Journal articles: 'Rotational stiffness'

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Lu, Ya Fei, Qing Kun Zhou, De Jun Sheng, Da Peng Fan, and Zhi Yong Zhang. "Stiffness Analysis for Large-Travel Rotational Butterfly Pivot." Key Engineering Materials 455 (December 2010): 694–99. http://dx.doi.org/10.4028/www.scientific.net/kem.455.694.

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Butterfly pivot is a large-travel rotational flexure pivot, which can provide elastic support for the rotational shaft in several ten degrees. Because of the complex structure, stiffness calculation of butterfly pivot is always completed by the method of Finite Element Analysis (FEA), which is not suitable for parameter design and optimization. The serial structure of four-blade isosceles-trapezoid (FBIT)is proposed to simplified the complex structure of the butterfly pivot. The FBIT is analyzed and the theoretical formula of stiffness calculation for rotation stiffness is derived in detail based on the essential theory of Mechanics of Materials. Design and optimization of rotation stiffness for each element can be achieved easily with the obtained the theoretical formula of rotation stiffness. The total rotation stiffness of the whole butterfly pivot is calculated and the rotation stiffness comparison between using the theoretical method and by the method of FEA is performed. The error between the theoretical rotation stiffness and the result of the FEA is less than 10%. It is acceptable and without any influence on the validity of the work and concept presented in this paper.

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Ghafoor, Abdul, Jian S. Dai, and Joseph Duffy. "Stiffness Modeling of the Soft-Finger Contact in Robotic Grasping." Journal of Mechanical Design 126, no. 4 (July 1, 2004): 646–56. http://dx.doi.org/10.1115/1.1758255.

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This paper investigates the soft-finger contact by presenting the contact with a set of line springs based on screw theory, reveals the rotational effects, and identifies the stiffness properties of the contact. An elastic model of a soft-finger contact is proposed and a generalized contact stiffness matrix is developed by applying the congruence transformation and by introducing stiffness mapping of the line springs in translational directions and rotational axes. The effective stiffnesses along these directions and axes are hence obtained and the rotational stiffnesses are revealed. This helps create a screw representation of a six-dimensional soft-finger contact and produce an approach of analyzing and synthesizing a robotic grasp without resorting to the point contact representation. The correlation between the rotational stiffness, the number of equivalent point contacts and the number of equivalent contours is given and the stiffness synthesis is presented with both modular and direct approaches. The grasp thus achieved from the stiffness analysis contributes to both translational and rotational restraint and the stiffness matrix so developed is proven to be symmetric and positive definite. Case studies are presented with a two-soft-finger grasp and a three-soft-finger grasp. The grasps are analyzed with a general stiffness matrix which is used to control the fine displacements of a grasped object by changing the preload on the contact.

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Wang, Wei, and Xinming Qiu. "The Mechanical Properties of Origami Structure Determined by the Improved Virtual Crease Method." International Journal of Applied Mechanics 13, no. 01 (January 2021): 2150002. http://dx.doi.org/10.1142/s1758825121500022.

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The mechanical properties and deformation of Origami structures are studied in this paper. Usually, it is a coupling problem of crease rotation and shell deformation. Here, the creases are simplified as torsional springs, whose rotational stiffness [Formula: see text] is obtained by the experiment of compressing a creased shell. While the shells that may have large deformation are simplified as rigid plates connected by virtual creases, whose rotational stiffness is roughly expressed as bending stiffness divides width of the shell. Hence, a coupling factor [Formula: see text] is defined to evaluate the coupling effect of creases and shells. Implementing the obtained rotational stiffnesses of real and virtual creases into the expression of strain energy, an improved Virtual Crease Method (VCM) is proposed. By analyzing the bi-stability of creased shell and Miura-Ori structure, the accuracy and convergence of this improved VCM is proved.

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Ling, Samuel KK, Tun Hing Lui, Yan Sui Faan, Paulina WY Lui, and Wai Kit Ngai. "Post-traumatic elbow rotational stiffness." Shoulder & Elbow 6, no. 2 (March 3, 2014): 119–23. http://dx.doi.org/10.1177/1758573214524935.

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Melchers, R. E. "Rotational stiffness of shallow footings." Computers and Geotechnics 13, no. 1 (January 1992): 21–35. http://dx.doi.org/10.1016/0266-352x(92)90009-i.

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Button, Keith D., Paige Thornton, Jerrod E. Braman, Feng Wei, and Roger C. Haut. "The effect of rotational stiffness on ankle tibiocalcaneal motion and ligament strain during external rotation." Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology 230, no. 4 (August 1, 2016): 264–74. http://dx.doi.org/10.1177/1754337115623886.

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The rotational stiffness of footwear has been previously shown to have an effect on ankle kinematics and injury risk, but this relationship has not yet been modeled. The aim of this study was to derive equations from experimental data that were able to predict ankle kinematics under various torsional stiffness constraints and use these equations to estimate ligament strains. Three athletic tapes were tested for their ability to constrain the ankle during external rotation. Six subjects then performed a voluntary external foot rotation using the selected tape designs to constrain the ankle, as well as with no constraints. The motion of the calcaneus with respect to the tibia (tibiocalcaneal motion) from 0° to 15° of tibia rotation and predictive equations were determined to establish tibiocalcaneal rotation, eversion, and flexion as a function of gross tibia motion and tape stiffness. These predictive equations were then used to drive a computational model in which ankle ligament strains were determined at 15° of tibia rotation and for ankle constraint stiffness ranging from 0 to 30 N m/deg. The three tapes provided significantly different constraint stiffnesses during external foot rotation. There was no statistical effect of ankle constraint on the dorsiflexion response of the ankle (p = 0.461). In contrast, there was an effect of constraint stiffness on tibiocalcaneal external rotation (p < 0.001) and tibiocalcaneal eversion (p < 0.001). Results of the model simulation revealed the highest ligament strains in the anterior tibiotalar ligament and anterior tibiofibular ligament. Anterior tibiotalar ligament strain increased with increasing constraint stiffness, while there was little effect of constraint stiffness on anterior tibiofibular ligament strain. Results from this study could aid in the design of footwear, as well as the analysis of clinical injuries.

