Research on Axisymmetric Vibration of Gear with Stepped Variable Thickness

2011 ◽  
Vol 320 ◽  
pp. 269-274
Author(s):  
Yin Zhu She ◽  
Ming Lv ◽  
Shi Ying Wang
Keyword(s):  
Natural Frequency ◽  
Variable Thickness ◽  
Plate Theory ◽  
Great Influence ◽  
Special Kind ◽  
Structure Characteristic ◽  
Axisymmetric Vibration ◽  
Bending Vibration ◽  
Factors Affecting ◽  
Application Range

Ultrasonic gear honing is a kind of precision processing technology with great application prospect. The gear is a special kind of load in ultrasonic machining, and its vibration characteristic and natural frequency has great influence on processing frequency of the system. According to the structure characteristic of the gear with stepped variable thickness, its equations of axisymmetric bending vibration frequency were derived on the basis of the thick plate theory in this paper, and then the gear’s natural frequency is obtained which is in accordance with the results of FEM computation. Besides, the main factors affecting the calculation accuracy are analyzed with some examples in this paper The analysis shows that within the application range of Mindlin’s plate theory, the gears’ frequency obtained by the suggested method is accurate.

scholarly journals Investigation of the Damping Capacity of CFRP Raft Frames

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 653
Author(s):  
Jinguang Zhang ◽  
Jun Rao ◽  
Lei Ma ◽  
Xianglong Wen
Keyword(s):  
Natural Frequency ◽  
Simulation Analysis ◽  
Plate Theory ◽  
Damping Ratio ◽  
Great Influence ◽  
Maximum Error ◽  
Bottom Plate ◽  
Damping Capacity ◽  
Element Analysis ◽  
First Order

In this paper, based on the composite laminated plate theory and a strain energy model, the damping capacity of a Carbon Fiber Reinforced Plastics (CFRP) raft frame was studied. According to the finite element analysis (FEA) and damping ratio prediction model, the influences of different layups on the damping capacity of the raft frame and its components (top/bottom plate and I-support) were discussed. Comparing the FEA results with the test results, it can be figured out that the CFRP laminate layup has a great influence on the damping ratio of the raft frame, and the maximum error of the first-order natural frequency and damping ratio of the top/bottom plate were 5.6% and 15.1%, respectively. The maximum error of the first-order natural frequency of the I-support between the FEA result and the test result was 7.5%, suggesting that because of the stress concentration, the error of the damping ratio was relatively large. As for the raft frame, the damping performance was affected by the I-support arrangement and the simulation analysis was in good agreement with the experimental results. This study can provide a useful reference for improving the damping performance of CFRP raft frames.

scholarly journals Vibrational analysis of nanoplate with surface irregularity via Kirchhoff plate theory

2021 ◽  
Vol 11 ◽  
pp. 184798042110011
Author(s):  
Mahmoud M Selim ◽  
Taher A Nofal
Keyword(s):  
Natural Frequency ◽  
Plate Theory ◽  
Vibrational Analysis ◽  
Equation Of Motion ◽  
Frequency Equation ◽  
Kirchhoff Plate ◽  
Surface Irregularity ◽  
Structural Element ◽  
Kirchhoff Plate Theory ◽  
Parabolic Form

In this work, an attempt is done to apply the Kirchhoff plate theory to find out the vibrational analyses of a nanoplate incorporating surface irregularity effects. The effects of surface irregularity on natural frequency of vibration of nanomaterials, especially for nanoplates, have not been investigated before, and most of the previous research have been carried for regular nanoplates. Therefore, it must be emphasized that the vibrations of irregular nanoplate are novel and applicable for the nanodevices, in which nanoplates act as the main structure of the nanocomposite. The surface irregularity is assumed in the parabolic form at the surface of the nanoplate. A novel equation of motion and frequency equation is derived. The obtained results provide a better representation of the vibration behavior of irregular nanoplates. It has been observed that the presence of surface irregularity affects considerably on the natural frequency of vibrational nanoplates. In addition, it has been seen that the natural frequency of nanoplate decreases with the increase of surface irregularity parameter. Finally, it can be concluded that the present results may serve as useful references for the application and design of nano-oscillators and nanodevices, in which nanoplates act as the most prevalent nanocomposites structural element.

