Analysis of Parametric Resonances in In-Plane Vibrations of Electrostrictive Hyperelastic Plates

2018 ◽  
Vol 13 (9) ◽  
Author(s):  
Astitva Tripathi ◽  
Anil K. Bajaj
Keyword(s):  
Electric Field ◽  
Parametric Resonance ◽  
Mechanical Response ◽  
Element Model ◽  
Mode Shapes ◽  
Principal Parametric Resonance ◽  
Parametric Resonances ◽  
Second Mode ◽  
Electrostrictive Polymer ◽  
Large Amplitude Vibrations

Electrostriction is a recent actuation mechanism which is being explored for a variety of new micro- and millimeter scale devices along with macroscale applications such as artificial muscles. The general characteristics of these materials and the nature of actuation lend itself to possible production of very rich nonlinear dynamic behavior. In this work, principal parametric resonance of the second mode in in-plane vibrations of appropriately designed electrostrictive plates is investigated. The plates are made of an electrostrictive polymer whose mechanical response can be approximated by Mooney Rivlin model, and the induced strain is assumed to have quadratic dependence on the applied electric field. A finite element model (FEM) formulation is used to develop mode shapes of the linearized structure whose lowest two natural frequencies are designed to be close to be in 1:2 ratio. Using these two structural modes and the complete Lagrangian, a nonlinear two-mode model of the electrostrictive plate structure is developed. Application of a harmonic electric field results in in-plane parametric oscillations. The nonlinear response of the structure is studied using averaging on the two-mode model. The structure exhibits 1:2 internal resonance and large amplitude vibrations through the route of parametric excitation. The principal parametric resonance of the second mode is investigated in detail, and the time response of the averaged system is also computed at few frequencies to demonstrate stability of branches. Some results for the case of principal parametric resonance of the first mode are also presented.

On 1:2 Internal Resonances in In-Plane Vibrations of Electrostrictive Plates

2014 ◽  
Author(s):  
Astitva Tripathi ◽  
Anil K. Bajaj
Keyword(s):  
Electric Field ◽  
Nonlinear Response ◽  
Mechanical Response ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Artificial Muscles ◽  
Internal Resonances ◽  
Large Amplitude Vibrations ◽  
New Generation ◽  
Constitutive Parameters

Electrostrictive polymers are popular materials being employed in fabrication of high-strain actuators for use in new generation micro- and nano-scale devices along with applications such as artificial muscles. In this work, possibility of 1:2 internal resonances in in-plane vibrations of appropriately designed electrostrictive plates is investigated. The polymer is assumed to have mechanical response similar to that of a Mooney Rivlin material and the induced strain having a quadratic dependence on the applied external electric field. A Finite Element Method (FEM) formulation is used to develop mode shapes of a structure whose lowest two natural frequencies have been brought close to the ratio of 1:2. Using the mode shapes thus obtained, a more complete Lagrangian formulation is used to develop a nonlinear two-mode model of the electrostrictive plate structure. Application of a harmonic electric field results in in-plane parametric oscillations of the structure. The nonlinear response of the structure is developed using averaging on the two-mode model. The structure exhibits 1:2 internal resonance due to the large amplitude vibrations through the route of parametric excitation. The effects of material constitutive parameters on the nonlinear response are investigated.

scholarly journals On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Nguyen Van Dung ◽  
Nguyen Chi Tho ◽  
Nguyen Manh Ha ◽  
Vu Trong Hieu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Mechanical Response ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Engineering Practice

Rotating structures can be easily encountered in engineering practice such as turbines, helicopter propellers, railroad tracks in turning positions, and so on. In such cases, it can be seen as a moving beam that rotates around a fixed axis. These structures commonly operate in hot weather; as a result, the arising temperature significantly changes their mechanical response, so studying the mechanical behavior of these structures in a temperature environment has great implications for design and use in practice. This work is the first exploration using the new shear deformation theory-type hyperbolic sine functions to carry out the free vibration analysis of the rotating functionally graded graphene beam resting on the elastic foundation taking into account the effects of both temperature and the initial geometrical imperfection. Equations for determining the fundamental frequencies as well as the vibration mode shapes of the beam are established, as mentioned, by the finite element method. The beam material is reinforced with graphene platelets (GPLs) with three types of GPL distribution ratios. The numerical results show numerous new points that have not been published before, especially the influence of the rotational speed, temperature, and material distribution on the free vibration response of the structure.

