In this article, free vibration behavior of magneto–electro–thermo-elastic functionally graded nanobeams is investigated based on a higher order shear deformation beam theory. Four types of thermal loading including uniform and linear temperature change as well as heat conduction and sinusoidal temperature rise through the thickness are assumed. Magneto–electro–thermo-elastic properties of FG nanobeam are supposed to change continuously throughout the thickness based on power-law model. Via nonlocal elasticity theory of Eringen, the small size effects are adopted. Based upon Hamilton’s principle, the coupled nonlocal governing equations for higher order shear deformable METE-FG nanobeams are obtained and they are solved applying analytical solution. It is shown that the vibrational behavior of METE-FG nanobeams is significantly affected by various temperature rises, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio.

Dynamic modeling of a thermo–piezo-electrically actuated nanosize beam subjected to a magnetic field

Free vibration behaviour of multiphase and layered magneto-electro-elastic beam

Wave band gaps in two-dimensional piezoelectric/piezomagnetic phononic crystals

The present paper examines the thermal buckling of nonlocal magneto-electro-thermo-elastic functionally graded (METE-FG) beams under various types of thermal loading namely uniform, linear and sinusoidal temperature rise and also heat conduction. The material properties of nanobeam are graded in the thickness direction according to the power-law distribution. Based on a higher order beam theory as well as Hamilton's principle, nonlocal governing equations for METE-FG nanobeam are derived and are solved using Navier type method. The small size effect is captured using Eringen's nonlocal elasticity theory. The most beneficial feature of the present beam model is to provide a parabolic variation of the transverse shear strains across the thickness direction and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. Various numerical examples are presented investigating the influences of thermo-mechanical loadings, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on thermal buckling behavior of nanobeams made of METE-FG materials.

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Buckling Analysis of Smart Size-Dependent Higher Order Magneto-Electro-Thermo-Elastic Functionally Graded Nanosize Beams

In this paper, size-dependent effect of an embedded magneto-electro-elastic (MEE) nanoshell subjected to thermo-electro-magnetic loadings on free vibration behavior is investigated. Also, the surrounding elastic medium has been considered as the model of Winkler characterized by the spring. The size-dependent MEE nanoshell is investigated on the basis of the modified couple stress theory. Taking attention to the first-order shear deformation theory (FSDT), the modeled nanoshell and its equations of motion are derived using principle of minimum potential energy. The accuracy of the presented model is validated with some cases in the literature. Finally, using the Navier-type method, an analytical solution of governing equations for vibration behavior of simply supported MEE cylindrical nanoshell under combined loadings is presented and the effects of material length scale parameter, temperature changes, external electric potential, external magnetic potential, circumferential wave numbers, constant of spring, shear correction factor and length-to-radius ratio of the nanoshell on natural frequency are identified. Since there has been no research about size-dependent analysis MEE cylindrical nanoshell under combined loadings based on FSDT, numerical results are presented to be served as benchmarks for future analysis of MEE nanoshells using the modified couple stress theory.

Free vibration analysis of embedded magneto-electro-thermo-elastic cylindrical nanoshell based on the modified couple stress theory

The free vibrations of simply supported magneto-electro-elastic cylindrical shells are studied. A series solution is assumed in the circumferential and axial directions of the shell to preserve the three-dimensional character of the structure. The constitutive equations of the magneto-electro-elastic medium involving mechanical, electrical and magnetic fields are used to derive the finite element model for the system. The influence of the piezomagnetic effect on the structural frequencies of the cylindrical shell is studied. A comparison is made between a shell with a layered configuration and one with a multiphase system. The study is carried out for a typical shell with simply supported boundary conditions for different ratios of length to radius and radius to thickness to analyse the frequency behaviour.

Free vibrations of simply supported layered and multiphase magneto-electro-elastic cylindrical shells

Free vibrations of clamped–clamped magneto-electro-elastic cylindrical shells

Analysis of a new single degree-of-freedom eight link leg mechanism for walking machine

The simulation studies performed on walking quadruped robot, with 8 link coplanar Desai’s walking leg mechanism, is conducted using SAM 6.1 software along with the kinematic analysis and motion analysis of a quadruped robot performed in SOLIDWORKS software. The optimised link lengths of each leg in Quadruped robot are obtained based on motion along a straight path and a staircase. The foot profile of optimised model is compared with Desai’s, Theos Jansen’s, and Joe Klann’s walking leg mechanisms. 

Anandkumar R. Annigeri

Papers

Free vibration behaviour of multiphase and layered magneto-electro-elastic beam

Free vibrations of simply supported layered and multiphase magneto-electro-elastic cylindrical shells

Free vibrations of clamped–clamped magneto-electro-elastic cylindrical shells

Analysis of a new single degree-of-freedom eight link leg mechanism for walking machine

Performance analysis of quadruped robot designed with Desai’s walking leg mechanism