• Structural Engineering and Mechanics
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• v.15 no.6
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• pp.705-716
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• 2003

Gradient elastic flexural beams are dynamically analysed by analytic means. The governing equation of flexural beam motion is obtained by combining the Bernoulli-Euler beam theory and the simple gradient elasticity theory due to Aifantis. All possible boundary conditions (classical and non-classical or gradient type) are obtained with the aid of a variational statement. A wave propagation analysis reveals the existence of wave dispersion in gradient elastic beams. Free vibrations of gradient elastic beams are analysed and natural frequencies and modal shapes are obtained. Forced vibrations of these beams are also analysed with the aid of the Laplace transform with respect to time and their response to loads with any time variation is obtained. Numerical examples are presented for both free and forced vibrations of a simply supported and a cantilever beam, respectively, in order to assess the gradient effect on the natural frequencies, modal shapes and beam response.

• Structural Engineering and Mechanics
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• v.82 no.6
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• pp.747-756
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• 2022

This study presents the nonlinear free and forced vibrations of a cracked atomic force microscopy (AFM) cantilever by using the modified couple stress. The cracked section of the AFM cantilever is considered and modeled as rotational spring. In the frame work of Euler-Bernoulli beam theory, Von-Karman type of geometric nonlinear equation and the modified couple stress theory, the nonlinear equation of motion for the cracked AFM is derived by Hamilton's principle and then discretized by using the Galerkin's method. The semi-inverse method is utilized for analysis nonlinear free oscillation of the system. Then the method of multiple scale is employed to investigate primary resonance of the system. Some numerical examples are presented to illustrate the effects of some parameters such as depth of the crack, length scale parameter, Tip-Mass, the magnitude and the location of the external excitation force on the nonlinear free and forced vibration behavior of the system.

• Interaction and multiscale mechanics
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• v.2 no.2
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• pp.189-207
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• 2009

Dynamics of the electric system for the toroidal drive under mechanical disturbance is presented. Using the method of perturbation, free vibrations of the electric system under mechanical disturbance are studied. The forced responses of the electric system to voltage excitation under mechanical disturbance are also presented. We show that as the time grows, the resonance vibration caused by voltage excitation still exists and the vibrations caused by mechanical disturbance are enlarged. The coupled resonance vibration caused by mechanical disturbance and voltage excitation is discussed. The conditions of the occurrence of coupled resonance are studied.

• Structural Engineering and Mechanics
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• v.71 no.5
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• pp.553-562
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• 2019

This paper presents the results of a study into the dynamic behaviour of a support structure of a mobile elevating work platform. The vibrations of the mechanical system of the observed structure are examined analytically, numerically, and experimentally. Within the analytical examination, a simple mathematical model is developed to describe free and forced vibrations. The dynamic analysis of the mechanical system is conducted using a discrete dynamic model with a reduced number of vibrational degrees of freedom. On the basis of the expression for the system energy, and by applying Lagrange's equations of the second kind, differential equations are derived for system vibrations, frequencies are determined, and the laws of forced platform vibration are established. At the same time, a nonlinear FEM model is developed and the laws of free and forced vibration are determined. The experimental and numerical part of the study deal with the examination of the real structure in extreme conditions, taking into account: the lowest eigenfrequency, forced actions that could endanger the general stability, the maximal amplitudes, and the acceleration of the work platform. The obtained analytical and numerical results are compared with the experiments. The experimental verification points to the adverse behaviour of the platform in excitation cases - swaying. In such a situation, even a relatively small physical force can lead to unacceptably high amplitudes of displacement and acceleration - exceeding the usual work values.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.598-604
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• 2003

In order to meet the growing demands for higher storage density as well as lower noise level, the spindles In hard disk drives are to be supported by hydrodynamic bearings in place of conventional ones. However, the existing models are inappropriate to apply to accurate Prediction or vibration characteristics because the Inn spindle tends to take quite a complex shape to secure the performance of the new type bearings. In this context, this paper treats analysis of free and forced vibrations of such-designed HDD spindles based on more sophisticated models and validation by means of experiments. Remarkably, to this end each component in the system is modeled as elastic adopting the finite element method.