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Qin, Shujie, Na Yang, and Lu Dai. "Rotational Behavior of Column Footing Joint and Its Effect on the Dynamic Characteristics of Traditional Chinese Timber Structure." Shock and Vibration 2018 (July 5, 2018): 1–13. http://dx.doi.org/10.1155/2018/9726852.

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Chinese heritage timber buildings are of high historical and cultural values. The column footing joint is an important connection influencing the structural performance under dynamic load. The moment-rotation relationship of a column footing joint is studied and the effects of vertical load and ratio of column height to diameter on its rotational behavior are analyzed. A spring elements model is proposed to simulate the column footing joint and its stiffness matrix can be simplified to include only one stiffness parameter K with some assumptions. A component-based finite-element model of a timber pavilion is then developed to investigate the effect of rotational stiffness on the structural dynamic characteristics. Results show that a heavier vertical load may lead to larger ultimate moment capacity of the joint. The initial rotational stiffness and ultimate moment capacity decrease with increasing column height to diameter ratio. The modal frequency of the structure studied changes remarkably when the rotational stiffness K varies from 104 to 108 N▪m/rad. The column footing joints should be regarded as semirigid connections in the structural dynamic analysis. A field experiment was also conducted to further demonstrate that the rotational stiffness of column footing joint has notable influence on the dynamic characteristics of traditional Chinese timber structure.

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Wu, Guanglei, and Ping Zou. "Stiffness analysis and comparison of a Biglide parallel grinder with alternative spatial modular parallelograms." Robotica 35, no. 6 (February 8, 2016): 1310–26. http://dx.doi.org/10.1017/s0263574716000059.

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SUMMARYThis paper deals with the stiffness modeling, analysis and comparison of a Biglide parallel grinder with two alternative modular parallelograms. It turns out that the Cartesian stiffness matrix of the manipulator has the property that it can be decoupled into two homogeneous matrices, corresponding to the translational and rotational aspects, through which the principal stiffnesses and the associated directions are identified by means of the eigenvalue problem, allowing the evaluation of the translational and rotational stiffness of the manipulator either at a given pose or the overall workspace. The stiffness comparison of the two alternative Biglide machines reveals the (dis)advantages of the two different spatial modular parallelograms.

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Borzouie, J., J. G. Chase, G. A. MacRae, G. W. Rodgers, and G. C. Clifton. "Spectral Assessment of the Effects of Base Flexibility on Seismic Demands of a Structure." Advances in Civil Engineering 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/3984149.

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Base flexibility of structures changes and can increase the demands on structural elements during earthquake excitation. Such flexibility may come from the base connection, foundation, and soil under the foundation. This research evaluates the effects of column base rotational stiffness on the seismic demand of single storey frames with a range of periods using linear and nonlinear time history analysis. The base rotational stiffness ranges considered are based on previous studies considering foundation and baseplate flexibility. Linear and nonlinear spectral analyses show that increasing base flexibility generally increases frame lateral displacement and top moment of the column. Furthermore, moments at the top of the columns and the nonlinear base rotation may also increase with increasing base flexibility, especially for shorter period structures. Since many commonly used baseplate connections may be categorized as being semirigid, it is essential to design and model structures using realistic base rotational stiffness rather than simply use a fixed base assumption. The overall results also illustrate the range of increased seismic demand as a function of normalized rotational stiffness and structural period for consideration in design.

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Liu, Lang, Shusheng Bi, and Qizi Yang. "Stiffness characteristics of inner–outer ring flexure pivots applied to the ultra-precision instruments." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 13 (July 28, 2017): 2441–57. http://dx.doi.org/10.1177/0954406217721725.

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The inner-outer ring flexure pivot (IORFP), composed of three straight springs that cross each other in space, is studied in this work. First, to emphasize the study value of IORFP, qualitative comparison is applied to IORFP and some of most commonly used flexure pivots. Then an analytical model for the rotational stiffness of IORFP is developed based on the strain energy formulation of a beam flexure, and model applicability is provided as well. Analysis of stiffness, buckling load, and the nonlinear of moment–rotation relation is then carried out. Subsequently, the analytical model is verified by finite element analysis. After that, seven prototypes of IORFP are manufactured, and their rotational stiffnesses are tested. The results show that the analytical model can be used for analysis and designing of compliant mechanisms that contain IORFP. Finally, the study quantitatively compares stiffness characteristics and axis drift of IORFP and the generalized cross-spring pivot, indicating that the former significantly outperforms the latter. IORFP possesses excellent performances and can be widely used to supplant generalized cross-spring pivot in compliant mechanisms and ultra-precision instruments.

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Li, Songyu, Liquan Wang, Shaoming Yao, Peng Jia, Feihong Yun, Wenxue Jin, and Dong Lv. "Modelling, simulation and experiment of the spherical flexible joint stiffness." Mechanical Sciences 9, no. 1 (February 19, 2018): 81–89. http://dx.doi.org/10.5194/ms-9-81-2018.

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Abstract. The spherical flexible joint is extensively used in engineering. It is designed to provide flexibility in rotation while bearing vertical compression load. The linear rotational stiffness of the flexible joint is formulated. The rotational stiffness of the bonded rubber layer is related to inner radius, thickness and two edge angles. FEM is used to verify the analytical solution and analyze the stiffness. The Mooney–Rivlin, Neo Hooke and Yeoh constitutive models are used in the simulation. The experiment is taken to obtain the material coefficient and validate the analytical and FEM results. The Yeoh model can reflect the deformation trend more accurately, but the error in the nearly linear district is bigger than the Mooney–Rivlin model. The Mooney–Rivlin model can fit the test result very well and the analytical solution can also be used when the rubber deformation in the flexible joint is small. The increase of Poisson's ratio of the rubber layers will enhance the vertical compression stiffness but barely have effect on the rotational stiffness.

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Kim, Hee Dong. "Evaluation of the Initial Rotational Stiffness of a Double Split Tee Connection." Journal of Korean Society of Steel Construction 26, no. 2 (2014): 133. http://dx.doi.org/10.7781/kjoss.2014.26.2.133.

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Lin, Wenlong. "A new expression to predict secant rotational stiffness of spudcan in undrained soils." E3S Web of Conferences 248 (2021): 03014. http://dx.doi.org/10.1051/e3sconf/202124803014.

