Elsevier

Composite Structures

Volume 143, 20 May 2016, Pages 93-102
Composite Structures

Aeroelastic characteristics of magneto-rheological fluid sandwich beams in supersonic airflow

https://doi.org/10.1016/j.compstruct.2016.02.015Get rights and content

Abstract

Supersonic aeroelastic instability of a three-layered sandwich beam of rectangular cross section with an adaptive magneto-rheological fluid (MRF) core layer is investigated. The panel is excited by an airflow along it’s longitudinal direction. The problem formulation is based on classical beam theory for the face layers, magnetic field dependent complex modulus approach for viscoelastic material model and the linear first-order piston theory for aerodynamic pressure. The classical Hamilton’s principle and the assumed mode method are used to set up the equations of motion. The validity of the derived formulation is confirmed through comparison with the available results in the literature. The effects of applied magnetic field, core layer thickness and constraining layer thickness on the critical aerodynamic pressure are studied. The onset of instability in terms of the critical value of the nondimensional aerodynamic pressure for the sandwich beam is calculated using the p-method scheme. Simply supported, clamped–clamped and clamped-free boundary conditions are considered. The results show that the magnetic field intensity and thickness ratios have significant effects on the instability bounds.

Introduction

Thin walled structural components exposed to high velocity airflow on the outer surface of aerospace vehicle may become unstable at a certain critical aerodynamic pressure. At this pressure the motion of the surface panels grows with time until the in-plane tensile stresses induced by the geometric nonlinearities restrain the vibration amplitude of the structure. This phenomena, is known as panel flutter and may occur frequently under transonic, supersonic or hypersonic environments as a result of interactions between the inertial force, elastic force and the aerodynamic loads induced by the airflow [1], [2], [3]. Oscillatory nature of the flutter can cause high stresses and result in the fatigue of thin walled components or supporting structures, excessive noise levels in vehicle compartments near the fluttering panel or functional failure of the equipment attached to the structure.

Since the panel flutter phenomenon first occurred on the early V-2 rockets, a large number of failures have been caused by the aeroelastic and aerothermoelastic flutters in the history of aerospace development [4], [5]. In order to reduce the possibility of catastrophic flight accidents caused by flutter, it is necessary to control and suppress the fluttering structure/components of an aerospace vehicle.

In order to improve the aeroelastic instability characteristics of an aerospace structure, one should manage to increase the instability bound by changing the structural complex eigenvalues. It is well known that the structural eigenvalues are related to the structural stiffness, damping and mass matrices. By changing the structural stiffness, damping and mass properties, the flutter characteristics of the structure may be possibly improved.

Adaptive structures are structures which can adopt, evolve or change their properties or behavior in response to the environment around them due to the incorporation of a controllable component such as piezoelectric [6], shape memory alloy (SMA) [7], electro-rheological (ER) [8] and magneto-rheological (MR) materials [9].

The stiffness and damping characteristics of adaptive structures comprising magneto and electro-rheological fluids can rapidly and reversibly be changed by application of external magnetic/electric field. Nowadays, these structures are being used increasingly in vibration and noise control [10], [11], [12], [13], [14]. These structures have other valuable advantages such as low energy loss, simplicity, robustness and easy controllability.

Constrained layer damping (CLD) is an effective approach for improving the dynamic behavior of flexible structures which is used mostly in aerospace and automotive engineering. Traditionally, viscoelastic materials are used in this approach to suppress excessive vibration, however due to fixed damping and stiffness properties of the usual viscoelastic materials, the vibration control performance of these structures is limited to a narrow frequency range. Recently, MR/ER materials have been utilized as a core in sandwich structure which leads to distributed stiffness and damping properties of the structure and facilitates vibration control over a broad range of frequencies. For the first time Gandhi et al. [15] experimentally analyzed application of ER materials as a core in a cantilevered sandwich beam and concluded that the structure damping ratio and natural frequencies increase with increase in electric filed. Another experimental investigation on a cantilevered beam locally linked by an electro-rheological fluid layer to ground was conducted by Haiqing et al. [16]. In this research the ER fluid layer was locally applied to the beam as a complex spring and it was found that the frequency response function curve of the beam changed drastically under electric field. It is also reported that the vibration characteristics of the cantilevered beam with locally applied ER fluid layer treatment is more sensitive to the electric field than a sandwich beam. Using Mead and Markus sandwich beam model [17], vibration characteristics of viscoelastically damped sandwich ER beam was calculated for clamped-free and clamped–clamped boundary conditions by Yalcintas and Coulter [18]. Hasheminajad and Maleki [8], studied the free and steady state forced vibration characteristics of a sandwich plate with ER fluid core and cross-ply elastic composite laminate face layers using Hamilton’s principles and Navier technique under simply supported boundary conditions for various electric field strength, geometric aspect ratio and ER core layer thicknesses. They concluded that the natural frequency increases monotonically with increasing electric field strength but loss factor of the structure increases to its maximum value and decreases with further increase in the field intensity. Furthermore, the natural frequencies increase with increasing geometric aspect ratio and decrease with increasing ER core layer thickness. Allahverdizade and his coworkers conducted a series of analytical and experimental studies on linear and nonlinear vibration behavior of functionally graded ER sandwich beams [19], [20], [21], [22].

