Relevant bibliographies by topics / Vibration equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Vibration equation'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Vibration equation"

1

AL-Hafidh, Manal H., and Ali Mohsen Rishem. "THE EFFECT OF LONGITUDINAL VIBRATION ON LAMINAR FORCED CONVECTION HEAT TRANSFER IN A HORIZONTAL TUBE." Journal of Engineering 12, no. 03 (2006): 863–79. http://dx.doi.org/10.31026/j.eng.2006.03.30.

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The effect of longitudinal vibration on the laminar forced convection heat transfer in a horizontal tube was studied in the present work. The flow investigated is an internal, laminar, incompressible, developing, steady and oscillatory flow. The vibration vector was parallel to the fluid flow direction. The boundary layer was studied in the entrance region for Prandtl numbers greater than one and the hydrodynamic boundary layer grows faster than thermal boundary layer. The governing equations which used were momentum equation in the axial direction, continuity and energy equation. The finite d
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Gunawan, Gani. "Penyelesaian khusus persamaan diferensial biasa ordo dua linier tak homogen dengan koefisien konstan untuk fungsi bagian demi bagian." Majalah Ilmiah Matematika dan Statistika 24, no. 1 (2024): 1. http://dx.doi.org/10.19184/mims.v24i1.38240.

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Spring mechanical vibration motion system with a damped degree of freedom and influenced by external forces, is mathematically expressed as an ordinary differential equation of order of two linear constant coefficients that are not homogeneous. If an external force acts on a stationary system expressed as a continuous function f(t) for any time t, then the system will experience mechanical vibrational motion which mathematically the equation of motion can be expressed as a superposition. The equation consists of as a solution to a homogeneous form with mechanical vibrations as a solution to a
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Yu, Yingjie, Ying Cao, Qinghui Lai, et al. "Design and Operation Parameters of Vibrating Harvester for Coffea arabica L." Agriculture 13, no. 3 (2023): 700. http://dx.doi.org/10.3390/agriculture13030700.

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This study designed a handheld vibrating coffee harvester to improve the mechanized harvesting of Coffea arabica L. The proposed device was used to vibrate branches of Coffea arabica L. trees, and the shedding of coffee fruit and the operation parameters of vibrational harvesting were analyzed. Images captured using high-speed photography were used to derive a force equation that represents the forced vibration of the coffee fruit-stalk joint. In addition, the vibrations of coffee berries and branches were theoretically analyzed, and the results were used to establish a dynamic vibration model
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Wang, Xiao Yan, Meng Ling Wu, and Zhong Kai Chen. "Application with Theory of Vibration Equivalence on Reliability Test Bed of Train Brake System." Applied Mechanics and Materials 34-35 (October 2010): 1978–82. http://dx.doi.org/10.4028/www.scientific.net/amm.34-35.1978.

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In order to design a reliability test bed for train brake system, theory of vibration equivalence was used to represent in laboratory the environmental vibration. Firstly, the root mean square (RMS) value of the acceleration was calculated for train brake system according to IEC 61373. Then, a configuration of vibrostand was proposed for the reliability test bed, which was mainly composed of vibrating table-board, vibrator motor, damp and four vibrating springs, as shown in figure 2. After that, an equation was got according to the RMS equivalency theory. Finally, the equation was solved accor
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Song, Yu Min, and Ding Jun Wu. "Establishment of Vibration Differential Equation and Analysis of Dynamics Characteristics for Curved Beam." Advanced Materials Research 250-253 (May 2011): 1329–33. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.1329.

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In this paper, a differential segment of curved beam in the vibration state is analyzed, and the internal force equilibrium equations are established, then the vibration differential equations of curved beam are derived by considering Timoshenko’s geometric equations and physical equations. The vibration differential equations derived are similar to the Vlasov’s static differential equation of curved beam. By analyzing the vibration differential equations, some characteristics of vibration are obtained, and ideas of solving the vibration differential equations are also proposed. The vibration
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Hussain, Muzamal, and Muhammad Nawaz Naeem. "Vibration analysis of single-walled carbon nanotubes using wave propagation approach." Mechanical Sciences 8, no. 1 (2017): 155–64. http://dx.doi.org/10.5194/ms-8-155-2017.