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The nonlinear behavior of spudcan foundation will lead to the decrease of the rotational stiffness of the spudcan, leading to the increase of the stress at the critical member of the offshore jack-up drilling platform. Secant rotational stiffness is used to represent the value of rotational stiffness of linear foundation model when the soil changes from elastic to elasto-plastic and then to plastic. In this paper, the “wished in-place” small strain finite element analysis (SSFE) analysis is used to simulate the load-displacement response of spudcans pre-embedded in the plastic soil, thus calculating the secant rotational stiffness of spudcans. New expressions of failure ratio and secant rotational stiffness are proposed with the coupling effect of horizontal force and moment taken into account.

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GEČYS, Tomas, and Alfonsas DANIŪNAS. "ROTATIONAL STIFFNESS DETERMINATION OF THE SEMI-RIGID TIMBER-STEEL CONNECTION." Journal of Civil Engineering and Management 23, no. 8 (November 20, 2017): 1021–28. http://dx.doi.org/10.3846/13923730.2017.1374305.

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In this research, the component method implementation for determination of the rotational stiffness of timber-steel connection is shown. Component method is one of the most commonly used methods for determination of the bending moment-rotation relation which later may be used in the practical analysis of the connection. The component method is not widely used for the analysis of the semi-rigid timber connections. There are only several investigations previously done on the component method implementation for the timber connections and most of them are based on only one basic component, i.e. timber compression or glued-in steel rod in tension. This article presents a new investigation of rotational stiffness determination algorithm of the semi-rigid timber-steel connection, which is based on the component method. The component method’s mechanical model of the connection combines all components which have influence on the rotational stiffness of the connection. The analysed timber-steel connection is subjected to pure bending. Stiffness coefficients of the steel part components are determined according to the Eurocode 3: design of steel structures Part 1-8: Design of joints. The timber part components are derived from the full-scale laboratory experiments and finite element modelling results, presented in the previous publications of the authors. The presented rotational stiffness determination results are well in line with the experimental and finite element modelling results, published in the previous publications.

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Garifullin, Marsel, Sami Pajunen, Kristo Mela, and Markku Heinisuo. "Initial rotational stiffness of tubular joints with axial force in chord." Rakenteiden Mekaniikka 50, no. 3 (August 22, 2017): 309–12. http://dx.doi.org/10.23998/rm.64857.

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In the frame analysis, the local model of the joint must follow the behavior of the joint. When completing the elastic global analysis, the initial rotational stiffness of joints should be known to obtain reliable moment distributions in frames. This paper consists of two parts. The first one evaluates the existing calculation approach for the initial rotational stiffness of welded rectangular hollow section T joints. The validation with the experimental data shows that the current approach significantly underestimates the initial rotational stiffness. An improvement for determining the initial stiffness of T joints is proposed. The second part deals with the influence of the axial force in the main member on the rotational stiffness of the joint. The conducted numerical study shows the extreme reduction of the initial stiffness, when the main member is loaded by axial loads. To consider this effect in the frame analysis, the paper proposes a chord stress function for the initial rotational stiffness for square hollow section T joints, using the curve fitting technique.

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Zhao, Jian Li. "Model of the Initial Stiffness in Extended End-Plate Connection." Applied Mechanics and Materials 321-324 (June 2013): 1766–69. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.1766.

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Extend end-plat bolted connections are widely used in steel frames. The rotational stiffness has great influence on steel frame stiffness and deformation. The decrease of the frame lateral stiffness, due to connection rotational deformability, leads to the increase of the period of vibration and the frame sensitivity to second-order effects. This thesis divides the end plate into several parts equivalent to different Timoshenkos beams to determine their contribution to rotational stiffness of the connection. Then stiffness of all parts and bolts is given, and then the component method is used to calculate rotational initial stiffness of extended end-plate connections. Comparisons with results of ANSYS and related tests show that the proposed equations have excellent precision. And the calculating process is simple and easily applicable in practice.

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Cashaback, Joshua G. A., and Jim R. Potvin. "Knee muscle contributions to joint rotational stiffness." Human Movement Science 31, no. 1 (February 2012): 118–28. http://dx.doi.org/10.1016/j.humov.2010.12.005.

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Sun, Wei Wei, and Feng Wei. "Numerical Investigation on Block Shear of Coped Beams with a Welded End Connection." Advanced Materials Research 163-167 (December 2010): 274–78. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.274.

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A numerical investigation on the block shear failure behavior of coped beams with double welded clip angle connection was conducted. Parametric study was conducted based on the validated finite element model. The parameters included the web block aspect ratio and the connection rotational stiffness. Based on the mechanical model of double angle connection, the pitch and the beam element length-to-angle thickness (L/t) ratio of the outstanding leg were selected as two importance parameters to consider the effect of the connection rotational stiffness. The results of parametric study show that the connection rotational stiffness has a great influence on the block shear capacity of coped beams with double welded clip angle connection. This is contributed to the fact that for the connections with a smaller connection rotational stiffness, the shear stresses of the shear area were much less than those of the connections with a larger connection rotational stiffness.

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Attary, Navid, M. Symans, and S. Nagarajaiah. "Development of a rotation-based negative stiffness device for seismic protection of structures." Journal of Vibration and Control 23, no. 5 (August 9, 2016): 853–67. http://dx.doi.org/10.1177/1077546315585435.

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Researchers worldwide have developed various semi-active control devices for seismic protection of structures. Most of these devices are electromechanical in nature and thus require a power source for their operation. In this paper, a newly developed rotation-based mechanical adaptive passive device is presented. These unique devices are able to mechanically change stiffness, either by adding positive or negative stiffness, by using different types of rotational elements. The devices are compact due to their use of rotational elements, facilitating their implementation in structures. The conceptual development of these devices is presented herein along with analytical models and numerical simulation results that demonstrate their potential for providing seismic protection. In addition, an extension of the stiffness modulation concept is introduced wherein damping is modulated.

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Shirokov, Viacheslav S., Vadim Yu Alpatov, and Evgeniy A. Gordeyev. "Research into the stiffness of beam-column joints of modular prefabricated buildings." Vestnik MGSU, no. 1 (January 2021): 20–29. http://dx.doi.org/10.22227/1997-0935.2021.1.20-29.

