• Steel and Composite Structures
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• 제52권5호
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• pp.525-541
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• 2024

This study uses the state-space approach to study the bending behavior of Levy-type functionally graded (FG) plates sandwiched between two piezoelectric layers. The coupled governing equations are obtained using Hamilton's principle and Maxwell's equation based on the efficient four-variable refined plate theory. The partial differential equations (PDEs) are converted using Levy's solution technique to ordinary differential equations (ODEs). In the context of the state-space method, the higher-order ODEs are simplified to a system of first-order equations and then solved. The results are compared with those reported in available references and those obtained from Abaqus FE simulations, and good agreements between results confirm the accuracy and efficiency of the approach. Also, the effect of different parameters such as power-law index, aspect ratio, type of boundary conditions, thickness-to-side ratio, and piezoelectric thickness are studied.

• 대한기계학회논문집A
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• 제24권9호
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• pp.2201-2210
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• 2000

Vibration of a rotating disk-spindle system is analyzed by using Hamilton's principle, FEM and substructure synthesis. A rotating disk undergoes the rigid body motion and the elastic deformation. It s equation of motion is derived by Kirchhoff plate theory and von Karman nonlinear strain. A rotating shaft is described by Rayleigh beam theory considering the axial rigid body motion. The stationay shaft supporting the rotating disk-spindle-bearing system is modeled by Euler beam theory, and the stiffness of ball bearing is determined by A.B.Jones' theory. FEM is used to solve the derived governing equations, and substructure synthesis is introduced to assemble each structure of the rotating disk-spindle system. The developed theory is applied to the spindle system of a 35' computer hard disk drive with 3 disks to verify the simulation results. The simulation results agree very well with the experimental ones. The proposed theory may be effectively expanded to the complex structure of a disk-spindle system.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.153-158
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• 2004

In this paper, we proposed a two-stage control of the container crane. The first stage control is time-optimal control for the purpose of fast trolley traveling. With suitable trolley velocity patterns, the sway which is generated during trolley moving is minimized. At the second stage control feedback control law is investigated for the quick suppression of residual vibration after the trolley motion. For more practical system, the container crane system is modeled as a partial differential equation (PDE) system with flexible cable. The dynamics of the cable is derived as a moving system with tension caused by payload using Hamilton's principle for the systems. A control law based upon the Lyapunov's method is derived. It is revealed that a time-varying control force and a suitable passive damping at the actuator can successfully suppress the transverse vibrations.

• Advances in nano research
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• 제6권2호
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• pp.113-133
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• 2018

In this work, free vibration characteristics of functionally graded piezoelectric (FGP) nanobeams based on third order parabolic shear deformation beam theory are studied by presenting a Navier type solution as the first attempt. Electro-mechanical properties of FGP nanobeam are supposed to change continuously throughout the thickness based on power-law model. To capture the small size effects, Eringen's nonlocal elasticity theory is adopted. Using Hamilton's principle, the nonlocal governing equations for third order shear deformable piezoelectric FG nanobeams are obtained and they are solved applying analytical solution. By presenting some numerical results, it is demonstrated that the suggested model presents accurate frequency results of the FGP nanobeams. The influences of several parameters including, external electric voltage, power-law exponent, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams is discussed in detail.

• Advances in aircraft and spacecraft science
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• 제5권6호
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• pp.671-689
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• 2018

Bending, buckling and free vibration responses of functionally graded (FG) higher-order beams resting on two parameter (Winkler-Pasternak) elastic foundation are studied using a new inverse hyperbolic beam theory. The material properties of the beam are graded along the thickness direction according to the power-law distribution. In the present theory, the axial displacement accounts for an inverse hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Hamilton's principle is employed to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending, bucking and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and foundation parameter on the displacements, stresses, critical buckling loads and frequencies. Numerical results by using parabolic beam theory of Reddy and first-order beam theory of Timoshenko are specially generated for comparison of present results and found in excellent agreement with each other.

• 한국소음진동공학회논문집
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• 제19권6호
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• pp.569-574
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• 2009

The paper presents the influences of the external damping and the tip mass on dynamic stability of a vertical cantilevered pipe conveying fluid. In general, real pipe systems may have some valves and attached mechanical parts, which can be regarded as attached lumped masses and support-dampers. The support-dampers can be assumed as viscous dampers. The equations of motion are derived by energy expressions using extended Hamilton's principle, and some numerical results using Galerkin's method are presented. Critical flow velocities and stability maps of the pipe with external dampers and tip mass are obtained for various tip mass ratios, external damping coefficients and positions of the viscous dampers.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2012년도 추계학술대회 논문집
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• pp.653-660
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• 2012

In this paper free vibration analysis of symmetric and cross-ply elastic laminated shells based on FSDT with two different boundary conditions(C-C, S-S) was performed through discretization of equations of motion and boundary condition. Model of laminated composite cylindrical shells subjected to a combination of magnetic and thermal fields is developed via Hamilton's variational principle. These coupled equations of motion are based on the electromagnetic equations (Faraday, Ampere, Ohm, and Lorenz equations) and thermal equations which are involved in constitutive equations. Variations of dynamic characteristics of composite shells with applied magnetic field, temperature gradient, and stacking sequence for each boundary conditions are investigated and pertinent conclusions are derived.

• Computers and Concrete
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• 제24권6호
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• pp.579-586
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• 2019

In this research paper, the free vibrational behavior of the simply supported FG nano-plate is studied using the nonlocal two variables integral refined plate theory. The present model takes into account the small scale effect. The effective's properties of the plate change according to the power law variation (P-FGM). The equations of motion of the system are determined and resolved via Hamilton's principle and Navier procedure, respectively. The validity and efficiency of the current model are confirmed by comparing the results with those given in the literature. At the last section, several numerical results are presented to show the various parameters influencing the vibrational behavior such as the small-scale effect, geometry ratio, material index and aspect ratio.

• 한국안전학회지
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• 제11권2호
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• pp.116-121
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• 1996

On the stability of Timoshenko cantilever beam subjected to a follower force, the influence of the characteristics of elastic constraints at the free end Is studied. The equations of motion and boundary conditions of this nonconservative elastic system are estabilished by using the Hamilton's principle. Upon evaluation of the stability of this system, the effect of shear deformation and rotatory inertia is considered in calculation. Using cowper's formulae Timoshenko's shear coefficient K'are determined. From this imvestigation it is found that the constrain parameter have an appreciable stabilizing effect in this nonconservative system. Moreover, it is obvious that the small values of K'decrease the flutter load of this system.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 추계학술대회논문집
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• pp.465-468
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• 2005

The paper deals with the influences of external damping and tip mass on dynamic stability of a vertical cantilevered pipe conveying fluid. In general, real pipe systems may have some valves and attached parts, which can be regarded as attached lumped masses and support-dampers. The support-dampers can be assumed as viscous dampers. The equations of motion are derived by energy expressions using extended Hamilton's principle, and some numerical results using Galerkin's method are presented. Critical flow velocities and stability maps of the pipe with external dampers and tip mass are obtained for various tip mass ratios, external damping coefficients and positions of the viscous dampers.