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Abstract. In this paper, influence of boundary conditions on free vibrations of single- walled carbon nanotubes (SWCNTs) is examined. The Flügge's shell dynamical equations are utilized for governing vibrations for carbon nanotubes. The wave propagation approach (WPA) is engaged to determine vibration frequency equation in standard eigenvalue form. The axial modal dependence is measured by the complex exponential functions implicating the axial modal numbers. These numbers are associated with boundary conditions specified at edges of a carbon nanotube. Computer programming is performed to obta
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Ragaišis, L., R. Jonušas, K. Ragulskis, and V. Jurėnas. "Research of Possibilities of Energy Transformation Using an Autovibrating System, Excited by Small Outer Excitement." Solid State Phenomena 113 (June 2006): 207–12. http://dx.doi.org/10.4028/www.scientific.net/ssp.113.207.

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There are lots of sources of disturbance in people’s surrounding environment - e.g. wind, sea, river flow, and intensive acoustic noise. These sources can cause auto vibrations of particular dynamic systems. Such phenomenon could be used for converting mechanical vibration energy to electrical energy. Solving this problem is topical because it could help to create autonomic sources of renewable energy. Dynamic model, described by a presumptive differential motion equation, of auto vibrating system, affected by airflow is made and inspected. Possible modes of vibrations and different states of
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Zhang, Yinquan, Kun Huang, and Changxing Zhang. "Nonlinear Vibrations of Carbon Nanotubes with Thermal-Electro-Mechanical Coupling." Applied Sciences 13, no. 4 (2023): 2031. http://dx.doi.org/10.3390/app13042031.

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Carbon nanotubes (CNTs) have wide-ranging applications due to their excellent mechanical and electrical properties. However, there is little research on the nonlinear mechanical properties of thermal-electro-mechanical coupling. In this paper, we study the nonlinear vibrations of CNTs by a thermal-electro-mechanical coupling beam theory. The Galerkin method is used to discretize the partial differential equation and obtain two nonlinear ordinary differential equations that describe the first- and second-order mode vibrations. Then, we obtain the approximate analytical solutions of the two equa
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Kononov, Yuriy. "On the solution of a complicated biharmonic equation in a hydroelasticity problem." Ukrainian Mathematical Bulletin 20, no. 2 (2023): 203–18. http://dx.doi.org/10.37069/1810-3200-2023-20-2-3.

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A hydroelastic problem of free vibrations of a thin plate that horizontally separates ideal incompressible liquids of different densities in a rigid cylindrical tank with an arbitrary cross-section has been considered in the linear formulation. To solve the corresponding complicated inhomogeneous biharmonic equation, the fundamental system of the solutions of biharmonic equation (FSS) and the eigenmodes of ideal liquid oscillations in a cylindrical cavity were used. The frequency equation was obtained for arbitrary fixation of the plate contour. On the example of a clamped plate, the frequency
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Chau, K. T. "Vibrations of Transversely Isotropic Finite Circular Cylinders." Journal of Applied Mechanics 61, no. 4 (1994): 964–70. http://dx.doi.org/10.1115/1.2901587.

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This paper investigates the exact frequency equations for all the possible natural vibrations in a transversely isotropic cylinder of finite length. Two wave potentials are used to uncouple the equations of motion; the resulting hyperbolic equations are solved analytically for the vibration frequencies of a finite cylinder with zero shear tractions and zero axial displacement on the end surfaces and with zero tractions on the curved surfaces. In general, the mode shapes and the frequency equations of vibrations depend on both the range of the frequency and the elastic properties of the materia
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Dissertations / Theses on the topic "Vibration equation"

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De, Villiers Magdaline. "Existence theory for linear vibration models of elastic bodies." Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-10072009-201522.

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Medeiros, Luiz Adauto, and Juan Límaco. "On the Kirchhoff equation in noncylindrical domains of R." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97270.

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Zhang, Lei, University of Western Sydney, of Science Technology and Environment College, and School of Engineering and Industrial Design. "Exact solution for vibration of stepped circular Mindlin plates." THESIS_CSTE_EID_Zhang_L.xml, 2002. http://handle.uws.edu.au:8081/1959.7/64.

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This thesis presents the first-known exact solutions for vibration of stepped circular Mindlin plates. The considered circular plate is of several step-wise variation in thickness in the radial direction. The Mindlin first order shear deformable plate theory is employed to derive the governing differential equations for the annular and circular segments. The exact solutions to these differential equations may be expressed in terms of the Bessel functions of the first and second kinds and the modified Bessel functions of the first and second kinds. The governing homogenous system of equations i
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Gouttel, Badraoui Hadjira. "Approche des matrices de rigidité dynamique exactes pour l'analyse des structures." Rouen, 2000. http://www.theses.fr/2000ROUES032.