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Introduction. Rotational stiffness of a joint in modular building frames is the subject of this research. The stiffness of joints has a direct impact on the analysis of building structures. However, Russian design standards lack any clear instructions concerning this characteristic. Modular buildings have non-standard joints; therefore, it is necessary to study their rotational stiffness. The purpose of this work is to differentiate rigid joints, connecting a channel beam to a square pipe column, from semi-rigid ones. Materials and methods. Joints are classified according to Eurocode 3, that sets the limits for pinned, rigid and semi-rigid joints. The component-based finite element model implemented in the IDEA StatiCA software package is used to calculate the value of initial rotational stiffness. Two types of joints were studied: one that has an angle stiffener, and the other that has none. Results. The values of rotational stiffness of beam-column joints are obtained. It’s been identified that the joints of spans, typical for modular buildings, having no angle stiffeners, should be classified as semi-rigid and their rotational stiffness should be taken into account in designs. The variability of rotational stiffness of joints, having angle stiffeners, is nonlinear. If the dimensions of an angle stiffener are close to those of the cross section of a column, rotational stiffness rises steeply and joints turn rigid. Conclusions. A nomogram was made for various sections of channels and pipes having minimum angle stiffener dimensions, ensuring the rigidity of beam-column joints. The nomogram is recommended as a guidance for setting angle stiffener dimensions. Acknowledgements. The co-authors would like to express gratitude to the editorial staff for the fast preparation of this article for publication. The co-authors are also grateful to the reviewer for his constructive feedback that has enabled them to improve the text of the article.

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Wu, Guanglei, Shaoping Bai, and Jørgen Kepler. "Stiffness characterization of a 3-PPR planar parallel manipulator with actuation compliance." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 12 (November 4, 2014): 2291–302. http://dx.doi.org/10.1177/0954406214557341.

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This paper investigates the stiffness of a compliant planar parallel manipulator. Instead of establishing stiffness matrix directly for planar mechanisms, we adopt the modeling approach for spatial mechanisms, which allows us to derive two decoupled homogeneous matrices, corresponding to the translational and rotational stiffness. This is achieved by resorting to the generalized eigenvalue problem, through which the eigenscrew decomposition is implemented to yield six screw springs. The principal stiffnesses and their directions are then identified from the eigenvalue problem of the two separated submatrices. In addition, the influence of the nonlinear actuation compliance to the manipulator stiffness is investigated, and the established stiffness model is experimentally verified.

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Bong, Jin Kyun, Hyung Do Lee, Seungjun Kim, Ho-Seong Mha, Dong-Kyun Yim, and Jeong-Hun Won. "Probabilistic Characteristics of Moment Capacity and Rotational Stiffness of Wedge Joints Used in Support Systems Reflecting Reused Members." Applied Sciences 9, no. 19 (September 27, 2019): 4056. http://dx.doi.org/10.3390/app9194056.

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The moment capacity and rotational stiffness of wedge joints, which connect vertical and horizontal members of assembled support systems, were evaluated experimentally considering the characteristics of reused members. Since temporary structures, such as supports, tend to be reused, experiments were conducted with reused members, and the normality of the measured data was assessed. The lower and upper limits of the 95% confidence intervals of the moment capacity and rotational stiffness of wedge joints with reused members were determined. Experiments were also conducted on a joint system with new members to analyze the influence of reused members. In integrating both new and reused members, the maximum moments of wedge joints were observed to be normally distributed. The lower limit of the 95% confidence interval of the maximum moment of joints was 0.997 kNm, and the upper limit was 1.074 kNm. The rotational stiffness of the wedge joint was evaluated using a trilinear model. The initial rotational stiffness decreased with continued use of the joint. The average rotational stiffness of the joint, analyzed by combining the results for new and reused members, was found to be 22.475 kNm/rad for the first interval, 4.705 kNm/rad for the second interval, and 1.577 kNm/rad for the third interval. The lower limit of the 95% confidence interval of the initial rotational stiffness was 20.688 kNm/rad, and the upper limit was 24.262 kNm/rad.

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Guo, Ting, Na Yang, Huichun Yan, and Fan Bai. "Experimental study of moment carrying behavior of typical Tibetan timber beam-column joints." Advances in Structural Engineering 24, no. 11 (March 18, 2021): 2402–12. http://dx.doi.org/10.1177/13694332211001503.

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This study aimed to investigate the moment carrying behavior of typical Tibetan timber beam-column joints under monotonic vertical static load and also evaluate the influence of length ratio of Gongmu to beam (LRGB) and dowels layout on the structural performance of the joint. Six full-scale specimens were fabricated with same construction but different Gongmu length and dowels position. The moment carrying performance of beam-column joints in terms of failure mode, moment resistance, and rotational stiffness of joints were obtained via monotonic loading tests. Test results indicated that all joints are characterized by compressive failure perpendicular to grain of Ludou. Additionally, it was found that greater LRGB leads to greater initial rotational stiffness and maximum moment of the joint by an increase of restraint length for beam end; however, offsetting dowels toward column resulted smaller stiffness and ultimate bending moment of joints, particularly, offsetting Beam-Gongmu dowels toward column changed the moment-rotation curve pattern of the beam-column joint, accompanied by a hardening stiffness at last phase. Furthermore, a simplified trilinear model was proposed to represent the moment-rotation relationship of the typical Tibetan timber beam-column joint.

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Kangkang, Li, Jiang Hongzhou, He Jingfeng, and Zhang Hui. "Variable-stiffness decoupling of redundant planar rotational parallel mechanisms with crossed legs." Journal of Vibration and Control 24, no. 23 (February 10, 2018): 5525–33. http://dx.doi.org/10.1177/1077546318756699.

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For redundant planar rotational parallel mechanisms (RPRPM), stiffness consists of active stiffness resulting from internal forces and passive stiffness caused by compliances of flexible elements, and the active stiffness is coupled with the passive stiffness. The stiffness variations with stretching internal force and compressing internal force of flexible elements are analyzed. By combining the leg-crossed RPRPM and leg-uncrossed RPRPM of different leg arrangements, the active stiffness is decoupled from the passive stiffness. The stiffness is modulated by changing the internal force and hence the spring stretching length independently to avoid being influenced by the passive stiffness. The stiffness variation multiple with given spring stretching length is maximized by decoupling the active stiffness from the passive stiffness. The variation of natural frequency of RPRPM is maximized by maximizing the stiffness variation, and the RPRPM can employ vibration of resonance to improve the working performance in a large range of driving frequency.

