Postdoctoral Research Fellow Irish Research Council for Science, Engineering & Technology Mechanical, Aeronautical and Biomedical Engineering, The Irish Centre for Composites Research MSSI, Materials & Surface Science Institute, University of Limerick, Limerick Republic of IRELAND
Dr Murmu is the winner of the prestigious IRCSET (Irish Research Council for Science, Engineering & Technology) EMPOWER Postdoc Fellowship for 2011 (Ireland). His present research focus is in understanding structural engineering at nanoscale. Dr Murmu obtained his PhD from IIT Kharagpur. Dr Murmu's research areas are multidisciplinary in nature and include Theory at Nanoscale; Nonlocal Elasticity; Molecular Dynamics; Graphene; CNTs; Buckyballs; Fracture and Fatigue; Nanostructures, Functionally Graded Materials, Nanocomposites; DQM. He has published 30 peer reviewed journal papers and 9 conference papers in these areas and attracted € 79000 research funding. He is editorial member of the journal ISRN Nanomaterials. He is a member of American Nano Society and is an active reviewer of 18 international journals. Before joining University of Limerick, Ireland as Postdoctoral fellow he was postdoctoral researcher in Swansea University, UK.
Abstract: Vibration analyses of coupled nanobeam system under initial compressive pre-stressed condition are presented. An elastically connected double-nanobeam-system is considered. Expressions for bending-vibration of pre-stressed double-nanobeam-system are formulated using Eringen's nonlocal elasticity model. An analytical method is proposed to obtain natural frequencies of the nonlocal double-nanobeam-system (NDNBS). Nano-scale effects and coupling spring effects in (i) in-phase type, (ii) out-of-phase type vibration; and (ii) vibration with one nanobeam fixed are examined. Scale effects in higher natural frequencies of NDNBS are also highlighted in this manuscript. Results reveal the difference (quantitatively) by which the pre-load affects the nonlocal frequency in the in-phase type and out-of-phase type vibrations mode of NDNBS. (C) 2011 Elsevier Masson SAS. All rights reserved.
Abstract: As a first endeavor, we propose nonlocal elasticity theory for carbon nanotube based cantilever biosensors. By using the frequency-shift of the fundamental vibration mode, we develop new nonlocal frequency sensor equations utilizing energy principles. Two physically realistic configurations of the added mass, namely, point mass and distributed mass are considered. Exact closed-form expressions relating the frequency-shift and the added mass have been derived for both the cases. The proposed nonlocal sensor-equations are general in nature and depend on three non-dimensional calibration constants namely, the stiffness calibration constant, the mass calibration constant and the nonlocal calibration constant. Explicit analytical expressions of these calibration constants are derived. An example of a single wall carbon nanotube with attached multiple strands of deoxythimidine is considered to illustrate the analytical results. Molecular mechanics simulation is used to validate the new nonlocal sensor equations. The optimal values of nonlocal parameter are obtained from the molecular mechanics simulation results. The nonlocal approach generally predicts the frequency shift accurately compared to the local approach. Numerical results show the importance of considering the distributed nature of the added mass while using the nonlocal theory. (C) 2011 Elsevier B.V. All rights reserved.
Abstract: This paper presents a multiscale approach for vibration frequency analysis of graphene/polymer composites. The graphene is modelled at the atomistic scale, and the matrix deformation is analysed by the continuum finite element method. Inter-connectivity between graphene and polymer matrix are assumed to be bonded by van der Waals interactions at the interface. The impact of geometrical configuration (armchair and zigzag), boundary conditions and length on the overall stiffness of the graphene reinforced plastics (GRP) is studied. The natural frequency and vibrational mode shapes of GRP studied have displayed dependence on the length and also the boundary conditions. The exceptional vibrational behaviour and large stiffness displayed by GRP makes them a potential replacement for conventional composite fibres such as carbon and glass fibres. (C) 2011 Elsevier B.V. All rights reserved.
