scholarly journals Nonlinear Forced Vibration Analysis of a Three Dimensional Tree Structure by the Incremental Transfer Stiffness Coefficient Method.

2001 ◽  
Vol 67 (660) ◽  
pp. 2442-2449
Author(s):  
Takumi SASAKI ◽  
Takahiro KONDOU ◽  
Takashi AYABE
Keyword(s):  
Forced Vibration ◽  
Vibration Analysis ◽  
Three Dimensional ◽  
Tree Structure ◽  
Stiffness Coefficient ◽  
Nonlinear Forced Vibration ◽  
Forced Vibration Analysis ◽  
Coefficient Method

Nonlinear forced vibration analysis of a rotating three-dimensional tapered cantilever beam

2020 ◽  
pp. 107754632094971 ◽  
Author(s):  
Yanxun Zhou ◽  
Yimin Zhang ◽  
Guo Yao
Keyword(s):  
Cantilever Beam ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Three Dimensional ◽  
Time History ◽  
Excitation Amplitude ◽  
Axial Deformation ◽  
Nonlinear Forced Vibration ◽  
Tapered Cantilever Beam ◽  
Forced Vibration Analysis

In this article, nonlinear forced vibration analysis is carried out for a rotating three-dimensional tapered cantilever beam subjected to a uniformly distributed load. Considering the effects of Coriolis terms, static axial deformation and geometric nonlinearity in modeling process, nonlinear partial motion equations of a rotating tapered Euler–Bernoulli beam are established by using Hamilton’s principle. Galerkin’s procedure is used to discretize the equations to obtain the dynamic response of the beam. Frequency responses, the time-history response, the phase diagram, and the Poincaré map are introduced to study the effects of the taper ratio, rotating velocity, radius of hub, and external excitation on the nonlinear resonances and detailed responses of the rotating three-dimensional tapered beam. Results show that the fundamental natural frequency increases with the increase of the taper ratio, radius of hub, and rotating velocity. Besides, by increasing the taper ratio and excitation amplitude and decreasing the rotating velocity and radius of hub, the nonlinearity and vibration amplitude of the rotating beam intensify.

Nonlinear Forced Vibration Analysis of FG-CNTRC Cylindrical Shells Under Thermal Loading Using a Numerical Strategy

2017 ◽  
Vol 09 (08) ◽  
pp. 1750108 ◽  
Author(s):  
Emad Hasrati ◽  
Reza Ansari ◽  
Jalal Torabi
Keyword(s):  
Frequency Response ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Cylindrical Shells ◽  
Continuation Method ◽  
Governing Equations ◽  
Nonlinear Forced Vibration ◽  
Forced Vibration Analysis ◽  
Numerical Strategy ◽  
Composite Cylindrical Shells

Employing an efficient numerical strategy, the nonlinear forced vibration analysis of composite cylindrical shells reinforced with single-walled carbon nanotubes (CNTs) is carried out. It is assumed that the distribution of CNTs along the thickness direction of the shell is uniform or functionally graded and the temperature dependency of the material properties is accounted. The governing equations are presented based on the first-order shear deformation theory along with von-Karman nonlinear strain-displacement relations. The vectorized form of energy functional is derived and directly discretized using numerical differential and integral operators. By the use of variational differential quadrature (VDQ) method, discretized nonlinear governing equations are obtained. Then, the time periodic differential operators are applied to perform the discretization procedure in time domain. Finally, the pseudo-arc length continuation method is employed to solve the nonlinear governing equations and trace the frequency response curve of the nanocomposite cylindrical shell. A comparison study is first presented to verify the efficiency and validity of the proposed numerical method. Comprehensive numerical results are then given to investigate the effects of the involved factors on the nonlinear forced vibration characteristics of the structure. The results show that the changes of fundamental vibrational mode shape have considerable effects on the frequency response curves of composite cylindrical shells reinforced with CNTs.

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