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Huang, Shuguang, and Joseph M. Schimmels. "A Classification of Spatial Stiffness Based on the Degree of Translational–Rotational Coupling." Journal of Mechanical Design 123, no. 3 (June 1, 1999): 353–58. http://dx.doi.org/10.1115/1.1374197.

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Previously, we have shown that, to realize an arbitrary spatial stiffness matrix, spring components that couple the translational and rotational behavior along/about an axis are required. We showed that, three such coupled components and three uncoupled components are sufficient to realize any full-rank spatial stiffness matrix and that, for some spatial stiffness matrices, three coupled components are necessary. In this paper, we show how to identify the minimum number of components that provide the translational-rotational coupling required to realize an arbitrarily specified spatial stiffness matrix. We establish a classification of spatial stiffness matrices based on this number which we refer to as the “degree of translational–rotational coupling” (DTRC). We show that the DTRC of a stiffness matrix is uniquely determined by the spatial stiffness mapping and is obtained by evaluating the eigenstiffnesses of the spatial stiffness matrix. The topological properties of each class are identified. In addition, the relationships between the DTRC and other properties identified in previous investigations of spatial stiffness behavior are discussed.

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Feng, Sheng, Haipeng Geng, Bo Zhang, Lihua Yang, and Lie Yu. "Axial stiffness of a rotating trunnion joint." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 16 (December 23, 2014): 2846–53. http://dx.doi.org/10.1177/0954406214566037.

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A trunnion joint is modeled as a circular plate with two types of outer boundary conditions. One is clamped supported and the other is simply supported. Symmetrical bending deflection is produced when an external force acts on the inner side of the circular plate. The governing equations of the circular plate with these two kinds of boundary conditions are solved by using finite difference method, and the axial stiffness of the circular plate is obtained according to the relationship between the external force and the bending deflection of the circular plate. In order to verify the accuracy of the finite difference method, a finite element method was also given. The effects of rotational speed and the ratio of inner radius to outer radius of the circular plate on the axial stiffness are studied. It is shown that the rotational speed can significantly affect the axial stiffness of the trunnion joint for these two cases, especially for a lower ratio of inner radius to outer radius of the circular plate. The axial stiffness increases monotonically with the increase in rotational speed. More specifically, for a lower ratio of inner radius to outer radius of the circular plate, the axial stiffness with the simply supported boundary condition at high rotational speed is more than twice as much as the case without considering the rotational speed. Correspondingly, it is more than one and a half times for the clamped supported boundary condition.

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Holmes, Michael W. R., and Peter J. Keir. "Muscle Contributions to Elbow Joint Rotational Stiffness in Preparation for Sudden External Arm Perturbations." Journal of Applied Biomechanics 30, no. 2 (April 2014): 282–89. http://dx.doi.org/10.1123/jab.2013-0135.

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Understanding joint stiffness and stability is beneficial for assessing injury risk. The purpose of this study was to examine joint rotational stiffness for individual muscles contributing to elbow joint stability. Fifteen male participants maintained combinations of three body orientations (standing, supine, sitting) and three hand preloads (no load, solid tube, fluid filled tube) while a device imposed a sudden elbow extension. Elbow angle and activity from nine muscles were inputs to a biomechanical model to determine relative contributions to elbow joint rotational stiffness, reported as percent of total stiffness. A body orientation by preload interaction was evident for most muscles (P< .001). Brachioradialis had the largest change in contribution while standing (no load, 18.5%; solid, 23.8%; fluid, 26.3%). Across trials, the greatest contributions were brachialis (30.4 ± 1.9%) and brachioradialis (21.7 ± 2.2%). Contributions from the forearm muscles and triceps were 5.5 ± 0.6% and 9.2 ± 1.9%, respectively. Contributions increased at time points closer to the perturbation (baseline to anticipatory), indicating increased neuromuscular response to resist rotation. This study quantified muscle contributions that resist elbow perturbations, found that forearm muscles contribute marginally and showed that orientation and preload should be considered when evaluating elbow joint stiffness and safety.

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Abdel-Jaber, M. S., R. G. Beale, M. H. R. Godley, and M. Abdel-Jaber. "Rotational strength and stiffness of tubular scaffold connectors." Proceedings of the Institution of Civil Engineers - Structures and Buildings 162, no. 6 (December 2009): 391–403. http://dx.doi.org/10.1680/stbu.2009.162.6.391.

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Silva, L. A. P., L. F. N. Neves, and F. C. T. Gomes. "Rotational Stiffness of Rectangular Hollow Sections Composite Joints." Journal of Structural Engineering 129, no. 4 (April 2003): 487–94. http://dx.doi.org/10.1061/(asce)0733-9445(2003)129:4(487).

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Rodas, Pablo Torres, Farzin Zareian, and Amit Kanvinde. "Rotational Stiffness of Deeply Embedded Column–Base Connections." Journal of Structural Engineering 143, no. 8 (August 2017): 04017064. http://dx.doi.org/10.1061/(asce)st.1943-541x.0001789.

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31

Ritt, MJPF, PR Stuart, LJ Berglund, RA Berger, RL Linscheid, WP Cooney, and K.-N. An. "Rotational laxity and stiffness of the radiocarpal joint." Clinical Biomechanics 11, no. 4 (June 1996): 227–32. http://dx.doi.org/10.1016/0268-0033(95)00074-7.

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32

Ballal, Moez S., Federico Giuseppe Usuelli, Umberto Alfieri Montrasio, Andy Molloy, Luigi La Barbera, Tomaso Villa, and Giuseppe Banfi. "Rotational and peak torque stiffness of rugby shoes." Foot 24, no. 3 (September 2014): 107–10. http://dx.doi.org/10.1016/j.foot.2014.06.006.