Abstract: In this paper the nonlocal shell and beam theories are used to study the transverse vibration of slender NTs. The agreement between the shell model and molecular dynamics simulations shows that the nonlocal effect originates predominantly from the atom-atom interaction in circumferential direction. It thus does not decrease with rising axial wavelength. In this case, a nearly constant nonlocal coefficient e(0) can be achieved for vibrating NTs. These behaviors however cannot be captured by the widely used nonlocal beam theory where only the axial nonlocal effect is included. Thus, caution must be taken when the one-dimensional nonlocal model is applied to slender NTs. (C) 2012 Elsevier Ltd. All rights reserved.
Abstract: The behaviour of carbon nanotubes in a magnetic field has attracted considerable attention in the scientific community. This paper reports the effects of a longitudinal magnetic field on the vibration of a magnetically sensitive double single-walled carbon nanotube system (DSWNTS). The two nanotubes of the DSWNTS are coupled by an elastic medium. The dynamical equations of the DSWNTS are derived using nonlocal elasticity theory. The two nanotubes are defined as an equivalent nonlocal double-Euler-Bernoulli beam system. Governing equations for nonlocal bending-vibration of the DSWNTS under a longitudinal magnetic field are derived considering the Lorentz magnetic force obtained from Maxwell's relation. An analytical method is proposed to obtain nonlocal natural frequencies of the DSWNTS. The influence of (i) nanoscale effects and (ii) strength of longitudinal magnetic field on the synchronous and asynchronous vibration phase of the DSWNTS is examined. Nonlocal effects with and without the effect of magnetic field are illustrated. Results reveal the difference (quantitatively) by which the longitudinal magnetic field affects the nonlocal frequency in the synchronous and asynchronous vibration modes of a DSWNTS. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4720084]
Abstract: This Letter considers the axial instability of double-nanobeam-systems. Eringen's nonlocal elasticity is utilized for modelling the double-nanobeam-systems. The nonlocal theory accounts for the small-scale effects arising at the nanoscale. The small-scale effects substantially influence the instability (or buckling) of double-nanobeam-systems. Results reveal that the small-scale effects are higher with increasing values of nonlocal parameter for the case of in-phase (synchronous) buckling modes than the out-of-phase (asynchronous) buckling modes. The increase of the stiffness of the coupling elastic medium in double-nanobeam-system reduces the small-scale effects during the out-of-phase (asynchronous) buckling modes. Analysis of the scale effects in higher buckling loads of double-nanobeam-system with synchronous and asynchronous modes is also discussed in this Letter. The theoretical development presented herein may serve as a reference for nonlocal theories as applied to the instability analysis of complex-nanobeam-system such as complex carbon nanotube system. (C) 2010 Elsevier B.V. All rights reserved.
Abstract: Nonlocal longitudinal vibration of single-walled-carbon-nanotubes (SWCNTs) with attached buckyballs is considered. Attached buckyball at the tip of a SWCNT can significantly influence the resonance frequency of the vibrating system. Closed-form nonlocal transcendental equation for vibrating system with arbitrary mass ratio i.e. mass of buckyball to mass of SWCNT is derived. Nonlocal elasticity concept is employed to develop the frequency equations. Explicit analytical expressions of axial frequencies are proposed when mass of the attached buckyball is larger than the mass of SWCNT. Nonlocal longitudinal frequencies are validated with existing molecular dynamic simulation result. For arbitrary mass ratios, the frequency shifts in SWCNT due to (i) added buckyballs and (ii) nonlocal-effects are investigated. The present communication may be useful when designing tuneable resonator in NEMS applications. (C) 2010 Elsevier Ltd. All rights reserved.
Abstract: In this paper, torsional vibration analysis of single-walled carbon nanotube-buckyball systems is carried out. The buckyball is attached to single-walled carbon nanotube (SWCNT) at one end and the other end of SWCNT is fixed. Such nanostructures are promising for tunable nanoresonators whose frequency can be altered by attaching different buckyballs. Nonlocal elasticity is utilized to examine the small-scale effect on the nanoresonators and derive the torsional frequency equation and nonlocal transcendental equation. Based on these equations, numerical results are obtained for the dependence of the frequency on the mass moment of inertia. The analytical expressions of nonlocal frequencies are also derived when the buckyballs mass moment of inertias are much larger than that of SWCNTs. In addition, effort is made to study the influence of nonlocal parameter and attached buckyball on the torsional frequency of the nanoresonators. (C) 2011 Elsevier B.V. All rights reserved.
