic instability behavior of cylindrical, spherical and hyperbolic panels. Finally, typical design charts showing DIRs in non-dimensional forms are also developed to obtain the excitation frequency and instability region of various frequently used isotropic clamped spherical panels of any dimension, any type of linearly varying in-plane load and any isotropic material directly from these charts without the use of any commercially available finite element software or any developed complex model.

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Design, Experiment, and Improvement of a Quasi-Zero-Stiffness Vibration Isolation System

Applied Sciences ◽

10.3390/app10072273 ◽

2020 ◽

Vol 10 (7) ◽

pp. 2273 ◽

Cited By ~ 1

Author(s):

Shuai Wang ◽

Wenpen Xin ◽

Yinghao Ning ◽

Bing Li ◽

Ying Hu

Keyword(s):

Vibration Isolation ◽

Damping Ratio ◽

Excitation Amplitude ◽

Isolation System ◽

Vibration Isolation System ◽

Linear Spring ◽

Isolation Effects ◽

Magnetic Rings ◽

The Relationship ◽

Force Displacement

This paper proposes a new kind of quasi-zero-stiffness (QZS) isolation system that has the property of low-dynamic but high-static stiffness. The negative stiffness was produced using two magnetic rings, the magnetization of which is axial. First, the force–displacement characteristic of the two coupled magnetic rings was developed and the relationship between the parameters of the magnetic rings and the stiffness of the system was investigated. Then, the dynamic response of the QZS was analyzed. The force transmissibility of the system was calculated and the effects of the damping ratio and excitation amplitude on the isolation performance were investigated. The prototype of the QZS system was developed to verify the isolation effects of the system based on a comparison with a linear vibration isolation platform. Lastly, the improvement of the QZS system was conducted based on changing the heights of the ring magnets and designing a proper non-linear spring. The analysis shows the QZS system after improvement shows better isolation effects than that of the non-improved system.

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Three-dimensional elasticity solution of simply supported functionally graded rectangular plates with internal elastic line supports

The Journal of Strain Analysis for Engineering Design ◽

10.1243/03093247jsa504 ◽

2009 ◽

Vol 44 (4) ◽

pp. 249-261 ◽

Cited By ~ 6

Author(s):

Y P Xu ◽

D Zhou

Keyword(s):

Boundary Conditions ◽

Young’S Modulus ◽

Young's Modulus ◽

Three Dimensional ◽

Lower Surface ◽

Functionally Graded ◽

Rectangular Plates ◽

Elastic Line ◽

Simply Supported ◽

Three Dimensional Elasticity

This paper studies the stress and displacement distributions of simply supported functionally graded rectangular plates with internal elastic line supports. The Young's modulus is graded through the thickness following the exponential law and the Poisson's ratio is kept constant. On the basis of three-dimensional elasticity theory, the solutions of displacements and stresses of the plate under static loads, which exactly satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the internal elastic line supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients in the solutions are then determined by the boundary conditions on the upper and lower surfaces of the plate. Convergence and comparison studies demonstrate the correctness and effectiveness of the proposed method. The effect of variations in Young's modulus on the displacements and stresses of rectangular plates and the effect of internal elastic line supports on the mechanical properties of plates are investigated.

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On the Free Vibration Modeling of Spindle Systems: A Calibrated Dynamic Stiffness Matrix

10.32920/14639511.v1 ◽

2021 ◽

Author(s):

Omar Gaber ◽

Seyed M. Hashemi

Keyword(s):

Boundary Conditions ◽

Fundamental Frequency ◽

Stiffness Matrix ◽

Dynamic Stiffness ◽

Dynamic Stiffness Matrix ◽

Simply Supported ◽

Multiple Components ◽

Stiffness Matrices ◽

Linear Spring ◽

Vibration Modeling

The effect of bearings on the vibrational behavior of machine tool spindles is investigated. This is done through the development of a calibrated dynamic stiffness matrix (CDSM) method, where the bearings flexibility is represented by mass less linear spring elements with tuneable stiffness. A dedicated MAT LAB code is written to develop and to assemble the element stiffness matrices for the system’s multiple components and to apply the boundary conditions.The developed method is applied to an illustrative example of spindle system.When the spindle bearings are modeled as simply supported boundary conditions, the DSM model results in a fundamental frequency much higher than the system’s nominal value.The simply supported boundary conditions are then replaced by linear spring elements, and the spring constants are adjusted such that the resulting calibrated CDSM model leads to the nominal fundamental frequency of the spindle system.The spindle frequency results are also validated against the experimental data.The proposed method can be effectively applied to predict the vibration characteristics of spindle systems supported by bearings.