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33

Zivkovic, Srdjan, Marija Spasojevic-Surdilovic, Dragana Turnic, and Marko Milosevic. "Comparative analysis of using degree of rigidity and rotational stiffness of connections in structural design." Facta universitatis - series: Architecture and Civil Engineering 16, no. 1 (2018): 17–27. http://dx.doi.org/10.2298/fuace160609002z.

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Using classical formulation of stiffness method, impact of semi-rigid connections on the stresses and strains can be analyzed by the degree of rigidity or by rotational stiffness of connections. In this paper, functional dependence between the degree of rigidity and rotational stiffness of connections is formulated and the comparative analysis of these two approaches in the analysis of semi-rigid connections behavior of members in real structures, is implemented.

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34

Tao, Gui Lan, and Si Yuan Dong. "Influence of Rotational Stiffness on the Distribution of Horizontal Forces on All-Vertical-Pile-Supported Wharf Structures." Applied Mechanics and Materials 405-408 (September 2013): 1453–57. http://dx.doi.org/10.4028/www.scientific.net/amm.405-408.1453.

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A calculation method of rotational stiffness of all-vertical-pile-supported (AVPS) wharf is discussed and a formula based on rotational stiffness is derived to evaluate the distribution of horizontal forces on an AVPS wharf. Combining with an engineering example, the rotational stiffness and the horizontal force distribution coefficients were calculated utilizing finite element method (FEM), the elastic support-rigid beam method (ESRBM) outlined in Chinese Harbor Code, as well as the proposed formula for the piles layout width-length ratio of 0.4, 0.5 and 0.6. Results indicate that the increase in width-length ratio will increase the rotational stiffness and make the distribution of horizontal forces on each bent to be more uniform. Results calculated by the proposed formula are agree well with the results by FEM. The maximum difference of the distribution coefficient on the first bent between the results obtained by the proposed formula and by ESRBM is approximately 22%.

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35

QIAO, PIZHONG, and LUYANG SHAN. "EXPLICIT LOCAL BUCKLING ANALYSIS OF ROTATIONALLY RESTRAINED COMPOSITE PLATES UNDER BIAXIAL LOADING." International Journal of Structural Stability and Dynamics 07, no. 03 (September 2007): 487–517. http://dx.doi.org/10.1142/s021945540700240x.

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A variational formulation of the Ritz method is used to establish an eigenvalue problem for the local buckling behavior of composite plates elastically restrained (R) along their four edges (the RRRR plates) and subjected to biaxial compression, and the explicit solution in terms of the rotational restraint stiffness (k) is presented. Based on the different boundary and loading conditions, the explicit local buckling solution for the rotationally restrained plates is simplified to several special cases (e.g. the SSSS, SSCC, CCSS, CCCC, SSRR, RRSS, CCRR, and RRCC plates) under biaxial compression (and further reduced to uniaxial compression) with a combination of simply-supported (S), clamped (C), and/or restrained (R) edge conditions. The deformation shape function is presented by using the unique harmonic functions in both the axes to account for the effect of elastic rotational restraint stiffness (k) along the four edges of the orthotropic plate. A parametric study is conducted to evaluate the influences of the loading ratio (α), the rotational restraint stiffness (k), the aspect ratio (γ), and the flexural-orthotropy parameters (α OR and β OR ) on the local buckling stress resultants of various rotationally restrained plates, and design plots with respect to these parameters are provided. The present explicit local buckling solution of the elastically restrained composite plates and the associated design plots can be employed to facilitate design analysis of composite structures (e.g. stiffened panels, thin-walled structures, and honeycomb cores).

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Liu, Zhifeng, Jingjing Xu, Qiang Cheng, Yongsheng Zhao, and Yanhu Pei. "Rotation-joint stiffness modeling for industrial robots considering contacts." Advances in Mechanical Engineering 10, no. 8 (August 2018): 168781401879306. http://dx.doi.org/10.1177/1687814018793063.

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Joint flexibility has a major impact on the motion accuracy of a robotic end effector, particularly at high speeds. This work proposes a technique of precisely modeling the torsional stiffness of the rotational joints for the industrial robots. This technique considers the contacts that exist in the joint system, which can have a significant effect on the overall joint stiffness. The torsional stiffness of the connections that commonly exist in the rotational joints, such as the belt connection, the connections using key, bolts, and pins, were modeled by combining the force analysis and the fractal theory. Through modeling the equivalent stiffness for the springs in serial and in parallel, the torsional stiffness of all joints for the ER3A-C60 robot were calculated and analyzed. The results show that the estimated stiffness based on the proposed technique is closer to the actual values than that based on the previous model without considering the contacts. The analysis is useful for controlling the dynamic characteristic of the industrial robots with the rotational joints while planning the trajectory for the end effector.

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Daniūnas, Alfonsas, and Kęstutis Urbonas. "INFLUENCE OF THE COLUMN WEB PANEL BEHAVIOUR ON THE CHARACTERISTICS OF A BEAM-TO-COLUMN JOINT." Journal of Civil Engineering and Management 19, no. 2 (April 18, 2013): 318–24. http://dx.doi.org/10.3846/13923730.2013.776628.

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The paper reviews the importance of evaluation of actual joint behaviour during the design and manufacture of frame construction. The authors applied the component method, which is used in Eurocode 3. Additionally, they provided a short overview of beam-to-column joint components. The research focuses on one part of the joint-column web panel. It investigates the influence of the column web panel to the rotational stiffness and design moment resistance of the joint. The article presents several possibilities for stiffening the column web panel plate. Calculation results illustrate the influence of the characteristics of column web panel to the rotational stiffness and design moment resistance of the joint. Calculations were carried out both with an unstiffened and with a stiffened column web panel plates. The results confirmed the expected assumptions, i.e. the column web panel is an essential part of the joint, and its behaviour has a significant influence on the rotational stiffness and design moment resistance of the joint. In all calculations where column web panel was stiffened, the rotational stiffness and design moment resistance of the joint increased.

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38

Dunning, Peter D. "On the co-rotational method for geometrically nonlinear topology optimization." Structural and Multidisciplinary Optimization 62, no. 5 (May 9, 2020): 2357–74. http://dx.doi.org/10.1007/s00158-020-02605-4.