Abstract: Nonlocal vibration of a double-nanoplate-system is considered. The two nanoplates are assumed to be bonded by an enclosing elastic medium. Situation of this type would arise in multiple graphene sheets dispersed in nanocomposites. Expressions for free bending-vibration of double-nanoplate-system are established utilising nonlocal elasticity. An analytical method is introduced for determining the natural frequencies of nonlocal double-nanoplate-system (NDNPS). Explicit closed-form expressions for natural frequencies are derived for the case when all four ends are simply-supported. Two single-layered graphene sheets coupled within bonding polymer matrix are considered. The study highlights that the small-scale effects considerably influence the transverse vibration of NDNPS. The small-scale effects in NDNPS are higher with the increasing values of nonlocal parameter for the case of synchronous modes of vibration than in the asynchronous modes. The increase of the stiffness of the coupling springs in NDNPS reduces the small-scale effects during the asynchronous modes of vibration. Further, the effect of aspect ratio and higher modes on the natural frequencies of NDNPS is studied in this manuscript. Present work may provide an analytical scale-based nonlocal approach which could serve as the starting point for further investigation of more complex n-nanoplates systems arising in future generation graphene based nanocomposites. (C) 2011 Elsevier Ltd. All rights reserved.
Abstract: This letter presents a study of the mechanisms of nonlocal effect on the transverse vibration of two-dimensional (2D) nanoplates, e. g., monolayer layer graphene and boron-nitride sheets. It is found that such a nonlocal effect stems from a distributed transverse force due to (1) the curvature change in the nanoplates and (2) the surface stress due to the nonlocal atom-atom interaction. A single equivalent vibration wavelength is defined to measure the nonlocal effect on the vibration of 2D nanoplates. The critical equivalent wavelength of order 0.55 to 2.23 nm is obtained for significant nonlocal effect on monolayer graphene. (C) 2011 American Institute of Physics. [doi:10.1063/1.3579249]
Abstract: Buckling behavior of a bonded, uni-axially compressed double-nanoplate-system is investigated in this work. Both the synchronous and asynchronous-type buckling is considered in detail. The two nanoplates are assumed elastically bonded by a polymer resin. The nano-scale effects of nanoplates are dealt with in the analysis by using nonlocal elasticity theory. The theory is utilized for deriving the expressions for a buckling load of a double-nanoplate-system. A simple analytical method is introduced for determining the buckling load of a nonlocal double-nanoplate-system. Explicit closed-form expressions for the buckling load are derived for the case when all four ends are simply supported. Single-layered graphene-sheets are considered for the study. The study highlights that the nonlocal effects considerably influence the buckling behavior of the double-graphene-sheet-system. Unlike the buckling behavior of a single graphene sheet, the double-graphene-sheet-system undergoes both synchronous as well as asynchronous buckling. The nonlocal effects in the double-graphene-sheet-system are higher with increasing values of the nonlocal parameter for the case of synchronous buckling modes than in the asynchronous buckling modes. The increase of the stiffness of the coupling springs in the double-graphene-sheet-system reduces the nonlocal effects during the asynchronous modes of buckling. Different aspect ratios of the double-graphene-sheet-system and higher buckling modes are also considered in the work. (C) 2011 American Institute of Physics. [doi:10.1063/1.3644908]
Abstract: Nonlocal elasticity theory is implemented to investigate the buckling behavior of single-layered graphene sheet (SLGS) embedded in an elastic medium. Nonlocal elasticity theory accounts for the small-size effects when dealing with nanostructures such as graphene sheets. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction between the graphene sheet and the surrounding elastic medium. Based on principle of virtual work, governing differential equations for the aforementioned problem are derived. Differential quadrature method is being employed and numerical solutions for the buckling loads of SLGS are obtained. Numerical results show that the buckling loads of SLGS are strongly dependent on the small scale coefficients and the stiffness of the surrounding elastic medium. With elastic medium modeled as Winkler-type foundation, the nonlocal effects are found to have decrease-increase-decrease pattern with increase in stiffness of elastic medium. (C) 2009 Elsevier B.V. All rights reserved.
