scholarly journals Nonlinear Dynamics of an Electrorheological Sandwich Beam with Rotary Oscillation

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Kexiang Wei ◽  
Wenming Zhang ◽  
Ping Xia ◽  
Yingchun Liu
Keyword(s):  
Dynamic Characteristics ◽  
Loss Factor ◽  
Natural Frequencies ◽  
Multiple Scales ◽  
Parametric Instability ◽  
Sandwich Beam ◽  
The Finite Element Method ◽  
Rotating Beam ◽  
Flexible Beams ◽  
Instability Regions

The dynamic characteristics and parametric instability of a rotating electrorheological (ER) sandwich beam with rotary oscillation are numerically analyzed. Assuming that the angular velocity of an ER sandwich beam varies harmonically, the dynamic equation of the rotating beam is first derived based on Hamilton's principle. Then the coupling and nonlinear equation is discretized and solved by the finite element method. The multiple scales method is employed to determine the parametric instability of the structures. The effects of electric field on the natural frequencies, loss factor, and regions of parametric instability are presented. The results obtained indicate that the ER material layer has a significant effect on the vibration characteristics and parametric instability regions, and the ER material can be used to adjust the dynamic characteristics and stability of the rotating flexible beams.

Variability Analysis of Modal Characteristics of Frequency-Dependent Visco-Elastic Three-Layered Sandwich Beams With Spatial Random Geometrical and Material Properties

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Frédéric Druesne ◽  
Mohamed Hamdaoui ◽  
Qi Yin ◽  
El Mostafa Daya
Keyword(s):  
Random Fields ◽  
Loss Factor ◽  
Natural Frequencies ◽  
Sandwich Beam ◽  
Frequency Dependent ◽  
Geometrical Properties ◽  
Variability Analysis ◽  
Output Variability ◽  
The Face ◽  
The Impact

Material and physical properties of a frequency-dependent visco-elastic sandwich beam are modeled as a set of spatial random fields and represented by means of the Karhunen–Loève expansion. Variability analysis of frequency and loss factor are performed. An efficient approach based on modal stability procedure (MSP) is used, the so-called Monte Carlo simulation (MCS)–MSP method. The latter provides very reliable results and allows to analyze the impact of the input variability of a high number of random spatial quantities on the output response. The effect of independent and correlated couples of spatial random fields is investigated. It is shown that the output variability is generally more important for damping than for natural frequencies. Moreover, it is demonstrated that the input variability in geometrical properties are the most impacting for damping and frequency. The influence of input coefficient of variation on output variability is also studied. It is shown that a negative correlation between the face and core thicknesses result in high levels of output variability, when one parameter increases as the other decreases.

scholarly journals Dynamic Characteristics of an Elastic Structure with Thermal Effects

2020 ◽  
Vol 25 (2) ◽  
pp. 200-208
Author(s):  
Guanhua Xu ◽  
Jianzhong Fu ◽  
Wen He ◽  
Yuetong Xu ◽  
Zhiwei Lin ◽  
...  
Keyword(s):  
Modal Analysis ◽  
Dynamic Characteristics ◽  
Thermal Effects ◽  
Natural Frequencies ◽  
Elastic Structure ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Environmental Testing ◽  
Temperature Changes ◽  
Property Changes

The vibration table in a combination environmental testing device suffers from temperature changes, which cause the dynamic characteristics of the vibration structure to vary. The mechanism of the thermal effect on the dynamic characteristics of an elastic structure is presented, and a modal analysis with thermal effects based on the finite-element method (FEM) is carried out. The results show that the natural frequencies for each order decrease as the temperature increases, while the mode shapes of the vibrator do not change with temperature. Although thermal stress may affect natural frequencies due to the additional initial stress element stiffness, this stress can be neglected in the modal analysis because it is negligible relative to the effect of the material property changes with temperature.

