• Structural Engineering and Mechanics
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• v.76 no.1
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• pp.141-151
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• 2020

This manuscript tends to investigate influences of nanoscale and surface energy on a static bending and free vibration of piezoelectric perforated nanobeam structural element, for the first time. Nonlocal differential elasticity theory of Eringen is manipulated to depict the long-range atoms interactions, by imposing length scale parameter. Surface energy dominated in nanoscale structure, is included in the proposed model by using Gurtin-Murdoch model. The coupling effect between nonlocal elasticity and surface energy is included in the proposed model. Constitutive and governing equations of nonlocal-surface perforated Euler-Bernoulli nanobeam are derived by Hamilton's principle. The distribution of electric potential for the piezoelectric nanobeam model is assumed to vary as a combination of a cosine and linear variation, which satisfies the Maxwell's equation. The proposed model is solved numerically by using the finite-element method (FEM). The present model is validated by comparing the obtained results with previously published works. The detailed parametric study is presented to examine effects of the number of holes, perforation size, nonlocal parameter, surface energy, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric perforated nanobeams. It is found that the effect of surface stresses becomes more significant as the thickness decreases in the range of nanometers. The effect of number of holes becomes significant in the region 0.2 ≤ α ≤ 0.8. The current model can be used in design of perforated nano-electro-mechanical systems (PNEMS).

• Journal of Astronomy and Space Sciences
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• v.26 no.1
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• pp.31-46
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• 2009

An Unscented Kalman Filter (UKF) for estimation of the attitude and rate of a spacecraft using only magnetometer vector measurement is developed. The attitude dynamics used in the estimation is the nonlinear Euler's rotational equation which is augmented with the quaternion kinematics to construct a process model. The filter is designed for small satellite in low Earth orbit, so the disturbance torques include gravity-gradient torque, magnetic disturbance torque, and aerodynamic drag torque. The magnetometer measurements are simulated based on time-varying position of the spacecraft. The filter has been tested not only in the standby mode but also in the detumbling mode. Two types of actuators have been modeled and applied in the simulation. The PD controller is used for the two types of actuators (reaction wheels and thrusters) to detumble the spacecraft. The estimation error converged to within 5 deg for attitude and 0.1 deg/s for rate respectively when the two types of actuators were used. A joint state parameter estimation has been tested and the effect of the process noise covariance on the parameter estimation has been indicated. Also, Monte-Carlo simulations have been performed to test the capability of the filter to converge with the initial conditions sampled from a uniform distribution. Finally, the UKF performance has been compared to that of the EKF and it demonstrates that UKF slightly outperforms EKF. The developed algorithm can be applied to any type of small satellites that are actuated by magnetic torquers, reaction wheels or thrusters with a capability of magnetometer vector measurements for attitude and rate estimation.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.11 s.104
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• pp.1287-1294
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• 2005

The purpose of this paper is to investigate free vibrations and critical loads of the Beck's columns with a tip spring, which carry a tip mass. The ordinary differential equation governing free vibrations of Beck's column subjected to a follower force is derived based on the Bernoulli-Euler beam theory Both the divergence and flutter critical loads are calculated from the load-frequency corves that are obtained by solving the differential equation numerically. The critical loads are presented in the figures as functions of various non-dimensional system parameters such as the subtangential parameter, mass ratio and spring parameter.

• Structural Monitoring and Maintenance
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• v.3 no.4
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• pp.349-375
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• 2016

The tension of an arch bridge hanger is estimated using a number of experimentally identified modal frequencies. The hanger is connected through metallic plates to the bridge deck and arch. Two different categories of model classes are considered to simulate the vibrations of the hanger: an analytical model based on the Euler-Bernoulli beam theory, and a high-fidelity finite element (FE) model. A Bayesian parameter estimation and model selection method is used to discriminate between models, select the best model, and estimate the hanger tension and its uncertainty. It is demonstrated that the end plate connections and boundary conditions of the hanger due to the flexibility of the deck/arch significantly affect the estimate of the axial load and its uncertainty. A fixed-end high fidelity FE model of the hanger underestimates the hanger tension by more than 20 compared to a baseline FE model with flexible supports. Simplified beam models can give fairly accurate results, close to the ones obtained from the high fidelity FE model with flexible support conditions, provided that the concept of equivalent length is introduced and/or end rotational springs are included to simulate the flexibility of the hanger ends. The effect of the number of experimentally identified modal frequencies on the estimates of the hanger tension and its uncertainty is investigated.

