• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.864-869
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• 2003

The purpose of this paper is to investigate the free vibration characteristics of tapered beams with translational and rotational springs and point masses at the ends. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest four natural frequencies are calculated over a range of non-dimensional system parameters.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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• pp.709-712
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• 2004

A study of the coupled flexural-torsional vibrations of thin-walled beams with monosymmetric cross-section is presented. The governing differential equations for free vibration of such beams are solved numerically to obtain natural frequencies and their corresponding mode shapes. The beam model is based on the Bernoulli-Euler beam theory and the effect of warping is taken into consideration. Numerical results are given for two specific examples of beams with free-free, clamped-free, hinged-hinged, clamped-hinged and clamped-clamped end constraints both including and excluding the effect of warping stiffness. The effect of warping stiffness on the natural frequencies and mode shapes is discussed and it is concluded that substantial error can be incurred if the effect is ignored.

• Structural Monitoring and Maintenance
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• 제3권4호
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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.

• Advances in nano research
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• 제12권4호
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• pp.365-374
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• 2022

Intermediate filaments are the mechanical ropes for both cytoskeleton and nucleoskeleton of the cell which provide tensile force to these skeletons. In providing the mechanical support to the cell, they are likely to buckle. We used conventional Euler buckling model to find the critical buckling force under different boundary conditions which they assume during different functions. However, there are many experimental and theoretical studies about other cytoskeleton components which demonstrate that due to mechanical coupling with the surrounding surface, the critical buckling force increases considerably. Motivated with these results, we also investigated the influence of surface effects on the critical buckling force of intermediate filaments. The surface effects become profound because of increasing ratio of surface area of intermediate filaments to bulk at nano-scale. The model has been solved analytically to obtain relations for the critical forces for the buckling of intermediate filaments without and with surface effects. We found that critical buckling force with surface effects increases to a large extent due to mechanical coupling of intermediate filaments with the surrounding surface. Our study may be useful to develop a unified experimental protocol to characterize the physical properties of Intermediate filaments and may be helpful in understanding many biological phenomenon involving intermediate filaments.

• Structural Engineering and Mechanics
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• 제47권2호
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• pp.149-166
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• 2013

Flexible behaviors in new aerospace structures can lead to a degradation of their control and guidance system and undesired performance. The objectives of the current work are to analyze the vibration resulting from the propulsion force on a Single Stage to Orbit (SSTO) launch vehicle (LV). This is modeled as a follower force on a free-free Euler-Bernoulli beam consisting of two concentrated masses at the two free ends. Once the effects on the oscillation of the actuators are studied, a solution to reduce these oscillations will also be developed. To pursue this goal, the stability of the beam model is studied using Ritz method. It is determined that the transverse and rotary inertia of the concentrated masses cause a change in the critical follower force. A new dynamic model and an adaptive control system for an SSTO LV have been developed that allow the aerospace structure to run on its maximum bearable propulsion force with the optimum effects on the oscillation of its actuators. Simulation results show that such a control model provides an effective way to reduce the undesirable oscillations of the actuators.

• 국제강구조저널
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• 제18권4호
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• pp.1440-1463
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• 2018

The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner's coefficient have been presented due to the limitation of Vlasov's buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler-Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair's formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.

• Steel and Composite Structures
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• 제35권4호
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• pp.555-566
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• 2020

This paper aims to present an analytical methodology to investigate influences of nanoscale and surface energy on buckling stability behavior of perforated nanobeam structural element, for the first time. The surface energy effect is exploited to consider the free energy on the surface of nanobeam by using Gurtin-Murdoch surface elasticity theory. Thin and thick beams are considered by using both classical beam of Euler and first order shear deformation of Timoshenko theories, respectively. Equivalent geometrical constant of regularly squared perforated beam are presented in simplified form. Problem formulation of nanostructure beam including surface energies is derived in detail. Explicit analytical solution for nanoscale beams are developed for both beam theories to evaluate the surface stress effects and size-dependent nanoscale on the critical buckling loads. The closed form solution is confirmed and proven by comparing the obtained results with previous works. Parametric studies are achieved to demonstrate impacts of beam filling ratio, the number of hole rows, surface material characteristics, beam slenderness ratio, boundary conditions as well as loading conditions on the non-classical buckling of perforated nanobeams in incidence of surface effects. It is found that, the surface residual stress has more significant effect on the critical buckling loads with the corresponding effect of the surface elasticity. The proposed model can be used as benchmarks in designing, analysis and manufacturing of perforated nanobeams.

• Advances in aircraft and spacecraft science
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• 제11권1호
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• pp.55-81
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• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• Structural Engineering and Mechanics
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• 제20권1호
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• pp.111-121
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• 2005

The dynamic interaction of vehicle-bridge is studied by using transfer matrix method in this paper. The vehicle model is simplified as a spring-damping-mass system. By adopting the idea of Newmark-${\beta}$ method, the partial differential equation of structure vibration is transformed into a differential equation irrelevant to time. Then, this differential equation is solved by transfer matrix method. The prospective application of this method in real engineering is finally demonstrated by several examples.

• 한국정밀공학회지
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• 제13권11호
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• pp.132-142
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• 1996

This paper presents a technique to model and control a manipulator which has a flexible link and moves in a vertical plane. The flexible link is modeled as an Euler-Bernoulli Beam. Elastic deformation of the flexible link is represented using the assumed modes method. A comparison function which satisfies all geometric and natural boundary conditions of a cantilever beam with an end mass is used as an assumed mode shape. Lagrange's equation is utilized for the development of a discretized model. This paper presents a simple technique to improve the correctness of the developed model. The final model including the shortening effect due to elastic deformation correlates very well with experimental results. The free body motion simulation shows that two assumed modes for the representation of the elastic deformation is proper in terms of the model size and correctness. A control algorithm is developed using PID control technique. The proportional, integral and derivative control gains are determined based on dominant pole placement method with a rigid one-link manipulator. A position control simulation shows that the control algorithm can be used to control the position and residual oscillation of the flexible one-link manipulator effectively.