Nonlinear Vibration Analysis of Timoshenko Beams Using the Differential Quadrature Method

Keywords

Nonlinear system, Vibration, Amplitude, Bernoulli's principle, Quadrature (astronomy)

References

• Differential Quadrature and Its Application in EngineeringC. Shu — 2000
• Literature Review : Nonlinear Analysis of Beams Part I: A Survey of Recent AdvancesM. Sathyamoorthy — 1982
• DIFFERENTIAL QUADRATURE AND LONG-TERM INTEGRATIONRichard Bellman, John L. Casti — 1971
• The Study on the Nonlinear Computations of the DQ and DC MethodsWen Chen, Tingxiu Zhong — 1999
• Nonlinear vibrations of beams considering shear deformation and rotary inertiaG. Venkateswara Rao, I. S. Raju, K. Kanaka Raju — 1976
• The Effect of Rotatory Inertia and of Shear Deformation on the Frequency and Normal Mode Equations of Uniform Beams With Simple End ConditionsT. C. Huang — 1961
• Literature Review : A Review of Mechanical Face Seal DynamicsI. Etsion — 1982
• Application of the quadrature method to flexural vibration analysis of a geometrically nonlinear beamYusheng Feng, C. W. Bert — 1992
• DIFFERENTIAL QUADRATURE: A TECHNIQUE FOR THE RAPID SOLUTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONSRichard Bellman, B. G. Kashef, John L. Casti — 1972
• Literature Review : Nonlinear Analysis of Beams Part Ii: Finite Element MethodsM. Sathyamoorthy — 1982
• Large-amplitude free vibrations of beams—A discussion on various formulations and assumptionsGajbir Singh, Ankit Sharma, G. Venkateswara Rao — 1990
• Nonlinear vibrations of beams with various boundary conditions.D. A. Evensen — 1968
• Galerkin finite element method for non-linear beam vibrationsG.R. Bhashyam, Gangan Prathap — 1980
• ON THE DQ ANALYSIS OF GEOMETRICALLY NON-LINEAR VIBRATION OF IMMOVABLY SIMPLY-SUPPORTED BEAMSWen Chen, T. Zhong, Shuncai Liang — 1997
• APPLICATION OF GENERALIZED DIFFERENTIAL QUADRATURE TO SOLVE TWO-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONSC. Shu, B. E. Richards — 1992
• ON OPTIMAL SELECTION OF INTERIOR POINTS FOR APPLYING DISCRETIZED BOUNDARY CONDITIONS IN DQ VIBRATION ANALYSIS OF BEAMS AND PLATESC. Shu, Wei Chen — 1999
• Analysis of Vibrating Timoshenko Beams Using the Method of Differential QuadratureP.A.A. Laura, R.H. Gutiérrez — 1993
• On the Timoshenko theory of transverse beam vibrationsC. L. Dolph — 1954
• The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular platesWen Chen, C. Shu, Weiguang He — 1999
• Flexural Vibrations in Uniform Beams According to the Timoshenko TheoryRobert A. Anderson — 1953

Cited by

• Increasing the image quality of atomic force microscope by using improved double tapered micro cantileverAli Sadeghi — 2011
• Nonlinear analysis of nonprismatic Timoshenko beam for different geometric nonlinearity modelsPiotr Ruta, Józef Szybiński — 2015
• Nonlinear vibration of rectangular atomic force microscope cantilevers by considering the Hertzian contact theoryAli Sadeghi, Hassan Zohoor — 2010
• Differential quadrature large amplitude free vibration analysis of laminated skew plates based on FSDTP. Malekzadeh — 2008
• Application of the homotopy method for the analytic approach of the nonlinear free vibration analysis of the simple end beams using four engineering theoriesMohammad H. Kargarnovin, Ramazan‐Ali Jafari‐Talookolaei — 2010
• Regular and chaotic oscillations of a Timoshenko beam subjected to mechanical and thermal loadingsAnna Warmińska, Emil Manoach, Jerzy Warmiński — 2015
• Surface and nonlocal effects on the nonlinear free vibration of non-uniform nanobeamsP. Malekzadeh, M. Shojaee — 2013
• Free Vibration Analysis of a Microbeam Subjected to a Symmetric Electrostatic FieldYiming Fu, Jin Zhang — 2013
• Nonlinear vibration analysis of tapered Timoshenko beamsMinmao Liao, Hongzhi Zhong — 2008
• A differential quadrature nonlinear free vibration analysis of laminated composite skew thin platesP. Malekzadeh — 2007
• Nonlinear flutter of a two-dimension thin plate subjected to aerodynamic heating by differential quadrature methodDalin Chen, Yiren Yang, Chenguang Fan — 2008
• On an exact bending curvature model for nonlinear free vibration analysis shear deformable anisotropic laminated beamsZhi-Min Li, Pizhong Qiao — 2014
• A Semianalytical Method for Nonlinear Vibration of Euler-Bernoulli Beams with General Boundary ConditionsPeng Jian-she, Yan Liu, Jie Yang — 2010
• Nonlinear free vibration of embedded double-walled carbon nanotubes with layerwise boundary conditionsR. Ansari, R. Gholami, Mohammad Ali Darabi — 2012
• DQM large amplitude vibration of composite beams on nonlinear elastic foundations with restrained edgesP. Malekzadeh, A.R. Vosoughi — 2009
• Nonlinear dynamic analysis of Timoshenko beams by BEM. Part I: Theory and numerical implementationE.J. Sapountzakis, J.A. Dourakopoulos — 2009
• A fresh insight into the non-linear vibration of double-tapered atomic force microscope cantilevers by considering the Hertzian contact theoryAli Sadeghi, Hassan Zohoor — 2011
• The flexural vibration of V shaped atomic force microscope cantilevers by using the Timoshenko beam theoryAli Sadeghi — 2012
• Free Vibrations of Timoshenko Beam with Constant VolumeByoung Koo Lee, Tae-Eun Lee, Hee-Min Yoon — 2012
• Free Vibrations of Tapered Timoshenko Beam by using 4th Order Ordinary Differential EquationByoung Koo Lee, Park Kwang-Kyou, Tae‐Eun Lee — 2012

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