Abstract: In this paper, nonlocal beam model is applied to the buckling analysis of single-walled carbon nanotubes (SWCNT) with effect of temperature change and surrounding elastic medium. The SWCNT is considered to be embedded in a Winkler-type elastic medium. The small scale and the thermal effects in SWCNT are incorporated through the nonlocal and thermal elasticity mechanics, respectively. Small-scale effects on buckling load are examined considering various parameters. These parameters include temperature change, aspect ratios, stiffness of Winkler-type elastic medium and mode numbers. The present study shows that at low temperature changes and large scale coefficient, the difference between local buckling load and nonlocal buckling load is comparatively large. Further it is found that the influence of temperature change on buckling load decreases in case of stiffer elastic medium. (C) 2009 Elsevier B.V. All rights reserved.
Abstract: In this article, a single nonlocal beam model is developed and applied to investigate the flapwise bending-vibration characteristics of a rotating nanocantilever. A rotating nanocantilever is found as blades of a nanoturbine. Employing Eringen's nonlocal elasticity theory, the governing differential equations for the abovementioned problem are derived. Differential quadrature method (DQM) is being utilized and nondimensional nonlocal frequencies are obtained. The effects of the small-scale, angular velocity and hub radius are examined and discussed. It is shown that small-scale effects play a significant role in the vibration response of a rotating nanocantilever. Further as rotational angular velocity increases, the small-scale effect on the frequency response is increased for first modes of vibration while it is decreased for higher modes of vibration. (C) 2010 Elsevier B.V. All rights reserved.
Abstract: Vibration analysis of double-nanobeam-systems is considered. Double-nanobeam-systems are important in nano-optomechanical systems and sensor applications. Expressions for free bending-vibration of double-nanobeam-system are established within the framework of Eringen's nonlocal elasticity theory. An analytical method is developed for determining the natural frequencies of the nonlocal double-nanobeam-system. Explicit closed-form expressions for natural frequencies are derived for the case when all four ends are simply-supported. The study highlights that the small-scale effects considerably influence the transverse vibration of double-nanobeam-systems. The nonlocal natural frequencies of double-nanobeam-system are smaller when compared to the corresponding local frequency values. The small-scale effects in the vibrating system are higher with increasing values of nonlocal parameter for the case of in-phase modes of vibration than in the out-of-phase modes of vibration. The increase in the stiffness of the coupling springs in double-nanobeam-system reduces the nonlocal effects during the out-of-phase modes of vibration. (C) 2010 American Institute of Physics. [doi:10.1063/1.3496627]
Abstract: This paper presents an investigation on the longitudinal vibration of a double-nanorod-system (DNRS). The double-nanorod-systems are important in nanooptomechanical systems (NOMS). For the development of the governing equations, Eringen's nonlocal elasticity is utilized. It is assumed that the two nanorods of the DNRS are coupled by longitudinally directed distributed springs. An analytical method is developed for solving the nonlocal frequencies of longitudinally vibrating DNRS. Clamped-clamped and clamped-free boundary conditions are employed and their explicit relationships are derived. Numerical studies are carried out for coupled double-carbon-nanotube-rod system. This study highlights that the nonlocal effect considerably influences the axial vibration of DNRS. The results obtained in this paper can be useful for the study of axially vibrating complex multiple-nanobeam system in NOMS. (C) 2010 Elsevier B.V. All rights reserved.