Compared to the works on structures embedded with ER fluids, limited results are available on MR based sandwich structures. First investigation on the use of MR fluid in sandwich structures conducted by Yalcintas and Dai [23]. They compared effectiveness of using MR and ER fluids in adaptive structures and concluded that by using MR materials as a core, the natural frequencies of the structure increases almost two times compared with ER counterpart. The controllable capabilities of an MR sandwich beam have been investigated theoretically and experimentally by Sun et al. [24]. They used oscillatory rheometry technique to derive the relationship between the magnetic field intensity and complex shear modulus of MR materials. Yeh and Shih [25] determined the regions of dynamic stability and dynamic response of an MR simply supported sandwich beam subjected to the axial harmonic load using incremental harmonic balance (IHB) method. Kumar and Ganesan [26] used finite element formulation to study the effects of core thickness, electric voltage and magnetic field on the vibration and damping behavior of the clamped free hollow sandwich box column containing a viscoelastic, electro-rheological or magneto-rheological fluid core. Rajamohan et al. [27] used finite element method and Ritz formulation to study the vibration characteristics of a sandwich beam with MR fluid core with various boundary conditions. They also validated their formulations through experimental study on a cantilevered sandwich beam. In addition, they estimated complex shear modulus of the MR fluid based on the single-degree-of-freedom (SDOF) vibration behavior according to the procedure proposed by Choi et al. [28]. They concluded that increasing the magnetic field intensity increases natural frequencies for all modes and loss factor at higher modes. It has been observed that simply supported boundary condition has the highest loss factor at lower modes and clamped-free one at higher modes. Furthermore, it is observed that by increasing the thickness of the MR layer, natural frequencies at all modes decreases while the loss factor increases at the first two modes. Rajamohan et al. [29] investigated the influence of length and location of the MR fluid layer segment under different magnetic field intensities in the dynamic characteristics of a partially treated MR fluid beam for different boundary conditions and compared the results with the fully treated counterpart. It is observed, in addition to the intensity of the applied magnetic field and boundary conditions, the location and length of the fluid pocket strongly affects the natural frequencies and transverse displacement response of the partially treated MR beam. Optimal locations for the MR fluid treatment in partially filled MR sandwich beam to individually and simultaneously attain to maximum modal damping related to the first five flexural vibration mode of the beam is obtained by Rajamohan et al. [30] using genetic algorithm and sequential quadratic programming algorithm. Semi active optimal vibration control of fully and partially treated clamped-free MR sandwich beam conducted using linear quadratic regulator (LQR) optimal control strategy by Rajamohan et al. [12]. The results suggested about 85% reduction in the free vibration settling time and 25% reduction in the tip deflection. Ndemanou et al. [31] carried out a study on vibration suppression of a cantilevered Timoshenko beam subjected to the earthquake load by a magneto-rheological damper localized at a specific point of the beam. Ramamoorthy et al. [10] numerically and experimentally analyzed free and forced vibration behavior of a partially treated laminated composite MR fluid sandwich plate. The study concluded more pronounced effect of using MR fluid segment in partial region of large components on vibration amplitude reduction and decreasing the magnitude of the peak response at all vibration modes with increase in magnetic field intensity. Manoharan et al. [11] investigated the effect of magnetic field intensity, thickness of MR fluid layer and the ply orientation of the composite face layers on the natural frequencies and loss factors of a laminated composite MR fluid sandwich rectangular plate using finite element formulation. In a recent numerical and experimental study, Eshaghi et al. [32] analyzed the effect of variation in the magnetic flux, core layer thickness and plate aspect ratio on the vibration behavior of an MR sandwich plate.

Many research works have been carried out on vibrating and damping behavior of MR/ER sandwich adaptive structures; however, a limited number of analyses are available on aeroelastic behavior of MR/ER based adaptive structures. The first study on the flutter suppression capability of ER sandwich beams was conducted by Hasheminejad et al. [33]. They used sliding mode control algorithm to suppress the supersonic flutter instability of a simply supported sandwich beam coupled to an elastic foundation. Supersonic flutter analysis of a sandwich ER rectangular plate with orthotropic face layers was conducted by Rahiminasab and Rezaeepazhand [34]. Various parametric studies were performed in terms of variations of the critical aerodynamic pressure as functions of the applied electric field, thickness of the ER fluid layer, electro-rheological fluid type, constraining layer thickness and fiber angle of orthotropic faces for simply supported and fully clamped boundary conditions. Hasheminajad and his coworkers [35], [36], [37] further investigated supersonic panel flutter semi active control of ER based rectangular sandwich plates and cylindrical shell using sliding mode control method and Rung-Kutta time integration algorithm.

