• Advances in nano research
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• 제16권1호
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• pp.27-40
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• 2024

This work is the first of its kind to integrate Mindlin's theory with analytical methods in order to produce an exact solution to a specific vibration issue as well as a bending problem involving a nanoplate that is supported by a viscoelastic foundation. The plate is exposed to the simultaneous effects of a compressive load in the plate plane and a force operating perpendicular to the plane of the nanoplate. In addition, the flexoelecity effect is included into the plate. The strain gradient component is taken into consideration while calculating the plate equilibrium equation using the nonlocal theory and Hamilton's principle. The free vibration and static responses of the nanoplate seem to be both real and imaginary components because of the appearance of the viscoelastic drag coefficient of the viscoelastic foundation. This study also shows that when analyzing the mechanical response for nanostructure, taking into account the flexoelectricity effect and the influence of the nonlocal parameter, the results will be completely different from the case in which this parameter is ignored. This indicates that it is vital to take into consideration the effects of nonlocal parameters on the nanosheet structure while also taking into consideration the effect of flexoelectricity.

• Structural Engineering and Mechanics
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• 제64권6권
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• pp.683-693
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• 2017

According to a generalized nonlocal strain gradient theory (NSGT), dynamic modeling and free vibrational analysis of nanoporous inhomogeneous nanoplates is presented. The present model incorporates two scale coefficients to examine vibration behavior of nanoplates much accurately. Porosity-dependent material properties of the nanoplate are defined via a modified power-law function. The nanoplate is resting on a viscoelastic substrate and is subjected to hygro-thermal environment and in-plane linearly varying mechanical loads. The governing equations and related classical and non-classical boundary conditions are derived based on Hamilton's principle. These equations are solved for hinged nanoplates via Galerkin's method. Obtained results show the importance of hygro-thermal loading, viscoelastic medium, in-plane bending load, gradient index, nonlocal parameter, strain gradient parameter and porosities on vibrational characteristics of size-dependent FG nanoplates.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2007년도 추계학술대회논문집
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• pp.178-188
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• 2007

In this paper, a half-scaled substructure test was performed to evaluate the buckling and structural safety of an existing transmission tower subjected to wind load. A loading scheme was devised to reproduce the dead and wind loads of a prototype transmission tower, which uses a triangular jig that is mounted on the reduced model to which the similarity law of a half length was applied. As a result of the preliminary numerical analysis carried out to evaluate the stability of a specimen for the design load, it was confirmed that the calculated axial forces of tower leg members were distributed to $80{\sim}90%$ of an admissible buckling load. When the substructured transmission tower was loaded by 270% of its maximum admissible buckling load, it was failed due to the local buckling that is occurred in joints with weak constraints for out-of-plane behavior of leg members. By inspection of load-displacement curves, displacements and strains of members, it is considered that this local buckling was due to additional eccentric force by unbalanced deformation because the time that is reached to yielding stress due to the bending moment is different at each point of a same section.

• 한국지반공학회논문집
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• 제31권4호
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• pp.45-55
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• 2015

발파에 대한 주변 구조물이나 사면의 안정성은 경험적 진동감쇠식 또는 발파진동 동적 수치해석을 통하여 평가한다. 동적해석을 수행하기 위해서는 발파하중과 지반 감쇠비의 산정이 필요하다. 발파하중에 대해서는 다양한 경험적 방법이 제시되었지만 암반의 감쇠비에 대한 연구는 제한적이며 해석 시 이를 무시하거나 명확한 근거 없이 가정하여 해석에 적용하고 있다. 암반의 감쇠비는 절리의 영향을 크게 받으므로 이를 고려해서 산정해야 한다. 또한, 평면파로 가정할 수 있는 지진파와는 다르게 발파 시에는 구면파가 생성되며 이를 2차원 해석에서 모사하는 경우에는 이의 기하학적 확산을 고려하기 위하여 감쇠비를 조정해야 한다. 본 연구에서는 위의 두 가지 영향이 고려된 2차원 평면변형률 연속체 해석에 적용 가능한 암반의 등가감쇠비를 제안하였다. 이를 위하여 다양한 강성의 암반에 대한 2차원 동적해석을 수행하여 암반의 감쇠비에 따른 진동전파 특성을 분석하였으며 해석결과를 기반으로 진동감쇠식-전단파속도-등가감쇠비와의 상관관계를 규명하였다. 제시된 상관관계는 경험적 진동감쇠식에 상응하는 감쇠비를 산정한 최초의 시도로 중요한 의미가 있으며 동시에 실무에도 쉽게 적용될 수 있는 유용한 방법이다.