Abstract: Understanding the dynamic behavior of rotating nanostructures is important for practical development of nanomachines. At the nanoscale, the nonlocal effects often become prominent. In this study, we investigate the nonlocal effects in bending-vibration of an initially prestressed single-walled carbon nanotube via nonlocal elasticity. The carbon nanotube is assumed to be attached to a molecular hub and is undergoing rotation. Nonlocal Euler-Bernoulli beam theory is employed to formulate the governing equations. Differential quadrature method is being utilized and the nonlocal bending frequencies of the rotating system are determined. The effects of the initial preload on vibration characteristics of rotating carbon nanotube are examined. Further, influence of (a) nonlocal effects (b) angular velocities, (c) hub radii and (d) higher mode frequencies are studied. It is explicitly shown that the bending vibration of a rotating carbon nanotube is significantly influenced by the existence of a preload, angular velocity and the nonlocal parameter. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3520404]
Abstract: Nonlocal elasticity theory is a popular growing technique for the mechanical analyses of MEMS and NEMS structures. The nonlocal parameter accounts for the small-size effects when dealing with nano-size structures such as single-walled carbon nanotubes (SWCNTs). In this article, nonlocal elasticity and Timoshenko beam theory are implemented to investigate the stability response of SWCNT embedded in an elastic medium. For the first time, both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of the (SWCNT) with the surrounding elastic medium. A differential quadrature approach is utilized and numerical solutions for the critical buckling loads are obtained. Influences of nonlocal effects, Winkler modulus parameter. Pasternak shear modulus parameter and aspect ratio of the SWCNT on the critical buckling loads are analyzed and discussed. The present study illustrates that the critical buckling loads of SWCNT are strongly dependent on the nonlocal small-scale coefficients and on the stiffness of the surrounding medium. (C) 2009 Elsevier B.V. All rights reserved.
Abstract: Nonlocal elasticity theory is a growing technique for the mechanical analyses of microelectromechanical (MEMS) and nanoelectromechanical (NEMS) based structures. The nonlocal parameter accounts for the small size effects when dealing with nanosize structures such as single-walled carbon nanotubes (SWCNTs). In this article, nonlocal elasticity and Timoshenko beam theory are implemented to study the vibration response of SWCNT embedded in an elastic medium. Influence of the surrounding elastic medium on the fundamental frequencies of the SWCNT is investigated. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of the SWCNT with the surrounding elastic medium. A differential quadrature approach is being utilized and numerical solutions for the natural frequencies are obtained. Influences of nonlocal effects, Winkler modulus parameter, Pasternak shear modulus parameter, and aspect ratio on the frequency of SWCNT are analyzed and discussed. The present study illustrates that the frequencies of embedded SWCNT are significantly dependent on the nonlocal parameter and on the stiffness of the surrounding elastic medium. (c) 2009 American Institute of Physics. [DOI: 10.1063/1.3151703]
Abstract: Thermo-mechanical vibration analysis of functionally graded (FG) beams and functionally graded sandwich (FGSW) beams are presented. The functionally graded material (FGM) beams are considered to be resting on variable (i) Winkler foundation and (ii) two-parameter elastic foundation. The material properties of these beams are assumed to be varying ill the thickness direction. The governing differential equations for beam vibration are being solved using the modified differential quadrature method (MDQM). The applied kinematic boundary conditions are implemented using the modified weighting coefficient matrix (MWCM). The weighting coefficients are generated from the Chebyshev basis function. Present results for the vibration of isotropic beam with variable Winkler foundation are in good agreement with those reported in the literature. Parametric study oil the vibration response of FG beams and FGSW beams are being investigated. These parameters include (i) temperature distributions, (ii) power-law index, (iii) variable Winkler foundation modulus, (iv) two-parameter elastic foundation modulus and (v) normalized core thickness of FGSW beams. (C) 2008 Elsevier Ltd. All rights reserved.
Abstract: In the present work, nonlocal elasticity theory has been implemented to study the vibration response of single-layered graphene (SLGS) sheets. The nonlocal elasticity theory accounts for the small size effects when dealing with nanostructures. Influence of the surrounding elastic medium on the fundamental frequencies of the SLGS is investigated. Both Winkler-type and Pasternak-type models are employed to simulate the interaction of the graphene sheets with a surrounding elastic medium. On the basis of Hamilton's principle governing differential equations for the aforementioned problems are derived. The nonlocal small scale coefficients get introduced into the nonlocal theory through the constitutive relations. Differential quadrature method is being employed and numerical solutions for the frequencies are obtained. Numerical results show that the fundamental frequencies of SLGS are strongly dependent on the small scale coefficients. Further, a nonlinear frequency response is observed for the SLGS with larger nonlocal effects and "Winkler-type modeled" surrounding medium.