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Abstract This paper investigates the application of the co-rotational method to solve geometrically nonlinear topology optimization problems. The main benefit of this approach is that the tangent stiffness matrix is naturally positive definite, which avoids some numerical issues encountered when using other approaches. Three different methods for constructing the tangent stiffness matrix are investigated: a simplified method, where the linear elastic stiffness matrix is simply rotated; the consistent method, where the tangent stiffness is derived by differentiating residual forces by displacements; and a symmetrized method, where the consistent tangent stiffness is approximated by a symmetric matrix. The co-rotational method is implemented for 2D plane quadrilateral elements and 3-node shell elements. Matlab code is given in the appendix to modify an existing, freely available, density-based topology optimization code so it can solve 2D problems with geometric nonlinear analysis using the co-rotational method. The approach is used to solve four benchmark problems from the literature, including optimizing for stiffness, compliant mechanism design, and a plate problem. The solutions are comparable with those obtained with other methods, demonstrating the potential of the co-rotational method as an alternative approach for geometrically nonlinear topology optimization. However, there are differences between the methods in terms of implementation effort, computational cost, final design, and objective value. In summary, schemes involving the symmetrized tangent stiffness did not outperform the other schemes. For problems where the optimal design has relatively small displacements, then the simplified method is suitable. Otherwise, it is recommended to use the consistent method, as it is the most accurate.

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Sun, Xiaoluan, Yiheng Qu, Weiqing Liu, Weidong Lu, and Shenglin Yuan. "Rotational behavior and modeling of bolted glulam beam-to-column connections with slotted-in steel plate." Advances in Structural Engineering 23, no. 9 (February 14, 2020): 1989–2000. http://dx.doi.org/10.1177/1369433220906223.

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In this article, the rotational behavior of typical bolted glulam beam-to-column connections with slotted-in steel plate was studied in the numerical method. In order to describe the complicated behavior of wood more closely, an elastic–plastic damage constitutive law combining the Hill yielding criterion and a modified Hashin failure criterion was embedded in the commercial ABAQUS software in the form of a VUMAT subroutine. Subsequently, a three-dimensional finite element model based on the constitutive law proposed was established, with the failure mode and moment–rotation curve compared to some similar experiments. Based on this finite element model, a parametric study concentrating on the influence of the width of the beam, bolt diameter, and assembly clearance was carried out. It was found that the numerical method using the proposed constitutive law showed a good capacity to study the rotational behavior of the connections. Besides, the initial rotational stiffness increased with the increase in beam width and bolt diameter, and the assembly clearances between bolts and bolt holes would affect the initial rotational stiffness while the assembly clearance between beam and column affected little.

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40

JAYACHANDRAN, S. ARUL, V. KALYANARAMAN, and R. NARAYANAN. "A CO-ROTATION BASED SECANT MATRIX PROCEDURE FOR ELASTIC POSTBUCKLING ANALYSIS OF TRUSS STRUCTURES." International Journal of Structural Stability and Dynamics 04, no. 01 (March 2004): 1–19. http://dx.doi.org/10.1142/s0219455404001124.

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To investigate the geometrically nonlinear behavior of space structures using finite elements, the total Lagrangian (TL), updated Lagrangian (UL) and co-rotational (CR) procedures have been used by researchers. For 3D truss structures, the CR formulation has been reported to be computationally more efficient as it possesses the rigid body displacement components during deformations. In this paper, the secant stiffness matrix of truss element will be derived using a simple co-rotational, total Lagrangian (CR–TL) formulation. The incremental rotation matrix, which is the pivotal quantity in the CR formulation, is derived from geometric principles. The secant stiffness matrix is presented in terms of the natural degrees-of-freedom of the truss element. The efficiency and reliability of the present formulation is demonstrated in the solution of several truss problems involving the postbuckling behavior.

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41

Chaofeng, Li, Tang Qiansheng, Miao Boqing, and Wen Bangchun. "The sensibility on dynamic characteristics of pre-pressure thin-wall pipe under elastic boundary conditions." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 6 (August 9, 2016): 995–1009. http://dx.doi.org/10.1177/0954406216631371.

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Consideration is given to dynamic behavior of cylindrical pressure pipe with elastic boundary conditions. Based on Sanders’ shell theory and Hamilton principle, the system equations are established for integrating the uniform distributed pressure into the elastic boundary condition. In the analytical formulation, the Rayleigh–Ritz method with a set of displacement shape functions is used to deduce mass, damping, and stiffness matrices of the pipe system. The displacements in three directions are represented by the characteristic orthogonal polynomial series and trigonometric functions which are satisfied with the elastic boundary conditions, which are represented as four sets of independent springs placed at the ends including three sets of linear springs and one set of rotational spring. The pressure pipe always suffers a uniform distributed pressure in radial direction. To verify the accuracy and reliability of the present method, several numerical examples with classical boundary condition, including free and simply supported supports are listed and comparisons are made with open literature. Then the influences of boundary restraint stiffness and the distributed pressure on natural frequency and the forced vibration response are studied: The natural frequencies increase significantly as the restraint stiffness or the distributed pressure increases. Compared to the rotational spring stiffness, the stiffnesses of axial, radial, and circumferential springs have more significant effect on natural frequency. And the lower modes are more sensitive on restraint stiffness than higher modes. But the variation of natural frequency with respect to the spring stiffness decreases monotonically with the increasing distributed pressure. The forced vibration response is also affected by the restraint stiffness.

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Sobota, P. M., and K. A. Seffen. "Effects of boundary conditions on bistable behaviour in axisymmetrical shallow shells." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2203 (July 2017): 20170230. http://dx.doi.org/10.1098/rspa.2017.0230.

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Multistable shells are thin-walled structures that have more than one stable state of self-stress. We consider isotropic axisymmetrical shallow shells of arbitrary polynomial shapes using a Föppl–von Kármán analytical model. By employing a Rayleigh–Ritz approach, we identify stable shapes from local minima in the strain energy formulation, and we formally characterize the level of influence of the boundary conditions on the critical geometry for achieving bistable inversion—an effect not directly answered in the literature. Systematic insight is afforded by connecting the boundary to ground through sets of extensional and rotational linear springs. For typical cap-like shells, it is shown that bistability is generally enhanced when the extensional spring stiffness increases and when the rotational spring stiffness decreases, i.e. when boundary movements in-plane are resisted but when their rotations are not; however, for certain other shapes and large in-plane stiffness values, bistability can be enhanced by resisting but not entirely preventing edge rotations. Our predictions are furnished as detailed regime maps of the critical geometry, which are accurately correlated against finite-element analysis. Furthermore, the suitabilities of single degree-of-freedom models, for which solutions are achieved in closed form, are evaluated and compared to our more accurate predictions.

