Advances in Acoustics and Vibration

Volume 2017 (2017), Article ID 5674032, 10 pages

https://doi.org/10.1155/2017/5674032

## The Tenability of Vibration Parameters of a Sandwich Beam Featuring Controllable Core: Experimental Investigation

^{1}Mechanical Engineering Department, Jain University, Bengaluru, Karnataka State, India^{2}Mechanical Engineering Department, Satara College of Engineering & Management Limb, Satara, Maharashtra State 415015, India^{3}Centre for Incubation, Innovation, Research & Consultancy, Bengaluru, Karnataka State, India^{4}Division of Automotive & Mechanical Engineering, Kongju National University, Cheonan-si, Chungnam 31080, Republic of Korea^{5}Department of Mechanical Engineering, Inha University, No. 253, Yonghyun-dong, Nam-gu, Incheon 402-751, Republic of Korea

Correspondence should be addressed to Seung-Bok Choi; rk.ca.ahni@kobgnues

Received 23 June 2017; Revised 18 August 2017; Accepted 24 September 2017; Published 19 October 2017

Academic Editor: Kim M. Liew

Copyright © 2017 Shreedhar Kolekar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This study presents experimental results of the vibration parameters of a sandwich beam featuring magnetorheological (MR) fluid as core material. For simplicity, the sandwich beam is considered as a single-degree-of-freedom (SDOF) system and the governing equation is derived in time and frequency domains. Then, from the governing equation, the vibration parameters which can be controllable by external stimuli are defined or obtained. These are the field-dependent natural frequency, damping factor, loss factor, and quality factor of the sandwich beam. Subsequently, a sandwich beam incorporating with controllable MR fluid core is fabricated and tested to evaluate the vibration parameters. MR fluid is prepared using the engine oil, iron particles, and grease as an additive and it is filled into the void zone (core) of the sandwich beam. The fabricated beam is then tested at four different conditions and the vibration parameters are numerically identified at each test. It is shown that both the natural frequency and damping property can be tuned by controlling the intensity of the magnetic field applied to MR fluid domain.

#### 1. Introduction

The development of sandwich structural systems with integrated control capabilities of modal characteristics is crucial to control unwanted vibrations and to avoid resonance problem due to external disturbances. These systems can provide higher flexural stiffness to weight ratio, lower lateral deformations, higher buckling resistance, and higher the natural frequencies. The distributed control force throughout the sandwich structures could be achieved by embedding controllable smart materials as cores or layers between two base structures. This approach can facilitate structure vibration control over a broad range of frequencies through variations in distributed stiffness and damping properties in response to applied stimuli. These structures are called smart sandwich structures like a smart structure in which both the natural frequency and damping property can be controlled by applying external fields such as voltage and current. The development of electrorheological (ER) fluid based sandwich structures was initiated by Gandhi et al. [1–3]. In this work, it has been shown that the dynamic characteristics of ER fluid based sandwich structures can be tuned showing the increment of damping ratio and natural frequencies as the electric field increases. As extension works, Choi et al. showed that the transient vibration of a flexible link robot could be effectively controlled by applying control voltage and also demonstrated that mode shapes of sandwich plate with ER fluid core could be controlled by localizing core zones [4–7]. Experiments were also performed using various ER fluid cores including corn starch, corn oil, and zeolite-silicone oil. Substantial variations in natural frequencies of sandwich beams with these cores were observed by changing the applied electric field [8, 9]. Leng et al. [10] experimentally investigated the vibration analysis of ER fluid composite sandwich beam. It was concluded that the first three modes of natural frequencies and damping factors were increased with increasing the applied electric field. Yalcintas and Coulter [11] developed an analytical model to characterize the forced vibration response of a simply supported ER sandwich beam using RKU (Ross-Kervin-Ungar) model. The numerical solutions were validated through experimental measurements. Yeh and Chen [12, 13] evaluated the variation in the stiffness and natural frequency of the sandwich plate with ER fluid by varying the applied electric field. They concluded that the resonance frequencies of the sandwich plate could be increased with increase in electric field and decreased with increase in thickness of the ER fluid core. It was also found that the thickness of the core has a significant effect on the stability of the sandwich structure system.