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Methodology for Modeling of Passive Shunt Damping of Systems With Bonded Piezocomposites

Recent Advances in Solids and Structures ◽

10.1115/imece2005-79338 ◽

2005 ◽

Cited By ~ 1

Author(s):

Anil Saigal ◽

Robert Greif ◽

Jane Ng

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Cantilever Beam ◽

Loss Factor ◽

Heat Dissipation ◽

Damping Ratio ◽

Modeling Tools ◽

Simply Supported ◽

In Series ◽

The Impact

An aluminum cantilever beam bonded with 1-3 piezocomposite dampers is modeled by means of ANSYS finite element and SIMULINK simulation softwares. ANSYS currently cannot account for heat dissipation in piezoelectric materials. As such, ANSYS is used to obtain strain energies to be input into the SIMULINK model to investigate the dynamic behavior of the system and calculate the damping ratio. The impact of two different shunting arrangements, a damper in conjunction with a simple resistive electrical circuit in series and parallel, is investigated. In addition, a simply supported beam and a simply supported straight pipe are also analyzed for their wide applications in industry, and as an indication of the utility of this methodology to analyze complex structural configurations. For a typical cantilever beam, energy dissipation and transient analysis are used to calculate the tip displacement as a function of time and the damping ratio. Then using ANSYS, with the parameter BETAD to incorporate damping as a stiffness multiplier, a comparison of the transient results is used to quantify the damping response of aluminum beams with bonded 1-3 piezocomposite dampers. The system loss factor due to the piezoelectric damping is also compared to the inherent loss factor of different beam materials. The results show that circuits in series provides a better damping ratio (0.000581) as compared to circuits in parallel (0.000374). In addition, for different boundary conditions (cantilever, simply supported), the damping ratios (0.000581, 0.000202) and the BETAD values (6.3 E-6, 0.7 E-6), respectively, are functions of the boundary conditions and are not directly related to each other. Finally, damping using 1-3 piezocomposites effectively increases the overall system loss factor by at least 100% to almost 300% as compared to the inherent material damping. In general, this methodology of combining finite element method (ANSYS) and transient modeling tools (SIMULINK) can be used to study damping characteristics of any structural system damped with 1-3 piezocomposites.

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On the Free Vibration Modeling of Spindle Systems: A Calibrated Dynamic Stiffness Matrix

Shock and Vibration ◽

10.1155/2014/787518 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 6

Author(s):

Omar Gaber ◽

Seyed M. Hashemi

Keyword(s):

Boundary Conditions ◽

Fundamental Frequency ◽

Stiffness Matrix ◽

Dynamic Stiffness ◽

Dynamic Stiffness Matrix ◽

Spindle System ◽

Simply Supported ◽

Multiple Components ◽

Stiffness Matrices ◽

Linear Spring

The effect of bearings on the vibrational behavior of machine tool spindles is investigated. This is done through the development of a calibrated dynamic stiffness matrix (CDSM) method, where the bearings flexibility is represented by massless linear spring elements with tuneable stiffness. A dedicated MATLAB code is written to develop and to assemble the element stiffness matrices for the system’s multiple components and to apply the boundary conditions. The developed method is applied to an illustrative example of spindle system. When the spindle bearings are modeled as simply supported boundary conditions, the DSM model results in a fundamental frequency much higher than the system’s nominal value. The simply supported boundary conditions are then replaced by linear spring elements, and the spring constants are adjusted such that the resulting calibrated CDSM model leads to the nominal fundamental frequency of the spindle system. The spindle frequency results are also validated against the experimental data. The proposed method can be effectively applied to predict the vibration characteristics of spindle systems supported by bearings.

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Design and Analysis of a High-Static-Low-Dynamic Stiffness Isolator Using the Cam-Roller-Spring Mechanism

Journal of Vibration and Acoustics ◽

10.1115/1.4045583 ◽

2020 ◽

Vol 142 (2) ◽

Author(s):

Yuhui Yao ◽

Xiaojian Wang ◽

Hongguang Li

Keyword(s):

Harmonic Balance ◽

Vibration Isolation ◽

Dynamic Stiffness ◽

Damping Ratio ◽

Harmonic Balance Method ◽

Interaction Force ◽

Linear Spring ◽

Cam Profile ◽

Force Transmissibility ◽

Spring Mechanism

Abstract This paper presents a new design of a high-static-low-dynamic stiffness (HSLDS) isolator with an adjustable cam profile. The interaction force between the cam and roller provides the negative stiffness force and the linear spring provides the positive stiffness force in the HSLDS isolator. Unlike previous studies, the cam profile in this paper can be individually designed to meet different working conditions. Firstly, the harmonic balance method is used to acquire the dynamic response of the HSLDS isolator. Then, the effects of the damping ratio, stiffness ratio, and external force amplitude on the frequency response amplitude and force transmissibility are discussed. Finally, the frequency responses of four designed nonlinear HSLDS isolators and a linear isolator are acquired by the numerical method. The results show that the nonlinear isolator begins to achieve vibration isolation at 0.11 Hz and the linear one is 8.9 Hz. The proposed HSLDS isolator realizes lower vibration isolation frequency than the linear isolator.