• Smart Structures and Systems
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• v.25 no.2
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• pp.219-228
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• 2020

This work presents a modified continuum model to explore and investigate static and vibration behaviors of perforated piezoelectric NEMS structure. The perforated nanostructure is modeled as a thin perforated nanobeam element with Euler-Bernoulli kinematic assumptions. A size scale effect is considered by included a nonlocal constitutive equation of Eringen in differential form. Modifications of geometrical parameters of perforated nanobeams are presented in simplified forms. To satisfy the Maxwell's equation, the distribution of electric potential for the piezoelectric nanobeam model is assumed to be varied as a combination of a cosine and linear functions. Hamilton's principle is exploited to develop mathematical governing equations. Modified numerical finite model is adopted to solve the equation of motion and equilibrium equation. The proposed model is validated with previous respectable work. Numerical investigations are presented to illustrate effects of the number of perforated holes, perforation size, nonlocal parameter, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric nanobeams.

• Advances in nano research
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• v.6 no.1
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• pp.21-37
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• 2018

In the present article, wave dispersion behavior of a temperature-dependent functionally graded (FG) nanobeam undergoing rotation subjected to thermal loading is investigated according to nonlocal strain gradient theory, in which the stress numerates for both nonlocal stress field and the strain gradient stress field. The small size effects are taken into account by using the nonlocal strain gradient theory which contains two scale parameters. Mori-Tanaka distribution model is considered to express the gradually variation of material properties across the thickness. The governing equations are derived as a function of axial force due to centrifugal stiffening and displacements by applying Hamilton's principle according to Euler-Bernoulli beam theory. By applying an analytical solution, the dispersion relations of rotating FG nanobeam are obtained by solving an eigenvalue problem. Obviously, numerical results indicate that various parameters such as angular velocity, gradient index, temperature change, wave number and nonlocality parameter have significant influences on the wave characteristics of rotating FG nanobeams. Hence, the results of this research can provide useful information for the next generation studies and accurate deigns of nanomachines including nanoscale molecular bearings and nanogears, etc.

• Advances in nano research
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• v.6 no.1
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• pp.57-80
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• 2018

In this study, the thermal loading effect on free vibration characteristics of carbon nanotubes (CNTs) with multiple cracks is studied. Various boundary conditions for nanotube are taken in to account. In order to take the small scale effect, the nonlocal elasticity of Eringen is employed in the framework of Euler-Bernoulli beam theory. This theory states that the stress at a reference point is a function of strains at all points in the continuum. A cracked nanotube is assumed to be consisted of two segments that are connected by a rotational spring which is located in the position of the cracked section. Hamilton's principle is used to achieve the governing equations. Influences of the nonlocal parameter, crack severity, temperature change and the number of cracks on the system frequencies are investigated. Also, it is found that at room or lower temperature the natural frequency for CNT decreases as the value of temperature change increases, while at temperature higher than room temperature the natural frequency of CNT increases as the value of temperature change increases. Various boundary conditions have been applied to the nanotube.

• International Journal of Aeronautical and Space Sciences
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• v.15 no.1
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• pp.82-90
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• 2014

In this paper, the effect of Lorentz force on the stability of attitude orientation of a charged spacecraft moving in an elliptic orbit in the geomagnetic field is considered. Euler equations are used to derive the equations of attitude motion of a charged spacecraft. The equilibrium positions and its stability are investigated separately in the pitch, roll and yaw directions. In each direction, we use the Lorentz force to identify an attitude stabilization parameter. The analytical methods confirm that we can use the Lorentz force as a stabilization method. The charge-to-mass ratio is the main key of control, in addition to the components of the radius vector of the charged center of the spacecraft, relative to the center of mass of the spacecraft. The numerical results determine stable and unstable equilibrium positions. Therefore, in order to generate optimum charge, which may stabilize the attitude motion of a spacecraft, the amount of charge on the surface of spacecraft will need to be monitored for passive control.

• Structural Engineering and Mechanics
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• v.46 no.3
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• pp.417-431
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• 2013

This paper presents responses of the free end of a cantilever micro beam under the effect of an impact force based on the modified couple stress theory. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the difference of the modified couple stress theory and the classical beam theory is investigated for the wave propagation. A few of the obtained results are compared with the previously published results. The influences of the material length scale parameter on the wave propagation are investigated in detail. It is clearly seen from the results that the classical beam theory based on the modified couple stress theory must be used instead of the classical theory for small values of beam height.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.4
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• pp.730-737
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• 1988

Determining the robot motion using optimal technique has been studied often in recent years however the study of determining the optimal robot dimensions is very rare. In this paper, the authors attempted to find out the least driving torques at each joint as the optimization of link length refered to a 3R robot manipulator. For the given linear path with triangular velocity profile, the inverse kinematic and inverse dynamic problems are examined in order to lead into solution of problem suggested for optimal design of link lengths. Accordingly, optimal link lengths in the case of given linear path is obtained with respect to the parameter of link ratios.