Since magnetorheological (MR) fluid has same characteristics as ER fluid except external stimuli, several researchers have attempted to develop sandwich structures featuring MR fluid cores. Yalcintas and Dai [14, 15] investigated dynamic responses of MR fluid adaptive sandwich beam using the energy approach and compared the responses with the structure employing ER fluid. It was concluded that the natural frequencies of MR fluid based adaptive sandwich beam could be nearly twice those of ER fluid based sandwich beam. Sun et al. [16] analytically studied the dynamic responses of a MR fluid sandwich beam using the energy approach and the results are validated by experimental measured data. Oscillatory rheometry techniques were used to carry out experiments to develop the relationship between the applied magnetic field and complex shear modulus of the MR fluid. Yeh and Shih [17] studied theoretically the dynamic responses of MR material based adaptive beam under axial harmonic load using DiTaranto sandwich beam theory. Hu et al. [18] investigated the vibration characteristics of MR fluid based sandwich beam using DiTaranto sixth-order partial differential equation. It was shown that the natural frequencies and loss factors of the MRF beam were increased with increasing applied magnetic field strength. Vasudevan et al. [19] derived the governing differential equations of motion by FEM and Ritz formulations for a sandwich beam with MR fluid treatment and validated through experiments conducted on a cantilever sandwich beam. Various parametric studies were performed in terms of variations of the natural frequencies and loss factor as functions of the applied magnetic field and thickness of the MR fluid layer for various boundary conditions. Lara-Prieto et al. [20] experimentally investigated the controllability of vibration characteristics of MR fluid based sandwich beams under various magnetic field intensities. The effects of applied magnetic field at partial and full length of MR fluid sandwich beam were analyzed. The effectiveness of the linear quadratic regulator and flexible mode shape method based optimal control techniques on controlling transient and forced vibration responses of a fully and partially treated MR fluid sandwich were investigated by Vasudevan et al. [21]. The vibration response of a MR fluid sandwich plate was analyzed by Li et al. [22]. It was shown that the natural frequencies increase with increase in applied magnetic field. However, the loss factors decrease in higher modes with increase in magnetic field. Yeh [23] studied the free vibration characteristics of a magnetorheological elastomers based sandwich plate. The loss factor and the natural frequencies of the sandwich plate were evaluated under various magnetic fields. Rajamohan et al. [24] studied to find the properties and also vibration response of a partially treated multilayer MR fluid beam and governing equations have been derived for partially treated multilayer prototype beam using finite element and Ritz method and compared the results with experimental and Ritz method; the effects of length and locations of MR fluid layers on the properties of the beam are investigated under different magnetic field conditions and demonstrated upon the boundary conditions and mode of vibration to be controlled for the effective vibration suppression has been derived. Rajamohan et al. [25] investigated governing equations for a partially treated MR fluid layer using FEM and Ritz approach, two different configurations of a partially treated MRF sandwich beam are considered, and the parametric studies were performed to investigate the influence of intensity of an external magnetic field and location and length of MR fluid layers on the dynamic characteristics of the structure with different boundary conditions. Rajamohan et al. [26] worked on governing equations for nonhomogeneous multilayer MR beam which were derived under nonhomogeneous conditions using FEM and Ritz formulation; the beam is formed using three different types of MR fluid and has various shear modulus properties and results showed that natural frequency at higher modes could be controlled by locating the MR fluid layers at desired locations. The natural frequency at higher modes could be increased with decreasing the length of MR fluid layer and it confirms that amplitude of vibration could be easily reduced using controllable MR fluid having different shear modulus located at the desired location and applied to more critical parts to realize more efficient vibration control. Rajamohan and Natarajan [27] worked on the dynamic behaviour of a rotating MRF sandwich beam using FEM and Ritz approach; various parametric studies were performed to study the effect of magnetic field on natural frequency and loss factors. The effect of thickness of MR fluid on natural frequency and effect of rotational speed and hub radius on natural frequencies corresponding to all the modes of vibration of rotating MR sandwich beam increased significantly with the increase in applied magnetic field intensity. Momeni et al. [28] investigated MRF sandwich beam using both experimental and simulation processes. FEM model is used to simulate vibration response under random loading and FEM approach is validated with experimental one and shows that as the magnetic field increases correspondingly the natural frequency for the sandwich beam increases. Walikar et al. [29] worked on engine oil based MR fluid using nickel as magnetisable particle and oleic acid as a surfactant with variation in concentration of nickel particles and found that effect of different magnetic field and concentration of magnetisable particles increase the natural frequency of the beam and amplitude of vibration decreases. Joshi [30] worked on vibration control of cantilever sandwich beam using laboratory prepared MR fluid and observed the variations in vibration amplitude and shifts in magnitude of resonance natural frequency. So the variations usually decreases in vibration amplitude and loss factors and increase in natural frequency as electric/magnetic field increases. However the variations in above parameters were more effective in MR adaptive structures compared with ERF structures.

