• Wind and Structures
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• v.25 no.5
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• pp.459-474
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• 2017

In this study an analytical expression is derived for the natural frequency of the wind turbine towers supported on flexible foundation. The derivation is based on a Euler-Bernoulli beam model where the foundation is represented by a stiffness matrix. Previously the natural frequency of such a model is obtained from numerical or empirical method. The new expression is based on pure physical parameters and thus can be used for a quick assessment of the natural frequencies of both the real turbines and the small-scale models. Furthermore, a relationship between the diagonal and non-diagonal element in the stiffness matrix is introduced, so that the foundation stiffness can be obtained from either the p-y analysis or the loading test. The results of the proposed expression are compared with the measured frequencies of six real or model turbines reported in the literature. The comparison shows that the proposed analytical expression predicts the natural frequency with reasonable accuracy. For two of the model turbines, some errors were observed which might be attributed to the difference between the dynamic and static modulus of saturated soils. The proposed analytical solution is quite simple to use, and it is shown to be more reasonable than the analytical and the empirical formulas available in the literature.

• Wind and Structures
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• v.14 no.2
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• pp.85-112
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• 2011

Wind turbine structures are long slender columns with a rotor and blade assembly placed on the top. These slender structures vibrate due to dynamic environmental forces and its own dynamics. Analysis of the dynamic behavior of wind turbines is fundamental to the stability, performance, operation and safety of these systems. In this paper a simplied approach is outlined for free vibration analysis of these long, slender structures taking the soil-structure interaction into account. The analytical method is based on an Euler-Bernoulli beam-column with elastic end supports. The elastic end-supports are considered to model the flexible nature of the interaction of these systems with soil. A closed-form approximate expression has been derived for the first natural frequency of the system. This new expression is a function of geometric and elastic properties of wind turbine tower and properties of the foundation including soil. The proposed simple expression has been independently validated using an exact numerical method, laboratory based experimental measurement and field measurement of a real wind turbine structure. The results obtained in the paper shows that the proposed expression can be used for a quick assessment of the fundamental frequency of a wind turbine taking the soil-structure interaction into account.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.7
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• pp.562-569
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported pipe conveying fluid subject to the moving mass. The equation of motion Is derived by using Lagrange’s equation. The influences of the velocity of moving mass and the velocity of fluid flow and a crack have been studied on the dynamic behavior of a simply supported pipe system by numerical method. The presence of crack results In higher deflections of pipe. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. Totally. as the velocity of fluid flow and the crack severity are increased, the mid-span deflection of simply supported pipe conveying fluid Is Increased. The time which produce the maximum dynamic deflection of the simply supported pipe Is delayed according to the increment of the crack severity.

• Steel and Composite Structures
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• v.43 no.6
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• pp.809-819
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• 2022

This paper proposes a method to predict the deflection of prestressed concrete (PC) beams with corrugated steel web (CSW) under constant load concerning time-dependent variation in concrete material. Over time, the top and bottom concrete slabs subjected to asymmetric compression experience shrinkage and creep deformations. Here, the classical Euler-Bernoulli beam theory assumption that the plane sections remain plane is not valid due to shear deformation of CSW. Therefore, this study presents a method based on the first-order shear deformation to find the long-term deflection of the composite beams under bending by considering time effects. Two experimental prestressed beams of this type were monitored under their self-weight over time, and the theoretical results were compared with those data. Additionally, 3D analytical models of the experimental beams were used according to material properties, and the results were compared with two previous cases. There was good consistency between the analytical and numerical results with low error, which increased by wave radius. It is concluded that the proposed method could reliably be used for design purposes.

• Smart Structures and Systems
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• v.29 no.5
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• pp.705-714
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• 2022

In this paper, the effect of magnetic field on the vibration behavior of a Magnetorheological elastomer (MRE) sandwich MEMS actuated by electrostatic actuation with conductive skins are examined within the multiple scales (MMS) perturbation method. Magnetorheological smart materials have been widely used in vibration control of various systems due to their mechanical properties change under the influence of different magnetic fields. To investigate the vibrational behavior of the movable electrode, the Euler-Bernoulli beam theory, as well as Hamilton's principle is used to derive the equations and the related boundary conditions governing the dynamic behavior of the system are applied. The results of this study show that by placing the Magnetorheological elastomer core in the movable electrode and applying different magnetic fields on it, its natural vibrational frequency can be affected so that by increasing the applied magnetic field, the system's natural frequency increases. Also, the effect of various factors such as the electric potential difference between two electrodes, changes in the thickness of the core and the skins, electrode length, the distance between two electrodes and also change in vibration modes of the system on natural frequencies have been investigated.