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On the Free Vibration Modeling of Spindle Systems: A Calibrated Dynamic Stiffness Matrix

10.32920/14639511 ◽

2021 ◽

Author(s):

Omar Gaber ◽

Seyed M. Hashemi

Keyword(s):

Boundary Conditions ◽

Fundamental Frequency ◽

Stiffness Matrix ◽

Dynamic Stiffness ◽

Dynamic Stiffness Matrix ◽

Simply Supported ◽

Multiple Components ◽

Stiffness Matrices ◽

Linear Spring ◽

Vibration Modeling

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Identification of Dynamic Parameters of Pedestrian Walking Model Based on a Coupled Pedestrian–Structure System

Applied Sciences ◽

10.3390/app11146407 ◽

2021 ◽

Vol 11 (14) ◽

pp. 6407

Author(s):

Huiqi Liang ◽

Wenbo Xie ◽

Peizi Wei ◽

Dehao Ai ◽

Zhiqiang Zhang

Keyword(s):

Negative Correlation ◽

Dynamic Properties ◽

Damping Ratio ◽

Field Testing ◽

The Body ◽

Structural Vibration ◽

Pedestrian Dynamics ◽

Structure Interaction ◽

Mass Spring ◽

Stiffness And Damping

As human occupancy has an enormous effect on the dynamics of light, flexible, large-span, low-damping structures, which are sensitive to human-induced vibrations, it is essential to investigate the effects of pedestrian–structure interaction. The single-degree-of-freedom (SDOF) mass–spring–damping (MSD) model, the simplest dynamical model that considers how pedestrian mass, stiffness and damping impact the dynamic properties of structures, is widely used in civil engineering. With field testing methods and the SDOF MSD model, this study obtained pedestrian dynamics parameters from measured data of the properties of both empty structures and structures with pedestrian occupancy. The parameters identification procedure involved individuals at four walking frequencies. Body frequency is positively correlated to the walking frequency, while a negative correlation is observed between the body damping ratio and the walking frequency. The test results further show a negative correlation between the pedestrian’s frequency and his/her weight, but no significant correlation exists between one’s damping ratio and weight. The findings provide a reference for structural vibration serviceability assessments that would consider pedestrian–structure interaction effects.

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Free Vibration Analysis of a Graphene-Reinforced Porous Composite Plate with Different Boundary Conditions

Materials ◽

10.3390/ma14143879 ◽

2021 ◽

Vol 14 (14) ◽

pp. 3879

Author(s):

Hong-Gang Pan ◽

Yun-Shi Wu ◽

Jian-Nan Zhou ◽

Yan-Ming Fu ◽

Xin Liang ◽

...

Keyword(s):

Free Vibration ◽

Boundary Conditions ◽

Composite Plate ◽

Porous Plate ◽

Micromechanical Model ◽

Value Added ◽

Porous Composite ◽

Finite Element Software ◽

Free Vibration Frequency ◽

Graphene Platelets

Plates are commonly used in many engineering disciplines, including aerospace. With the continuous improvement in the capacity of high value-added airplanes, large transport aircrafts, and fighter planes that have high strength, high toughness, and corrosion resistance have gradually become the development direction of airplane plate structure production and research. The strength and stability of metal plate structures can be improved by adding reinforced materials. This paper studies graphene platelets (GPLs) reinforced with a free vibration porous composite plate. The porous plate is constructed with a multi-layer model in a metal matrix containing uniform or non-uniformly distributed open-cell internal pores. Considering the random and directional arrangement of graphene platelets in the matrix, the elastic modulus of graphene composites was estimated using the Halpin–Tsai micromechanical model, and the vibration frequencies of graphene composite were calculated using the differential quadrature method. The effects of the total number of layers, GPL distribution pattern, porosity coefficient, GPL weight fraction, and boundary conditions on the free vibration frequency of GPLs reinforced porous composite plates are studied, and the accuracy of the conclusions are verified by the finite element software.

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