scholarly journals Thermally Induced Principal Parametric Resonance in Circular Plates

2002 ◽  
Vol 9 (3) ◽  
pp. 143-150 ◽  
Author(s):  
Ali H. Nayfeh ◽  
Waleed Faris
Keyword(s):  
Parametric Resonance ◽  
Large Amplitude ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Temperature Fields ◽  
Circular Plates ◽  
Thermally Induced ◽  
Principal Parametric Resonance ◽  
Large Amplitude Vibrations ◽  
External Heat Flux

We consider the problem of large-amplitude vibrations of a simply supported circular flat plate subjected to harmonically varying temperature fields arising from an external heat flux (aeroheating for example). The plate is modeled using the von Karman equations. We used the method of multiple scales to determine an approximate solution for the case in which the frequency of the thermal variations is approximately twice the fundamental natural frequency of the plate; that is, the case of principal parametric resonance. The results show that such thermal loads produce large-amplitude vibrations, with associated multi-valued responses and subcritical instabilities.

TIME-AVERAGE HOLOGRAPHY TO ANALYZE DYNAMIC BEHAVIOR OF SKIN TISSUES UNDER DIFFERENT CONDITIONS

2017 ◽  
Vol 17 (01) ◽  
pp. 1750020
Author(s):  
ANTONIO BOCCACCIO ◽  
GAETANO GENCHI ◽  
LUCIANO LAMBERTI ◽  
CARMINE PAPPALETTERE
Keyword(s):  
Dynamic Behavior ◽  
Mechanical Response ◽  
Element Model ◽  
Mode Shapes ◽  
Tissue Samples ◽  
Use Of Time ◽  
Time Average ◽  
Set Up ◽  
Reliability And Robustness ◽  
Skin Samples

This study aims to investigate the feasibility of using time-average holography to verify the integrity of skin tissue samples and detect changes in their mechanical response caused by exposure to thermal perturbations, radiations and mechanical loading. For that purpose, chicken skin samples are put into vibration and the corresponding modes are monitored by means of an optical set up based on time average holographic interferometry. Mode shapes of base samples computed by a parametric finite element model are consistent with experimental data. The holographic set up correctly detects the presence of defects previously included in the sample. Dynamic behavior of skin samples under various conditions of low/high temperature and load or exposed, for different periods of time, to UV radiation and microwaves also is successfully monitored. The reliability and robustness of the proposed approach is tested by performing the holographic observations on a large number of samples under different conditions. Potential benefits that may derive from the use of time-average holography in dermatology and plastic surgery (for example, in the quality control of artificial skin tissues to be implanted) are finally discussed.

Numerical Study for Global Detection of Cracks Embedded in Beams

1999 ◽  
Author(s):  
S. A. Lipsey ◽  
Y. W. Kwon
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Natural Frequency ◽  
Mode Shape ◽  
Numerical Study ◽  
Element Model ◽  
Mode Shapes ◽  
Linear Effect ◽  
Modes Of Vibration ◽  
Damage Simulation

Abstract Damage reduces the flexural stiffness of a structure, thereby altering its dynamic response, specifically the natural frequency, damping values, and the mode shapes associated with each natural frequency. Considerable effort has been put into obtaining a correlation between the changes in these parameters and the location and amount of the damage in beam structures. Most numerical research employed elements with reduced beam dimensions or material properties such as modulus of elasticity to simulate damage in the beam. This approach to damage simulation neglects the non-linear effect that a crack has on the different modes of vibration and their corresponding natural frequencies. In this paper, finite element modeling techniques are utilized to directly represent an embedded crack. The results of the dynamic analysis are then compared to the results of the dynamic analysis of the reduced modulus finite element model. Different modal parameters including both mode shape displacement and mode shape curvature are investigated to determine the most sensitive indicator of damage and its location.