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43

Eberle, A. L., B. H. Dickerson, P. G. Reinhall, and T. L. Daniel. "A new twist on gyroscopic sensing: body rotations lead to torsion in flapping, flexing insect wings." Journal of The Royal Society Interface 12, no. 104 (March 2015): 20141088. http://dx.doi.org/10.1098/rsif.2014.1088.

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Insects perform fast rotational manoeuvres during flight. While two insect orders use flapping halteres (specialized organs evolved from wings) to detect body dynamics, it is unknown how other insects detect rotational motions. Like halteres, insect wings experience gyroscopic forces when they are flapped and rotated and recent evidence suggests that wings might indeed mediate reflexes to body rotations. But, can gyroscopic forces be detected using only changes in the structural dynamics of a flapping, flexing insect wing? We built computational and robotic models to rotate a flapping wing about an axis orthogonal to flapping. We recorded high-speed video of the model wing, which had a flexural stiffness similar to the wing of the Manduca sexta hawkmoth, while flapping it at the wingbeat frequency of Manduca (25 Hz). We compared the three-dimensional structural dynamics of the wing with and without a 3 Hz, 10° rotation about the yaw axis. Our computational model revealed that body rotation induces a new dynamic mode: torsion. We verified our result by measuring wing tip displacement, shear strain and normal strain of the robotic wing. The strains we observed could stimulate an insect's mechanoreceptors and trigger reflexive responses to body rotations.

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Gent, A. N., and Y.-W. Chang. "Stiffness and Bond Strength of Rubber-Filled Hinges." Rubber Chemistry and Technology 66, no. 5 (November 1, 1993): 733–41. http://dx.doi.org/10.5254/1.3538340.

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Abstract The stiffness of rubber-filled hinges for small rotations of the hinge plates has been determined by finite element analysis (FEA). The rubber is assumed to be linearly elastic and virtually incompressible, and the hinge is assumed to be long enough for the rubber to be in a state of plane strain, i.e., prevented from any displacement parallel to the hinge. Results have been obtained for hinges of a wide range of unstrained angle, ranging from 5° up to 360°. The calculated stiffnesses for long hinges vary by over four orders of magnitude over this range. For small angles, an approximate solution has been obtained by direct analysis—it is in good agreement with the FEA solution for hinge angles up to about 40°. Experimental measurements on several rubber-filled hinges are also reported. The measured rotational stiffnesses are in satisfactory agreement with theoretical predictions. Because a rubber-filled hinge constitutes a possible test method for bond strength, conditions are derived for bond rupture as a hinge is strained open.

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Andersson, Anette. "An Analytical Study of the Effect of the Contact Ratio on the Spur Gear Dynamic Response." Journal of Mechanical Design 122, no. 4 (May 1, 1999): 508–14. http://dx.doi.org/10.1115/1.1320819.

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A model was used, where the total gear mesh stiffness was approximated by two constant stiffness levels, in order to analyze the influence of the contact ratio on the dynamic response of spur gears. Due to the stiffness variation there is parametric excitation of the transmission error, which generally causes tooth separation at certain critical rotational speeds. The present paper discloses a method to analytically calculate which contact ratio to use in order to avoid tooth separation near a specific critical rotational speed. [S1050-0472(00)02604-0]

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YANG, Qizi. "Rotational Stiffness Characterization of GeneralizedTriple-cross-spring Flexure Pivots." Journal of Mechanical Engineering 51, no. 13 (2015): 189. http://dx.doi.org/10.3901/jme.2015.13.189.

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47

Seubert, Carl R., and Hanspeter Schaub. "Rotational Stiffness Study of Two-Element Tethered Coulomb Structures." Journal of Spacecraft and Rockets 48, no. 3 (May 2011): 488–97. http://dx.doi.org/10.2514/1.49772.

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48

IRIE, Yasutaka, and Junichi TSURUTA. "ROTATIONAL STIFFNESS CAUSED BY PERPENDICULAR COMPRESSION AT SASHIGAMOI JOINTS." AIJ Journal of Technology and Design 15, no. 29 (2009): 111–14. http://dx.doi.org/10.3130/aijt.15.111.

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49

Johanides, Marek, Lenka Kubíncová, David Mikolášek, Antonín Lokaj, Oldřich Sucharda, and Petr Mynarčík. "Analysis of Rotational Stiffness of the Timber Frame Connection." Sustainability 13, no. 1 (December 25, 2020): 156. http://dx.doi.org/10.3390/su13010156.

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Initially, timber was considered only as an easily accessible and processable material in nature; however, its excellent properties have since become better understood. During the discovery of new building materials and thanks to new technological development processes, industrial processing technologies and gradually drastically decreasing forest areas, wood has become an increasingly neglected material. Load-bearing structures are made mostly of reinforced concrete or steel elements. However, ecological changes, the obvious problems associated with environmental pollution and climate change, are drawing increasing attention to the importance of environmental awareness. These factors are attracting increased attention to wood as a building material. The increased demand for timber as a building material offers the possibility of improving its mechanical and physical properties, and so new wood-based composite materials or new joints of timber structures are being developed to ensure a better load capacity and stiffness of the structure. Therefore, this article deals with the improvement of the frame connection of the timber frame column and a diaphragm beam using mechanical fasteners. In common practice, bolts or a combination of bolts and pins are used for this type of connection. The subject of the research and its motivation was to replace these commonly used fasteners with more modern ones to shorten and simplify the assembly time and to improve the load capacity and rigidity of this type of frame connection.

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Roche, Stéphane, Geoffroy Mattoni, and Yves Weinand. "Rotational Stiffness at Ridges of Timber Folded-plate Structures." IABSE Symposium Report 104, no. 14 (May 13, 2015): 1–8. http://dx.doi.org/10.2749/222137815815775187.

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Journal articles on the topic 'Rotational stiffness'

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