Influence of Radial Slots on the Vibration Characteristics of Circular Saw Blade

2012 ◽  
Vol 226-228 ◽  
pp. 232-236
Author(s):  
Yuan Li
Keyword(s):  
Finite Element Method ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Matrix Perturbation ◽  
The Finite Element Method ◽  
Cutting Stability ◽  
Circular Saw ◽  
D’Alembert Principle ◽  
Circular Saw Blade ◽  
Saw Blade

In order to improve thin circular saw blade’s cutting stability, it’s nonlinear dynamic incremental equilibrium equation was obtained according to nonlinear vibration theory and D’Alembert principle. It could be concluded from the above equation that cutting several radial slots on the circumference of the saw blade will cause significant change of dynamic characteristics of the saw blade. This thesis, employing the finite element method and matrix perturbation principle, calculated and studied respectively the effect of number, length and width of the radial slots on natural frequencies of the saw blade. Results show that number and length have distinct influence on natural frequencies but hardly does width have. So proper choice of number, length and width of the radial slots can improve effectively the dynamic characteristics of the saw blade.

Effects of Locally Distributed Kelvin–Voigt Damping on Parametric Instability of Timoshenko Beams

2014 ◽  
Vol 14 (06) ◽  
pp. 1450014 ◽  
Author(s):  
Wei-Ren Chen ◽  
Chun-Sheng Chen
Keyword(s):  
Parametric Instability ◽  
Load Factor ◽  
Internal Damping ◽  
The Finite Element Method ◽  
Axial Loads ◽  
Linear Ordinary Differential Equations ◽  
Damped System ◽  
Instability Regions ◽  
Fixed End ◽  
Quadratic Eigenvalue

The effect of partially distributed internal damping of the Kelvin–Voigt type on the parametric instability of a Timoshenko beam subjected to periodic axial loads is studied. To model the dynamic behavior of the beam, a coupled set of second-order linear ordinary differential equations with periodic coefficients is established by the finite element method. A quadratic eigenvalue equation is derived for a parametrically excited damped system to determine the instability regions of the beam of concern based on Bolotin's method. The effects of internal damping, size and location of the damped segment, ratio of thickness to length and static load factor on the parametric instability of the beam are studied, along with the stabilizing effect of the Kelvin–Voigt damping on the primary parametric resonance presented. The results reveal that the beam with a larger damped segment positioned near the fixed end is dynamically more stable.

scholarly journals Free Vibration and Hardening Behavior of Truss Core Sandwich Beam

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
J. E. Chen ◽  
W. Zhang ◽  
M. Sun ◽  
M. H. Yao
Keyword(s):  
Natural Frequencies ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Sandwich Beam ◽  
Third Order ◽  
First Order ◽  
Hardening Behavior ◽  
Truss Core ◽  
Averaged Equations ◽  
Core Height

The dynamic characteristics of simply supported pyramidal truss core sandwich beam are investigated. The nonlinear governing equation of motion for the beam is obtained by using a Zig-Zag theory. The averaged equations of the beam with primary, subharmonic, and superharmonic resonances are derived by using the method of multiple scales and then the corresponding frequency response equations are obtained. The influences of strut radius and core height on the linear natural frequencies and hardening behaviors of the beam are studied. It is illustrated that the first-order natural frequency decreases continuously and the second-order and third-order natural frequencies initially increase and then decrease with the increase of strut radius, and the first three natural frequencies all increase with the rise of the core height. Furthermore, the results indicate that the hardening behaviors of the beam become weaker with the increase of the rise of strut radius and core height. The mechanisms of variations in hardening behavior of the sandwich beam with the three types of resonances are detailed and discussed.

Dynamic Morphing of Elastic Plates via Principal Parametric Resonance

2020 ◽  
Author(s):  
Andrea Arena ◽  
Walter Lacarbonara
Keyword(s):  
Mechanical Model ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Parametric Instability ◽  
Equation Of Motion ◽  
Elastic Plates ◽  
Asymptotic Approach ◽  
Threshold Voltages ◽  
Parametric Resonances ◽  
Instability Regions

Abstract Principal parametric resonances of elastic plates actuated by periodic in-plane stresses effected by embedded piezoelectric wires are investigated to describe the morphing scenarios of flexible, ultra-lightweight panels. A mechanical model of elastic plate including geometric nonlinearities and the parametric actuation provided by the piezoelectric wires, is adopted to formulate the nonlinear equation of motion. A bifurcation analysis is carried out by means of an asymptotic approach based on the method of multiple scales leading to a comprehensive parametric study on the effect of the wires width on the morphing regions (i.e., parametric instability regions) associated with the principal parametric resonances. The threshold voltages triggering the onset of the principal parametric resonances of the lowest three symmetric modes are also calculated as a function of the wires size so as to determine the voltage requirements for the morphing activation.