Analysis of Residual Stresses on the Vibration of a Circular Sensor Diaphragm with Surface Effects

2016 ◽  
Vol 33 (3) ◽  
pp. 323-329 ◽  
Author(s):  
S.-S. Zhou ◽  
S.-J. Zhou ◽  
A.-Q. Li ◽  
B.-L. Wang
Keyword(s):  
Residual Stresses ◽  
Natural Frequency ◽  
Flexural Rigidity ◽  
Plate Theory ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Transition Range ◽  
Biochemical Sensors ◽  
Tension Parameter ◽  
Wide Range

AbstractResonant micro-biochemical sensors play important roles in a wide range of emerging applications to detect biochemical molecules. As the resonators of micro-biochemical sensors, the vibration characteristics of circular sensor diaphragms are important for the design of diaphragm-based resonant micro-biochemical sensors. In this paper, the influence of residual stresses on the vibration of a circular sensor diaphragm with surface effects is analyzed. Based on the Kirchhoff's plate theory and surface elasticity theory, the governing equation is presented. The material characteristic lengths for different surface effects are obtained. The influences of residual stresses on the effective flexural rigidity and natural frequency of the diaphragm with surface effects are discussed. Results show that the influence of residual stresses on the effective flexural rigidity becomes obvious with the increasing of residual stresses. The first order natural frequency increases rapidly when the tension parameter is larger than 30 for the stiffened surfaces, while for the softened surfaces the value is 10. Moreover, surface effects can influence the transition range of diaphragm from the plate behavior to membrane behavior in terms of the tension parameter. The transition range can be enlarged by the stiffened surface and be shortened by the softened surface. The analysis and results are helpful for the design of sensor diaphragm-based resonant micro-biochemical sensors and some related researches.

Coupled Extensional and Flexural Motions of a Two-Layer Plate With Interface Slip

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Peng Li ◽  
Feng Jin ◽  
Weiqiu Chen ◽  
Jiashi Yang
Keyword(s):  
Plate Theory ◽  
Cutoff Frequency ◽  
Great Influence ◽  
Imperfect Interface ◽  
Mindlin Plate ◽  
Finite Plate ◽  
Mindlin Plate Theory ◽  
Interface Elasticity ◽  
Propagating Shear ◽  
Perfect Interface

The effect of imperfect interface on the coupled extensional and flexural motions in a two-layer elastic plate is investigated from views of theoretical analysis and numerical simulations. A set of full two-dimensional equations is obtained based on Mindlin plate theory and shear-slip model, which concerns the interface elasticity and tangential discontinuous displacements across the bonding imperfect interface. Some numerical examples are processed, including the propagation of straight-crested waves in an unbounded plate, the buckling of a finite plate, as well as the deflection of a finite plate under uniform load. It is revealed that the bending-evanescent wave in the composites with a perfect interface eventually cuts-on to a propagating shear-like wave with cutoff frequency when the two sublayers imperfectly bonded. The similar phenomenon has been verified once again for coupled face-shear and thickness-shear waves. It also has been pointed out that the interfacial parameter has a great influence on the performance of static buckling, in which the outcome can be reduced to classical buckling load of a simply supported plate when the interface is perfect.

scholarly journals Nonlinear Dynamic Analysis for Rectangular FGM Plates with Variable Thickness Subjected to Mechanical Load

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Khuc Van Phu ◽  
Le Xuan Doan ◽  
Nguyen Van Thanh
Keyword(s):  
Variable Thickness ◽  
Nonlinear Dynamic ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Nonlinear Dynamic Analysis ◽  
Dynamic Responses ◽  
Rectangular Plates ◽  
Classical Plate Theory

 In this paper, the governing equations of rectangular plates with variable thickness subjected to mechanical load are established by using the classical plate theory, the geometrical nonlinearity in von Karman-Donnell sense. Solutions of the problem are derived according to Galerkin method. Nonlinear dynamic responses, critical dynamic loads are obtained by using Runge-Kutta method and the Budiansky–Roth criterion. Effect of volume-fraction index k and some geometric factors are considered and presented in numerical results.