Abstract: In the present paper, small-scale effects on the free in-plane vibration (FIV) of nanoplates are investigated employing nonlocal continuum mechanics. Equations of motion of the nonlocal plate model for the aforementioned study are derived and presented. Explicit relations for natural frequencies are obtained through direct separation of variables. It has been shown that nonlocal effects are quite significant in in-plane vibration studies and need to be included in the continuum model of nanoplates such as in graphene sheets. (C) 2009 Elsevier B.V. All rights reserved.
Abstract: A single-elastic beam model has been developed to analyze the thermal vibration of single-walled carbon nanotubes (SWCNT) based on thermal elasticity mechanics, and nonlocal elasticity theory. The nonlocal elasticity takes into account the effect of small size into the formulation. Further, the SWCNT is assumed to be embedded in an elastic medium. A Winkler-type elastic foundation is employed to model the interaction of the SWCNT and the surrounding elastic medium. Differential quadrature method is being utilized and numerical solutions for thermal-vibration response of SWCNT is obtained. Influence of nonlocal small scale effects, temperature change, Winkler constant and vibration modes of the CNT on the frequency are investigated. The present study shows that for low temperature changes, the difference between local frequency and nonlocal frequency is comparatively high. With embedded CNT, for soft elastic medium and larger scale coefficients (e(0)a) the nonlocal frequencies are comparatively lower. The nonlocal model-frequencies are always found smaller than the local model-frequencies at all temperature changes considered. (C) 2009 Elsevier B.V. All rights reserved.
Abstract: In this article, the elastic buckling behavior of orthotropic small scale plates under biaxial compression is studied. Analysis is carried out with the consideration of small scale effects. Employing nonlocal elasticity theory (Eringen, 1983) governing equations for the aforementioned problems are derived. Explicit expressions for modified buckling loads are obtained for micro/nanoplates with isotropic and orthotropic properties; and under uniaxial and biaxial compressions. The effects of the small scale on the buckling loads of plates considering various material and geometrical parameters are examined. (C) 2009 Elsevier Ltd. All rights reserved.
Abstract: In this article, nonlocal elasticity theory is applied to investigate the vibration response of nanoplates under uniaxially prestressed conditions. Nonlocal elasticity theory takes into account the small-size effects when dealing with nanostructures. Nonlocal governing equations of the prestressed nanoplate are derived and presented. Differential quadrature method is being utilized and numerical frequency solutions are obtained. Influence of small scale and uniaxial preload on the nonlocal frequency solutions is investigated. It is observed that the frequencies for nanoplates under uniaxially prestressed conditions employing classical plate theory are overestimated compared to nonlocal plate solutions. Considering the nonlocal effects, smaller critical compressive load is required to reach the buckling state of a flexural mode compared to the classical plate theory. The present research work thus reveals that the nonlocal parameter, aspect ratios, boundary conditions, and initial uniaxial prestress have significant effects on vibration response of the nanoplates. (C) 2009 American Institute of Physics. [doi:10.1063/1.3233914]
Abstract: In this article, the small scale effect on the buckling analysis of biaxially compressed single-layered graphene sheets (SLGS) is studied using nonlocal continuum mechanics. The nonlocal mechanics accounts for the small size effects when dealing with nano size elements such as graphene sheets. Using the principle of virtual work the governing equations are derived for rectangular nanoplates. Solutions for buckling loads are computed using differential quadrature method (DQM). It is shown that the nonlocal effect is quite significant in graphene sheets and has a decreasing effect on the buckling loads. When compared with uniaxially compressed graphene, the biaxially compressed one show lower influence of nonlocal effects for the case of smaller side lengths and larger nonlocal parameter values. This difference in behavior between uniaxial and biaxial compressions decreases as the size of the graphene sheets increases. (C) 2009 Elsevier B.V. All rights reserved.
Abstract: In this article, vibration response of nanocantilever is investigated considering nonuniformity in the cross sections. Using nonlocal elasticity theory, governing differential equations are established. Differential quadrature (DQ) method is being employed and natural frequencies of the structure are obtained. The present study shows that the nonlocal frequency solutions of nanocantilever are larger compared to the classical (local) solutions till a critical height ratio (CHR). Beyond the CHR, nonlocal solutions are lower than the classical (local) solutions. (C) 2009 Elsevier B.V. All rights reserved.