• Advances in aircraft and spacecraft science
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• v.10 no.5
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• pp.419-437
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• 2023

This paper presents the study of the effects of rigid-body motion simultaneously with the presence of the effects of temporal variation due to the existence of morphing speed on the aeroelastic stability of the two-stage telescopic wings, and hence this is the main novelty of this study. To this aim, Euler-Bernoulli beam theory is used to model the bending-torsional dynamics of the wing. The aerodynamic loads on the wing in an incompressible flow regime are determined by using Peters' unsteady aerodynamic model. The governing aeroelastic equations are discretized employing a finite element method based on the beam-rod model. The effects of rigid-body motion on the length-based stability of the wing are determined by checking the eigenvalues of system. The obtained results are compared with those available in the literature, and a good agreement is observed. Furthermore, the effects of different parameters of rigid-body such as the mass, radius of gyration, fuselage center of gravity distance from wing elastic axis on the aeroelastic stability are discussed. It is found that some parameters can cause unpredictable changes in the critical length and frequency. Also, paying attention to the fuselage parameters and how they affect stability is very important and will play a significant role in the design.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.12
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• pp.2012-2018
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• 2004

The vibration of a semi-circular pipe conveying fluid is studied when the pipe is clamped at both ends. To consider the geometric nonlinearity, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived from the Galerkin method. The natural frequencies varying with the flow velocity are computed from the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized-$\alpha$ method. From these results, we should consider the geometric nonlinearity to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

• Advances in concrete construction
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• v.9 no.1
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• pp.43-54
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• 2020

This paper presents an innovative stress-function variational approach in formulating the interfacial shear and normal stresses in an externally bonded concrete joint using carbon fiber-reinforced plastic (CFRP) plies. The joint is subjected to surface traction loadings applied at both ends of the concrete substrate layer. By introducing two interfacial shear and normal stress functions on the CFRP-concrete interface, based on Euler-Bernoulli beam idea and static stress equations of equilibrium, the entire stress fields of the joint were determined. The complementary strain energy was minimized in order to solve the governing equation of the joint. This yields an ordinary differential equation from which the interfacial normal and shear stresses were proposed explicitly, satisfying all the multiple traction boundary conditions. Lamination theory for composite materials was also employed to obtain the interfacial stresses. The proposed approach was validated by the analytic models in the literature as well as through a comprehensive computational code generated by the authors. Furthermore, a numerical verification was carried out via the finite element software ABAQUS. In the end, a scaling analysis was conducted to analyze the interfacial stress field dependence of the joint upon effective issues using the devised code.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.3
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• pp.514-520
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• 2002

A new non-linear modelling of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends. Using the Euler-Bernoulli beam theory and the non-linear Lagrange strain theory, from the extended Hamilton's principle are derived the coupled non-linear equations of motion for the longitudinal and transverse displacements. These equations of motion are discretized by using the Galerkin method. After the discretized equations are linearized in the neighbourhood of the equilibrium position, the natural frequencies are computed from the linearized equations. On the other hand, the time histories for the displacements are also obtained by applying the generalized-$\alpha$ time integration method to the non-linear discretized equations. The validity of the new modelling is provided by comparing results from the proposed non-linear equations with those from the equations proposed by Paidoussis.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.793-798
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• 2004

The vibration of a curved pipe conveying fluid is studied when the pipe is clamped at both ends. To consider the geometric nonlinearity, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the extended Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the vibration characteristics of the system, the discretized equations of motion are derived from the Galerkin method. The natural frequencies varying with the flow velocity are computed from the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. From these results, we should consider the geometric nonlinearity to analyze the dynamics of a curved pipe conveying fluid more precisely.