• Steel and Composite Structures
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• v.32 no.5
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• pp.643-655
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• 2019

Perforation and cutouts of structures are compulsory in some modern applications such as in heat exchangers, nuclear power plants, filtration and microeletromicanical system (MEMS). This perforation complicates dynamic analyses of these structures. Thus, this work tends to introduce semi-analytical model capable of investigating the dynamic performance of perforated beam structure under free and forced conditions, for the first time. Closed forms for the equivalent geometrical and material characteristics of the regular square perforated beam regular square, are presented. The governing dynamical equation of motion is derived based on Euler-Bernoulli kinematic displacement. Closed forms for resonant frequencies, corresponding Eigen-mode functions and forced vibration time responses are derived. The proposed analytical procedure is proved and compared with both analytical and numerical analyses and good agreement is noticed. Parametric studies are conducted to illustrate effects of filling ratio and the number of holes on the free vibration characteristic, and forced vibration response of perforated beams. The obtained results are supportive in mechanical design of large devices and small systems (MEMS) based on perforated structure.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.1910-1919
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• 1994

The nonlinear behavior of continuous structural systems which possess external resonances as well as internal resonances are found be exhibit interesting reponses, arising because of the exhange of energy between the coupled modes. In this paper, the undamped forced vibrations was studied on the effect of primary resonance based on the concept of normal modes. By using the concept of normal mode the stability relation between free and forced vibrations was investigated in case of small exciting force. Numerical results show that the excitation of one unstable mode has a great influence on the response of the other mode but that of one stable mode does not.

• Structural Engineering and Mechanics
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• v.89 no.1
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• pp.33-46
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• 2024

The present research delves into the analysis of nonlinear free and forced vibrations of porous functionally graded (FG) shallow shells reinforced with oblique stiffeners, which are embedded in a nonlinear elastic foundation (NEF) subjected to external excitation. Two distinct types of PFG shallow shells, characterized by even and uneven porosity distribution along the thickness direction, are considered in the research. In order to model the stiffeners, Lekhnitskii's smeared stiffeners technique is implemented. With the stress function and first-order shear deformation theory (FSDT), the nonlinear model of the oblique stiffened shallow shells is established. The strain-displacement relationships for the system are derived via the FSDT and utilization of the von-Kármán's geometric assumptions. To discretize the nonlinear governing equations, the Galerkin method is employed. The model such developed allows analysis of the effects of the stiffeners with various angles as desired, in addition to the quantitative investigation on the influence of the surrounding nonlinear elastic foundations. To numerically solve the problem of vibrations, the 4th-order P-T method is used, as this method, known for its enhanced accuracy and reliability, proves to be an effective choice. The validation of the present research findings includes a comprehensive comparison with outcomes documented in existing literature. Additionally, a comparative analysis of the numerical results against those obtained using the 4th Runge-Kutta method is performed. The impact of stiffeners with varying angles and material parameters on the vibration characteristics of the present system is also explored. The researchers and engineers working in this field may use the results of this study as benchmarks in their design and research for the considered shell systems.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.11
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• pp.852-859
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• 2003

In order to meet the growing demands for higher storage density as well as lower noise level, the spindles in hard disk drives are to be supported by hydrodynamic bearings in place of conventional ball-type ones. However, the existing models are inappropriate to apply to accurate prediction of vibration characteristics because the HDD spindle tends to take quite a complex shape to secure its performance and cost-effectiveness. In this context, this paper treats analysis of free and forced vibrations of such-designed HDD spindles based on more sophisticated models and validations via experiments. Remarkably, to this end all the components in the system are modeled as elastic adopting the finite element method.

• Computational Structural Engineering
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• v.3 no.2
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• pp.67-75
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• 1990

A stepped beam with immovable ends under the free and forced vibrations with large amplitude is investigated by using the finite element method to show the effects of longitudinal displacement, shear deformation and rotary inertia. A modified harmonic force matrix is introduced for analysis of finite amplitude vibration of the stepped beam under uniform harmonic loading and a beam under nonuniform harmonic loading. Numerical examples are analysed for deflections and natural frequencies of stepped beam under various support conditions. Results show that the proposed method is valid and efficient.