Vibration of Planetary Gears With Elastically Deformable Ring Gears Parametrically Excited by Mesh Stiffness Fluctuations

2009 ◽  
Author(s):  
Robert G. Parker
Keyword(s):  
Natural Frequencies ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Parametric Instability ◽  
Invariant System ◽  
Mesh Stiffness ◽  
Elastic Continuum ◽  
Planetary Gears ◽  
Time Invariant ◽  
Time Invariant System

The parametric instability of planetary gears having elastic continuum ring gears is analytically investigated based on a hybrid continuous-discrete model. Mesh stiffness variations of the sun-planet and ring-planet meshes caused by the changing number of teeth in contact are the source of parametric instability. The natural frequencies of the time invariant system are either distinct or degenerate with multiplicity two, which indicates three types of combination instabilities: distinct-distinct, distinct-degenerate and degenerate-degenerate instabilities. By using the structured modal properties of planetary gears and the method of multiple scales, the instability boundaries are obtained as simple expressions in terms of mesh parameters. Instability existence rules for in-phase planet meshes are given. The instability boundaries are validated numerically.

Effects of magnetoelastic loads on free vibration characteristics of the magnetorheological-based sandwich beam

2020 ◽  
Vol 31 (7) ◽  
pp. 1015-1028 ◽  
Author(s):  
Mohammad Rayyat Rokn-Abadi ◽  
Pooriya Shahali ◽  
Hassan Haddadpour
Keyword(s):  
Free Vibration ◽  
Loss Factor ◽  
Magnetic Field Intensity ◽  
Sandwich Beam ◽  
Vibration Characteristics ◽  
The Finite Element Method ◽  
Deep Insight ◽  
Governing Equations ◽  
The Core ◽  
Comprehensive Survey

In this contribution, we have investigated the effects of magnetoelastic loads on free vibration characteristics of the magnetorheological-based sandwich beam. The considered sandwich beam consists of a magnetorheological core with elastic top and base layers. For these means, the structural governing equations are derived using the Hamilton principle and solved by the finite element method. The results are validated in comparison with the existing results in the literature. The effects of variation in the parameters such as magnetic field intensity and the thickness of the core and top layers on the deviation of the first natural frequency and the corresponding loss factor are studied as well. Finally, in order to provide deep insight, the effects of magnetoelastic loads on the dynamic behavior of the three-layered sandwich beam are examined through a comprehensive survey.

Dynamic Characteristics of Structures Bonded with Viscoelastic Unconstrained Layers

1986 ◽  
Vol 10 (3) ◽  
pp. 175-182
Author(s):  
A.K. Behera ◽  
B.K. Nanda
Keyword(s):  
Base Metal ◽  
Dynamic Characteristics ◽  
Loss Factor ◽  
Natural Frequencies ◽  
Structural Vibration ◽  
Damping Capacity ◽  
Static Stiffness ◽  
Design Data ◽  
Energy Principle ◽  
Theoretical Predictions

In order to control the intensity of troublesome vibration in the modern day structures, viscoelastic materials are sometimes bonded to one or both sides of those structures. This type of unconstrained damping layer treatment is quite effective for abating structural vibration. In this paper both theoretical and experimental investigation has been made on the dynamic characteristics of such beam-like structures in order to get sufficient design data. Theoretical analysis based on the energy principle is presented in a generalised form for predicting damped and undamped natural frequencies as well as logarithmic decrement of such beams. Expressions for the loss-factor and static stiffness are also found out in order to evaluate dimensional inter-relationship between base metal and damping layer for maximizing damping capacity of the structure without losing its stiffness. Experimental measurements for natural frequency and log-decrement bear out the fact that theoretical predictions are indeed accurate. It is found that there is an optimum value of thickness ratio between base metal and damping layer for maximizing damping in a structure with a single unconstrained damping layer. Results for beams having single damping layer as well as for symmetric damping layers on both sides are also presented for comparison.

Sign in / Sign up

Export Citation Format

Share Document