• Structural Engineering and Mechanics
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• 제75권2호
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• pp.247-269
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• 2020

A finite strip formulation was developed for buckling and free vibration analysis of laminated composite plates based on different shear deformation plate theories. The different shear deformation theories such as Zigzag higher order, Refined Plate Theory (RPT) and other higher order plate theories by variation of transverse shear strains through plate thickness in the parabolic form, sine and exponential were adopted here. The two loaded opposite edges of the plate were assumed to be simply supported and remaining edges were assumed to have arbitrary boundary conditions. The polynomial shape functions are applied to assess the in-plane and out-of-plane deflection and rotation of the normal cross-section of plates in the transverse direction. The finite strip procedure based on the virtual work principle was applied to derive the stiffness, geometric and mass matrices. Numerical results were obtained based on various shear deformation plate theories to verify the proposed formulation. The effects of length to thickness ratios, modulus ratios, boundary conditions, the number of layers and fiber orientation of cross-ply and angle-ply laminates were determined. The additional results on the same effects in the interaction of biaxial in-plane loadings on the critical buckling load were determined as well.

• Structural Engineering and Mechanics
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• 제72권4호
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• pp.525-540
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• 2019

The purpose of the present work was to study the dynamic instability of a three-layered, symmetric sandwich beam subjected to a periodic axial load resting on nonlinear elastic foundation. A higher-order theory was used for analysis of sandwich beams with soft core on elastic foundations. In the higher-order theory, the Reddy's third-order theory was used for the face sheets and quadratic and cubic functions were assumed for transverse and in-plane displacements of the core, respectively. The elastic foundation was modeled as nonlinear's type. The dynamic instability regions and free vibration were investigated for simply supported conditions by Bolotin's method. The results showed that the responses of the dynamic instability of the system were influenced by the excitation frequency, the coefficients of foundation, the core thickness, the dynamic and static load factor. Comparison of the present results with the published results in the literature for the special case confirmed the accuracy of the proposed theory.

• 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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• 제82권6호
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• pp.691-699
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• 2022

This paper is devoted to the presentation of a numerical study on vibration behavior of composite panels reinforced by glass fibres and carbon nanotubes (CNTs) subjected to thermal environments. The effect of temperature variation has been included as thermal load acting on in-plane direction of the panel. To model the composite material, a micromechanical model which contains random dispersion of nanotubes and single-direction fibers has been selected. The geometry of the panel has been considered to have a single curveture along its width. Based on the above assumptions, the governing equations have been derived by using thin shell theory capturing the panel curveture and also nonlinear deflections. Finally, the panel dependence on various factors such as the curveture, nanotube amount, fiber volume, fiber direction and temperature variation has been researched.

• 한국강구조학회 논문집
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• 제15권3호
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• pp.291-298
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• 2003

최근 건축물의 대형화로 구조물의 기초는 비균질지반에 지지된다. 본 연구는 면내력을 받는 후판의 진동해석을 한 것이다. 장방 형판은 등방, 균질의 선형 탄성재료로 구성되었다. 장방형 후판의 진동해석은 8절점과 9절점을 이용한 장방형 유한요소를 사용하여 행하였다. 본 연구에서 기초를 수직스프링으로 이상화한 Winkler지반에 전단지반층을 추가한 Pasternk지반으로 이상화하였다. 지반의 강성을 달리한 비균질 Pasternak지반에 지지된 판을 해석하기 위해 중앙부분과 가장자리 부분의 Winkler지반계수를 WFP1과 WFP2로 선택하였다. (그림 4.) Winkler지반계수 WFP1과 WFP2는 0, 10, $10^2$, $10^3$으로 변환시키고 전단지반강성은 0, 5, 10으로 하였다. 후판의 좌굴응력(${\sigma}_{cr}$)에 대한 면내력의 비는 각각 0.4, 0.8에 대해 적용하였다.

• Structural Engineering and Mechanics
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• 제9권5호
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• pp.483-490
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• 2000

After manufacturing a structure, the assembly of structural components is often not as perfect as expected due to the immaturity of current engineering techniques. Thus the actual buckling load for an element is sometimes not consistent with that predicted in the design. For design considerations, it is necessary to establish an analytical method for determining the buckling load experimentally. In this paper, a dynamic method is described for determining the linear buckling loads for elastic, perfectly flat plates. The proposed method does not require the application of in-plane loads and is feasible for arbitrary types of boundary conditions. It requires only the vibrational excitation of the plate. The buckling load is determined from the measured natural frequencies and vibration mode shapes.