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Cette thèse présente la méthode des matrices de rigidité dynamique exactes (MRD) pour la prévision des caractéristiques vibratoires des structures élastiques. La formulation est basée sur la solution exacte des équations d'équilibre du mouvement de la structure, conduisant à un problème aux valeurs propres non linéaire en fréquence de vibrations. Pour l'évaluation de la matrice de rigidité dynamique des différents éléments composant les systèmes unidimensionnels, nous utilisons différentes approches qui peuvent être appliquées pour toutes les structures unidimensionnelless dans leur comporteme
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Sepehri, Ali. "MULTI-SCALE DYNAMICS OF MECHANICAL SYSTEMS WITH FRICTION." OpenSIUC, 2010. https://opensiuc.lib.siu.edu/dissertations/205.

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Contact between rough surfaces occurs in numerous engineering systems and in many instances influences the macro behavior of the system. In many instances, the interaction between rough surfaces, affect the macro behavior of the system. Effective treatment of systems containing rough surface contact requires multiscale modeling and analysis approach. It is the goal of this research to develop simple methods for treating contact of rough surfaces so as to facilitate multiscale analysis of systems containing rough surface contact and friction. This dissertation considers a multi-scale approac
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Zhang, Lei. "Exact solution for vibration of stepped circular Mindlin plates." Thesis, View thesis, 2002. http://handle.uws.edu.au:8081/1959.7/64.

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This thesis presents the first-known exact solutions for vibration of stepped circular Mindlin plates. The considered circular plate is of several step-wise variation in thickness in the radial direction. The Mindlin first order shear deformable plate theory is employed to derive the governing differential equations for the annular and circular segments. The exact solutions to these differential equations may be expressed in terms of the Bessel functions of the first and second kinds and the modified Bessel functions of the first and second kinds. The governing homogenous system of equations i
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Grenat, Clément. "Nonlinear Normal Modes and multi-parametric continuation of bifurcations : Application to vibration absorbers and architectured MEMS sensors for mass detection." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSEI078/document.

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Un des buts de cette thèse est d’approfondir la compréhension de la dynamique non-linéaire, notamment celle des MEMS, en proposant de nouvelles méthodes d’analyse paramétrique et de calcul de modes normaux non-linéaires. Dans une première partie, les méthodes de détection, de localisation et de suivi de points de bifurcation selon un unique paramètre sont rappelées. Ensuite, une nouvelle méthode d’analyse multiparamétrique basée sur la continuation récursive d’extremums est présentée. Cette méthode est ensuite appliquée à un absorbeur de vibration non-linéaire afin de repousser l’apparition de
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Bilasse, Massamaesso. "Modélisation numérique des vibrations linéaires et non linéaires des structures sandwichs à âme viscoélastique." Thesis, Metz, 2010. http://www.theses.fr/2010METZ032S/document.

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On s'intéresse à la modélisation numérique des structures sandwichs trois couches à âme viscoélastique utilisées pour l'amortissement passif et le contrôle des vibrations dans divers domaines d’application tels que l’aéronautique, l’aérospatial, l’automobile et l’électroménager. La complexité de la modélisation en dynamique de ces structures est liée d'une part aux non linéarités matérielles dues à la dépendance en fréquence et en température de la rigidité et d'autre part aux non linéarités géométriques dues aux grands déplacements. Nous proposons dans ce travail un cadre de modélisation des
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Ma, Congcong. "The research of acoustic resonance in the waveguide associated with Galbrun equation." Electronic Thesis or Diss., Compiègne, 2020. http://www.theses.fr/2020COMP2560.

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Dans un système ouvert bidimensionnel, lorsque l’onde acoustique se propage dans un conduit avec la présence d’un obstacle, il y aura amplification de la pression acoustique autour de l’obstacle. Les modes piégés existent autour de l’obstacle au-dessous et au-dessus de la fréquence de coupure, et ils causent des dommages considérables au système. Dans les recherches précédentes, ils se sont principalement concentrés sur la résolution de l’équation de Helmholtz, ce qui signifie que l’écoulement non-potentiel n’était pas prise en compte. L’objectif de la thèse portent sur le développement de mét
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Iourtchenko, Daniil V. "Optimal bounded control and relevant response analysis for random vibrations." Link to electronic thesis, 2001. http://www.wpi.edu/Pubs/ETD/Available/etd-0525101-111407.

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Thesis (Ph. D.)--Worcester Polytechnic Institute.<br>Keywords: Stochastic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation; Random vibration. Keywords: Stochastic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation; Random vibration; energy balance method. Includes bibliographical references (p. 86-89).
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Books on the topic "Vibration equation"

1

Haraux, Alain. Nonlinear vibrations and the wave equation. Universidade Federal do Rio de Janeiro, Centro de Ciências Matemáticas e da Natureza, Instituto de Matemática, 1986.

