geometric nonlinear
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2021 ◽  
Vol 5 (5) ◽  
pp. 2029-2051
Author(s):  
Lucas Dezotti Tolentino ◽  
Luiz Antonio Farani de Souza ◽  
Romel Dias Vanderlei ◽  
Leandro Vanalli

Neste artigo, são desenvolvidos algoritmos baseados no método de Newton-Raphson associado às técnicas de Comprimento de Arco Linear, Comprimento de Arco Esférico e Comprimento de Arco Cilíndrico, com o objetivo de validar a equação proposta para o coeficiente de escala. As análises não lineares são efetuadas por meio do método Corrotacional dos Elementos Finitos considerando problemas de treliças espaciais com não linearidade geométrica, cujas trajetórias de equilíbrio apresentam pontos limites de força e deslocamento. Os resultados numéricos versam sobre o tempo de processamento, números totais de passos de carga e iterações acumuladas até a convergência para a solução, além do número médio de iterações por passo de carga. As técnicas de continuação são comparadas e os resultados evidenciam a eficácia do Comprimento de Arco Linear, decorrente da simplicidade da formulação e boa concordância com os resultados observados na literatura, além da não restrição quanto à aplicação em problemas de maior complexidade.


2021 ◽  
Author(s):  
Ryuichi Umehara ◽  
Sotaro Takei ◽  
Tomohiro Akaki ◽  
Hiroki Kitada

Abstract Turbine blades are used under increasingly severe conditions in order to increase the thermal efficiency of the gas turbines in operation. Friction dampers are often used to reduce the vibration of the blade and improve the plant reliability. Under platform dampers designed to generate friction between platforms and dampers have been widely adopted in gas turbines as one of the friction dampers. It is important to predict the vibration characteristics of such damper blades analytically during the design phase, and many analysis methods have been proposed vigorously. However, the phenomenon of the friction damper is not fully understood because of its complicated behavior due to nonlinearity such as contact and sliding. One of them is the variability of frequency generated in the under platform dampers. Recently, it has been reported on the variability of frequency in the mock-up blade test greatly under small excitation force, due to variability of contact surfaces. As different approach, mechanism of the variability of frequency is explained even if each damper pin has the same dimensions and characteristics of stiffness each other under the range of small vibration without slipped phenomena. In this paper, the phenomenon of this frequency variation is shown based on two physical phenomena. First, it shows the geometric nonlinear characteristics in which the normal load changes by the friction coefficient of the pin and the pin angle. Second, it shows the stiffness nonlinear characteristics in which the contact stiffness changes with the normal load of the pin. Based on the new proposed modeling of combining the geometric nonlinear characteristics and nonlinear stiffness characteristics, the phenomenon is shown in which the relative displacement of the pin changes the load and contact stiffness, and the frequency changes. It also shows that the maximum normal load before sliding is different depending on the friction coefficient and the pin angle, and that when the friction coefficient is large and the damper angle is large, the change in contact stiffness due to the normal load is large and the variability of frequency is large.


Author(s):  
Ming-Yi Tsai ◽  
H. Y. Liu

Abstract The ball-on-ring (BoR) test, one of the most popular biaxial bending tests, is thoroughly investigated in this study for determining the bending strength of thin silicon dies. The application of this test method with a linear theory to the thin dies is also reevaluated using a nonlinear finite element method (NFEM) by taking into account the geometric nonlinearities, including large-deflection (global) and contact (local) nonlinearities. Mechanics of the BoR test is also discussed in terms of geometric linearity and nonlinearity. It is found that the bending strength calculated by the existing linear theory for the BoR test is still valid for the non-thin die specimens, but not for thin ones. The reason is that the thin-die specimens in the test suffer a contact-nonlinearity effect, due to a maximum applied stress moving away from the loading pin center during the loading process. The global geometric nonlinear (large-deflection) behavior occurring in the three-point bending test is not observed in the test. For applications, the fitting equations of the maximum stress in terms of applied load are proposed based on the NFEM results. Those fitting equations only depend on the specimen thickness, the head radius of the loading pin, and the elastic modulus of the specimen, but not on the specimen radius, a supporting ring radius and the head radius of the ring. The 110 µm and 160 µm-thick silicon dies in the BoR test are also demonstrated with the related fitting equations.


2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Meng Yang ◽  
Jian Zhang ◽  
Xingjiu Luo

Firstly, this paper puts forward two new types of suspension vibration reduction systems (SVRSs) with geometric nonlinear damping based on general SVRS (GSVRS), which only has geometric nonlinear stiffness. Secondly, it derives the motion differential equations for the two new types of SVRS, respectively, and discusses the similarities and differences among the two types and GSVRS through the comparison of motion differential equations. Then, it conducts dimensionless processing of the motion differential equations for the two new types of SVRS and carries out a comparative study on the vibration isolation performance of the two types of SVRS under impact excitation and random excitation, respectively. At last, it performs the optimal computation of the chosen new type of SVRS through the ergodic optimization method and studies the influence rule of SVRS parameters on vibration isolation performance so as to realize the optimization of vibration isolation performance.


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