Assessing Low-Cost Housing Demand in Melaka: PLS-SEM Approach

2013 ◽  
Vol 838-841 ◽  
pp. 3156-3162 ◽  
Author(s):  
Noor Yasmin Zainun ◽  
Nadzirah Roslan ◽  
Aftab Hameed Memon
Keyword(s):  
Low Income ◽  
Goodness Of Fit ◽  
Housing Stock ◽  
Low Cost ◽  
Great Influence ◽  
Economic Factor ◽  
Housing Demand ◽  
Factors Affecting ◽  
Low Cost Housing ◽  
The Government

Housing is one of the basic needs of human. Population in Malaysia is increasing and expected to reach up to 35 million in year 2020. This phenomenon creates high demand for housing. To tackle the squatter problems, the government introduces low-cost housing. Low cost house is known as the government house, where the price is cheaper but still comfortable. Although there are many of low-cost housing projects have been completed to cope with the need of the citizen especially for low-income group. However, census report reveled that these is huge demand of low-cost housing. This demand might be because of various factors which are very essential to identify in order to meet the required demand of low cost houses. Hence, this study is carried out to assesse the demand of low cost housing in Melaka, determine the significant factors affecting demand of low-cost housing, and establish PLS-SEM model for assessing factors affecting low-cost housing demand. In this study, data are collected by distributing questionnaire in Melaka state. The collected data from survey was analyzed using statistical software SPSS and presented in graphs and chart. Further, factors affecting low cost housing demand in Melaka were modeled with the SmartPLS v2.0. The model shows the relationship between low cost housing demand and its indicators. The finding of the study showed that most significant indicators affecting the demand of low-cost housing in Melaka are the economic factors which include housing stock, inflation rate and Gross Domestic Products (GDP). The Goodness of Fit showed that the model has substantial explaining power for the assessing factors affecting low cost housing demand in Melaka which the values is 0.481. This means that the economic factor has a great influence on the low-cost housing demand in Melaka.

Some Results on Axisymmetric Vibration of Spherical Shells of Variable Thickness

1990 ◽  
Vol 112 (4) ◽  
pp. 432-437 ◽  
Author(s):  
A. V. Singh ◽  
S. Mirza
Keyword(s):  
Variable Thickness ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Spherical Shells ◽  
Varying Thickness ◽  
Wide Range

Natural frequencies and mode shapes are presented for the free axisymmetric vibration of spherical shells with linearly varying thickness along the meridian. Clamped and hinged edges corresponding to opening angles 30, 45, 60 and 90 deg have been considered in this technical brief to cover a wide range from shallow to deep spherical shells. Variations in thickness are seen to have very pronounced effects on the frequencies and mode shapes.

Vibration of Bending-Torsion Coupled Resonance in a Rotor

2013 ◽  
Author(s):  
Hiroyuki Fujiwara ◽  
Tadashi Tsuji ◽  
Osami Matsushita
Keyword(s):  
Numerical Simulations ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
Rotational Speed ◽  
Coupling Effect ◽  
The Other ◽  
Resonance Phenomenon ◽  
Horizontal Direction ◽  
Bending Vibration ◽  
Rotor Systems