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Forest Products Laboratory (U.S.), ed. Commentary on factors affecting transverse vibration using an idealized theoretical equation. U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory, 2000.

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(Christian), Constanda C., ed. Stationary oscillations of elastic plates: A boundary integral equation analysis. Birkhäuser, 2011.

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Burq, Nicolas. Contrôle de l'équation des plaques en présence d'obstacles strictement convexes. Société mathématique de France, 1993.

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E, Skelton Robert, and Langley Research Center, eds. Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection. National Aeronautics and Space Administration, Langley Research Center, 1991.

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E, Skelton Robert, and Langley Research Center, eds. Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection. National Aeronautics and Space Administration, Langley Research Center, 1991.

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Wijker, Jaap. Miles' Equation in Random Vibrations. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73114-8.

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Chevalier, Yvon. Mechanics of viscoelastic materials and wave dispersion. ISTE, 2010.

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Chevalier, Yvon. Mechanics of viscoelastic materials and wave dispersion. ISTE, 2010.

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Haraux, Alain. Nonlinear Vibrations and the Wave Equation. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78515-8.

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Book chapters on the topic "Vibration equation"

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Thomson, William T. "Lagrange’s Equation." In Theory of Vibration with Applications. Springer US, 1993. http://dx.doi.org/10.1007/978-1-4899-6872-2_8.

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Huang, Weiping, Xuemin Wu, Juan Liu, and Xinglan Bai. "Equation of Riser Vibration." In Dynamics of Deepwater Riser. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-2888-7_4.

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Wijker, Jaap. "Random Vibration Load Factors." In Miles' Equation in Random Vibrations. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73114-8_4.

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Caldwell, J. "Numerical Solution of a Model Nonlinear Wave Equation." In Industrial Vibration Modelling. Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-4480-0_17.

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Wijker, Jaap. "Equivalence Random and Sinusoidal Vibration." In Miles' Equation in Random Vibrations. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73114-8_9.

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Kovacic, Ivana, and Michael J. Brennan. "Forced Harmonic Vibration of an Asymmetric Duffing Oscillator." In The Duffing Equation. John Wiley & Sons, Ltd, 2011. http://dx.doi.org/10.1002/9780470977859.ch8.

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Yabuno, Hiroshi. "Free Vibration of a Duffing Oscillator with Viscous Damping." In The Duffing Equation. John Wiley & Sons, Ltd, 2011. http://dx.doi.org/10.1002/9780470977859.ch3.

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Wijker, Jaap. "Acoustic and Random Vibration Test Tailoring." In Miles' Equation in Random Vibrations. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73114-8_6.

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Hubert, J. Sanchez, and E. Sanchez Palencia. "The Helmholtz Equation in Unbounded Domains." In Vibration and Coupling of Continuous Systems. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-73782-4_8.

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Wijker, Jaap. "Characterisation and Synthesis of Random Acceleration Vibration Specifications." In Miles' Equation in Random Vibrations. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73114-8_10.

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Conference papers on the topic "Vibration equation"

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Qin, Wei, Zhuang Kang, Ruxin Song, Liping Sun, and Ying Wu. "A Power Equation Model for Vortex-Induced Vibration of Circular Cylinder." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10479.

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Based on a semi-empirical model of vortex-induced vibration of an elastically mounted circular cylinder, the general equation of dynamics is put forward to establish the power equation for free vortex-induced vibration in this paper. The derivation of the governing equation is the general method to analyze fluid-structure interaction without priori assumptions about the form of the governing equations, which is of good/strong applicability and expansibility. To estimate the reliability of power equation in free vibrations, the power equation acquiring flow field provided by CFD is solved and c
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Sun, Jiawei, Xiaoang Liu, Yi-Hong Ou Yang, and Wenbin Shangguan. "Material Parameter Identification Method for Rubber Mount Constitutive Equation." In Noise and Vibration Conference & Exhibition. SAE International, 2023. http://dx.doi.org/10.4271/2023-01-1154.