Despite many research works on sandwich structures having controllable cores such as ER and MR fluids, the study on the vibration parameters which characterize vibration motions of sandwich structures is considerably rare. It is noted that in order to define or explain the vibration parameters such as loss factor a specific and simple model which governs vibration motions needs to be adopted. Many of previous works on smart sandwich structures provide the vibration parameters which are directly obtained from experimental tests without the specific definition. Consequently, this work presents criteria to evaluate the vibration parameters of smart sandwich beams considering a single-degree-of freedom (SDOF). After defining the vibration parameters from the governing equation of the SDOF, a sandwich beam with controllable MR fluid as core was fabricated and tested under free and forced vibration conditions at different magnetic fields. Then, the field-dependent vibration parameters such as natural frequency and loss factor are obtained and compared at four different conditions: empty sandwich beam, MR fluid sandwich beam at 0 T, MR fluid sandwich beam at 0.1 T, and MR fluid sandwich beam at 0.2 T, respectively. It is shown that the vibration parameters heavily depend on the magnetic intensity.

#### 2. Vibration Parameters of SDOF Model

As mentioned in Introduction, several advantages can be achieved by applying smart sandwich structures due to the controllability of core materials. Some of advantages are as follows.

*(i) Control of Vibration Amplitude at Resonance*. Damping can be used to control the excessive resonance vibrations which may cause high stresses leading to the permanent failure. It should be used in conjunction with other appropriate measures to achieve the most satisfactory approach for random excitations and it is not possible to detune the system and design to keep random stresses with acceptable limit without ensuring that the damping in each mode at least exceeds a minimum specified value. This is a case for sonic fatigue of aircraft fuselage, wing, and control surface panels when they are excited by the jet noise and boundary layer turbulence induced excitations.

*(ii) Noise Control*. Damping is useful for the control of noise radiation from vibrating surfaces or control of noise transmission through a vibrating surface.

*(iii) Damping Phenomenon*. The damping is nothing but the energy dissipation in a vibrating structures. The energy which is dissipated in vibrating structures usually depends upon physical mechanisms that exist in the active structures and the physical mechanisms are very complicated physical processes and it is very difficult to analyze the system. The type of damping phenomenon that existed in the structures and usually depends upon the mechanism, which predominates under the given situation, is very essential. In a true physical situation, the development of a mathematical equation of motion for the vibrating structure with a physical damping mechanisms is very significant. In the year 1970, Scanlan [31] has found the mathematical damping model which does not give much information.

In order to define vibration parameters of smart sandwich structures featuring controllable core materials, the SODF shown in Figure 1 is adopted because spring-mass-damper model is an oversimplification of the most real structures. In a free vibration system under the undamped case, the vibration response of the SDOF system will never die out. The easiest approach to introduce a dissipation will take place in viscous dashpot system as shown in the figure. The damping force () which is directly proportional to instantaneous velocity is given bywhere is called a dashpot or viscous damping constant. The loss factor which measures damping phenomenon and is defined as the sinusoidal excitation of the system to the corresponding sinusoidal response of the system is as follows:where is the stiffness of the system. The above equation is similar to the equation for the viscoelastic systems developed by the Ungar and Kerwin’s [32]. Eq. (2) shows a linear dependence between loss factor to driving frequency and inversely proportional to the stiffness of the system. This kind of frequency dependence has been discussed by Crandall in the year 1970 [33], but in actual practices it is not possible this form and in such a case often resorts to an equivalent ideal dashpot system. The theoretical objections to the approximately constant value of damping over a range of frequency, as can be observed in aeroelasticity problems, have been raised by Naylor in the year 1970 [33]. From (2), the frequency- dependent dashpot system is given by From Figure 1, the frequency domain representation of equation of motion can be written as follows:where is the response function and is the excitation function. The viscous damping or dashpot has frequency dependence. Substituting (3) into (4) yields the following:where is the signum function. For the “time domain” representations of (3) and (4) are expressed as follows:Then, by assuming the response function as for the harmonic function at the frequency and also the phase , the relationship between forcing function to the excitation can be related bywhere is the stiffness. is called the loss factor for inertial and stiffness properties. The phase angle lies between 0° and 90°, and the loss factor lies between 0 and . The relationship exists between and values.