FEM Free Damage Detection of Beam Structures Using the Deflections Estimated by Modal Flexibility Matrix

2021 ◽  
pp. 2150128
Author(s):  
Wen-Yu He ◽  
Wei-Xin Ren ◽  
Lei Cao ◽  
Quan Wang
Keyword(s):  
Damage Detection ◽  
Structural Damage ◽  
Damage Index ◽  
Element Model ◽  
Mode Shapes ◽  
Beam Structures ◽  
Flexibility Matrix ◽  
Damage Quantification ◽  
Modal Flexibility ◽  
The Cost

The deflection of the beam estimated from modal flexibility matrix (MFM) indirectly is used in structural damage detection due to the fact that deflection is less sensitive to experimental noise than the element in MFM. However, the requirement for mass-normalized mode shapes (MMSs) with a high spatial resolution and the difficulty in damage quantification restricts the practicability of MFM-based deflection damage detection. A damage detection method using the deflections estimated from MFM is proposed for beam structures. The MMSs of beams are identified by using a parked vehicle. The MFM is then formulated to estimate the positive-bending-inspection-load (PBIL) caused deflection. The change of deflection curvature (CDC) is defined as a damage index to localize damage. The relationship between the damage severity and the deflection curvatures is further investigated and a damage quantification approach is proposed accordingly. Numerical and experimental examples indicated that the presented approach can detect damages with adequate accuracy at the cost of limited number of sensors. No finite element model (FEM) is required during the whole detection process.

Analysis of In-Plane Modal Characteristics of an Annular Disk With Multiple Point Supports

2009 ◽  
Author(s):  
S. Bashmal ◽  
R. Bhat ◽  
S. Rakheja
Keyword(s):  
Finite Element ◽  
Orthogonal Polynomials ◽  
Ritz Method ◽  
Element Model ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Multiple Point ◽  
Annular Disk ◽  
Free Boundary Conditions ◽  
Boundary Characteristic

In-plane free vibrations of an isotropic, elastic annular disk constrained at some points on the inner and outer boundaries are investigated. The presented study is relevant to various practical problems including disks clamped by bolts along the inner and outer edges or the railway wheel vibrations. The boundary characteristic orthogonal polynomials are employed in the Rayleigh-Ritz method to obtain the frequency parameters and the associated mode shapes. The boundary characteristic orthogonal polynomials are generated for the free boundary conditions of the disk while artificial springs are used to realize clamped conditions at discrete points. The frequency parameters for different point constraint conditions are evaluated and compared with those computed from a finite element model to demonstrate the validity of the proposed method. The computed mode shapes are presented for a disk with different point constraints at the inner and outer boundaries to demonstrate the free in-plane vibration behavior of the disk. Results show that addition of point supports causes some of the modes to split into two different frequencies with different mode shapes. The effects of different orientations of multiple point supports on the frequency parameters and mode shapes are also discussed.

scholarly journals Ageing simulation of a hydraulic engine mount: A data-informed finite element approach

2018 ◽  
Vol 233 (10) ◽  
pp. 2432-2442 ◽  
Author(s):  
Payam Soltani ◽  
Christophe Pinna ◽  
David J Wagg ◽  
Roly Whear
Keyword(s):  
Finite Element ◽  
Mechanical Response ◽  
Element Model ◽  
Experimental Results ◽  
Softening Effect ◽  
Engine Mounts ◽  
Ageing Behaviour ◽  
Ageing Model ◽  
Engine Mount ◽  
Vehicle Suspension System

Hydraulic engine mounts are key elements in an automotive vehicle suspension system that typically experience a change of their designed function during their working lifetime due to progressive material ageing, primarily from the elastomeric component. Ageing of the engine mount, resulting from severe and continuous mechanical and thermal loads, can have a detrimental impact on the ride and comfort and long-term customer satisfaction. This paper introduces a new practical methodology for simulating the ageing behaviour of engine mounts resulting from the change in properties of their elastomeric main spring component. To achieve this, a set of dynamic mechanical thermal analysis tests were conducted on elastomeric coupons taken from a set of engine mounts with different service and ageing conditions. These experimental results were used to characterise the change in mechanical response of the elastomer and to build up an empirical elastomer ageing model. Then a finite element model of the main spring was developed that used the elastomer ageing model so that the ageing behaviour of the engine mount could be simulated. The resulting ageing model was verified by using experimental results from a second batch of ex-service engine mounts. The results show an increasing trend of the vertical static stiffness of the engine mounts with distance travelled (or age) up to a certain distance (approximately 95,000 km). The trend is then reversed and a softening effect is observed. Moreover, the results reveal that both the maximum stiffness value and the distance travelled at the peak stiffness decrease as the temperature increases.

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