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&lt;div class="section abstract"&gt;&lt;div class="htmlview paragraph"&gt;As an important vibration damping element in automobile industries, the vibration transmitted from the engine to the frame can be reduced effectively because of rubber mount. The influence of preload on the static characteristics of rubber mount and the constitutive parameters identification of Mooney-Rivlin model under preload were studied. Firstly, a test rig for stiffness measurement of rubber mount under preload was designed and the influence of preload on the force versus displacement of mount was studied. Then, the
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Changqing, Li, Yu Zhiwu, and Jiang Lizhong. "Comparison of vibration equation's solution with wave equation;s theory solution." In 2011 International Conference on Electrical and Control Engineering (ICECE). IEEE, 2011. http://dx.doi.org/10.1109/iceceng.2011.6058268.

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Changqing, Li, Yu Zhiwu, and Jiang LiZhong. "The reasonableness of vibration equation being used to solve wave equation." In 2011 International Conference on Electrical and Control Engineering (ICECE). IEEE, 2011. http://dx.doi.org/10.1109/iceceng.2011.6058296.

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Chen, George (Huangxing), Piet Van Dalen, Gerrit Van Nijen, Zhengjiang Wu, and Li Fu. "Using Fourier Analysis and Theoretical Equation to Predict Bearing Raceway Waviness." In Noise and Vibration Conference & Exhibition. SAE International, 2021. http://dx.doi.org/10.4271/2021-01-1036.

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Shaska, Kastriot. "Characteristics of the SAM Combined with WLF Equation." In SAE 2009 Noise and Vibration Conference and Exhibition. SAE International, 2009. http://dx.doi.org/10.4271/2009-01-2131.

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Guasch, Oriol, and Jie Deng. "The Lippmann–Schwinger equation and renormalization for transmission path analysis in discrete mechanical systems." In NOise and Vibration Emerging Methods. ASA, 2025. https://doi.org/10.1121/2.0002044.

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Hoskoti, Lokanna, Ajay Misra, and Mahesh Manchakattil Sucheendran. "Vortex Induced Vibration of a Rotating Blade." In ASME 2017 Gas Turbine India Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gtindia2017-4709.

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The vortex-induced vibration (VIV) of a rotating blade is studied in this paper. Euler-Bernoulli beam equation and the nonlinear oscillator satisfying Van der Pol equation are used to model the rotating blade and vortex shedding, respectively. While the fluctuating lift due to vortex shedding acts on the blade and the blade is coupled with fluid through a linear inertial coupling, resulting in a fluid-structure interaction problem. The coupled equations are discretized by using modes which satisfy the Eigenvalue problem. The work attempts to understand the instabilities associated with the fre
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Ramirez, Miguel, and Joaquin Collado. "Attenuation vibration by parametric excitation using the Meissner equation." In 2016 13th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE). IEEE, 2016. http://dx.doi.org/10.1109/iceee.2016.7751253.

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Ogbonnaya, Ezenwa A., Hyginus U. Ugwu, Kombo Theophilus-Johnson, Peter B. Forsman, and Charles U. Orji. "Optimizing Gas Turbine Bearing Vibration Using 2D D’Alembert’s Equation." In ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/gt2012-68213.

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The ability to identify faulty equipment under severe conditions allows the manufacturers and operators to take appropriate proactive measures to rectify the faults and provide an assessment for early detection of the engine defects that could lead to catastrophic failure. This work therefore shows that such counter measures can be carried out by optimization, modeling, simulation or using a reliable analysis of gas turbine engine, rotor shaft and bearing vibration data through 2-Dimensional D’Alembert’s equation. Gas turbine plants on industrial duty for electricity generation were thus used
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Reports on the topic "Vibration equation"

1

Murphy, Joseph F. Commentary on factors affecting transverse vibration using an idealized theoretical equation. U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, 2000. http://dx.doi.org/10.2737/fpl-rn-276.

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Murphy, Joseph F. Transverse vibrations of wood-based products : equations and considerations. U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, 2011. http://dx.doi.org/10.2737/fpl-rn-0324.

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Murphy, Joseph F. Transverse vibrations of wood-based products : equations and considerations. U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, 2011. http://dx.doi.org/10.2737/fpl-rn-324.

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Hayek, Sabih I., and Jeffrey E. Boisvert. Equations of Motion for Nonaxisymmetric Vibrations of Prolate Spheroidal Shells. Defense Technical Information Center, 2000. http://dx.doi.org/10.21236/ada377034.

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Litvinov, Vladislav L. FINDING A PRIVATE CLASS OF SOLUTIONS OF THE DIFFERENTIAL EQUATION DESCRIBING THE TRANSVERSE VIBRATIONS OF A ROPE WITH BENDING STIFFNESS AND LYING ON THE ELASTIC BASIS. Bulletin of Science and Technical Development, 2018. http://dx.doi.org/10.18411/vntr2018-125-3.

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