To the author’s knowledge, no report is available on the aeroelastic behavior of MR sandwich structures under supersonic flow. A few studies on the aeroelastic behavior of ER based adaptive structures are available [33], [34], [35], [36]. These are limited to flutter control of a specific structure with inadequate parametric investigation on the effect of core and constraining layers thicknesses. Rigorous investigations involving the effect of various parameters such as boundary conditions, constraining and core layer thicknesses, and magnetic field strength on the instability boundary seem to be required. The main objective of this paper is to fill such a gap. In this study, the Hamilton’s principle along with the assumed mode method is adopted to obtain the aeroelastic characteristics of the sandwich beam. The classical beam theory is used for structural modeling of the face layers. Simply supported (S-S), clamped–clamped (C–C) and clamped-free (C-F) boundary conditions are taken into account. Effect of magnetic field strength, MR fluid layer thickness, and constraining layer thickness on non-dimensional aerodynamic pressure of the sandwich adaptive beam is investigated.

Section snippets

Mathematical modeling

Consider a three layer sandwich beam with magneto-rheological fluid core of length L, width b and thickness h which is subjected to a supersonic flow as shown in Fig. 1. The beam is composed of an elastic base layer of thickness hb, a constraining elastic layer of thickness hc and a MR fluid core of thickness hf.

Simplification is an integral part of any mathematical modeling. Here, some simplifications are considered to make the model of the problem. Since Young’s modulus of the MR fluid is

Validation of the present method

A computer code is developed to determine the critical non-dimensional aerodynamic pressure of the MR sandwich beam using the present formulation. The code is verified using the results of frequency analysis given by [45] letting ζ = 0. The dimensions and material properties of the sandwich beam with MR core are taken from Yalcintas and Dai [23]. The obtained results using the present formulation are given in Table 1 beside the results of Yeh and Shih [45], which used the model of Mead and Markus

Results and discussion

Many structure and fluid related parameters such as field intensity, thickness of the fluid layer, geometry of the beam, type of the MR fluid, thicknesses of the elastic face layers, boundary conditions, etc., may influence the aeroelastic behavior of the MR sandwich beam. The proposed assumed mode method is used to study the effect of variations in the constraining and fluid layer thicknesses, magnetic field intensity on the properties of the MR sandwich beam in terms of critical

Conclusion

The aeroelastic characteristics of MR sandwich beams exposed to supersonic airflow are presented. The governing differential equation of motion was derived by utilizing Hamilton’s principle. Assumed mode method has been used to solve governing equation of motion along with p-method for aeroelastic instability analysis. Various parametric studies were performed to investigate aeroelastic instability boundary of the MR fluid sandwich beam by the effect of magnetic field intensity, MR layer and

References (51)

  • Q. Sun et al.

    An adaptive beam model and dynamic characteristics of magnetorheological materials

    J Sound Vib

    (2003)
  • V. Rajamohan et al.

    Vibration analysis of a partially treated multi-layer beam with magnetorheological fluid

    J Sound Vib

    (2010)
  • S.M. Hasheminejad et al.

    Aeroelastic analysis and active flutter suppression of an electro-rheological sandwich cylindrical panel under yawed supersonic flow

    Aerosp Sci Technol

    (2015)
  • W.-H. Shin et al.

    Aeroelastic characteristics of cylindrical hybrid composite panels with viscoelastic damping treatments

    J Sound Vib

    (2006)
  • K.-N. Koo et al.

    Effects of hysteretic and aerodynamic damping on supersonic panel flutter of composite plates

    J Sound Vib

    (2004)
  • B. Nayak et al.

    Dynamic stability of magnetorheological elastomer based adaptive sandwich beam with conductive skins using FEM and the harmonic balance method

    Int J Mech Sci

    (2013)
  • W.P. Howson et al.

    Exact dynamic stiffness matrix for flexural vibration of three-layered sandwich beams

    J Sound Vib

    (2005)
  • Z.-G. Song et al.

    Active aeroelastic flutter analysis and vibration control of supersonic beams using the piezoelectric actuator/sensor pairs

    Smart Mater Struct

    (2011)
  • F. Daghia et al.

    Shape memory alloy hybrid composite plates for shape and stiffness control

    J Intell Mater Syst Struct

    (2008)
  • S.M. Hasheminejad et al.

    Free vibration and forced harmonic response of an electrorheological fluid-filled sandwich plate

    Smart Mater Struct

    (2009)
  • V. Lara-Prieto et al.

    Vibration characteristics of MR cantilever sandwich beams: experimental study

    Smart Mater Struct

    (2010)
  • M. Ramamoorthy et al.

    Vibration analysis of a partially treated laminated composite magnetorheological fluid sandwich plate

    J Vib Control

    (2016)
  • R. Manoharan et al.

    Dynamic characterization of a laminated composite magnetorheological fluid sandwich plate

    Smart Mater Struct

    (2014)
  • V. Rajamohan et al.

    Optimal vibration control of beams with total and partial MR-fluid treatments

    Smart Mater Struct

    (2011)
  • R. Tabassian et al.

    Dynamic stability of smart sandwich beams with electro-rheological core resting on elastic foundation

    J Sandwich Struct Mater

    (2013)
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