In certain rotor systems, bending-torsion coupled resonance occurs when the rotational speed Ω (= 2π Ωrps) is equal to the sum/difference of the bending natural frequency ωb (= 2π fb) and torsional natural frequency ωθ(= 2πfθ). This coupling effect is due to an unbalance in the rotor. In order to clarify this phenomenon, an equation was derived for the motion of the bending-torsion coupled 2 DOF system, and this coupled resonance was verified by numerical simulations. In stability analyses of an undamped model, unstable rotational speed ranges were found to exist at about Ωrps = fb + fθ. The conditions for stability were also derived from an analysis of a damped model. In rotational simulations, bending-torsion coupled resonance vibration was found to occur at Ωrps = fb − fθ and fb + fθ. In addition, confirmation of this resonance phenomenon was shown by an experiment. When the rotor was excited in the horizontal direction at bending natural frequency, large torsional vibration appeared. On the other hand, when the rotor was excited by torsion at torsional natural frequency, large bending vibration appeared. Therefore, bending-torsion coupled resonance was confirmed.

On the High-Temperature Free Vibration Analysis of Elastically Supported Functionally Graded Material Plates Under Mechanical In-PlaneForce Via GDQR

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Roshan Lal ◽  
Rahul Saini
Keyword(s):  
Mechanical Properties ◽  
Plate Theory ◽  
Elastic Equilibrium ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Effect Of Temperature ◽  
Axisymmetric Vibration ◽  
Thickness Direction ◽  
Classical Plate Theory ◽  
Linear Temperature

In this article, the effect of Pasternak foundation on free axisymmetric vibration of functionally graded circular plates subjected to mechanical in-plane force and a nonlinear temperature distribution (NTD) along the thickness direction has been investigated on the basis of classical plate theory. The plate material is graded in thickness direction according to a power-law distribution and its mechanical properties are assumed to be temperature-dependent (TD). At first, the equation for thermo-elastic equilibrium and then equation of motion for such a plate model have been derived by Hamilton's principle. Employing generalized differential quadrature rule (GDQR), the numerical values of thermal displacements and frequencies for clamped and simply supported plates vibrating in the first three modes have been computed. Values of in-plane force parameter for which the plate ceases to vibrate have been reported as critical buckling loads. The effect of temperature difference, material graded index, in-plane force, and foundation parameters on the frequencies has been analyzed. The benchmark results for uniform and linear temperature distributions (LTDs) have been computed. A study for plates made with the material having temperature-independent (TI) mechanical properties has also been performed as a special case. Comparison of results with the published work has been presented.

scholarly journals Research on the Resonance Characteristics of Rock under Harmonic Excitation

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Siqi Li ◽  
Shenglei Tian ◽  
Wei Li ◽  
Tie Yan ◽  
Fuqing Bi
Keyword(s):  
Resonance Frequency ◽  
Natural Frequency ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Theoretical Research ◽  
Transform Method ◽  
Factors Affecting ◽  
Least Action ◽  
Principle Of Least Action ◽  
Resonance Frequencies

In order to study the resonance characteristics of rock under harmonic excitation, two vibration models have been presented to estimate the natural frequency of rock encountered during the drilling. The first one is a developed single-DOF model which considers the properties and dimensions of the rock. The second one is a multi-DOF model based on the principle of least action. Subsequently, the modal characteristics, as well as the influence of excitation frequency, the mechanical properties, and dimensions of the rock on its resonance frequency, are analyzed by using FEM. Finally, the ultrasonic test on artificial sandstones and materials of drill tools are carried out indoor, and the FFT transform method is adopted to obtain their resonance frequencies. Based on the analysis undertaken, it can be concluded that the natural frequency of the rock increases with the change of vibration mode. For the same kind of rock, the resonance frequency is inversely proportional to mass, while for the different kinds of rocks, the mechanical parameters, such as density, elastic modulus, and Poisson’s ratio, determine the resonance frequency of the rock together. Besides, the shape of the rock is also one of the main factors affecting its resonance frequency. At last, the theoretical research results are further verified by ultrasonic tests.

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