Dynamic response of spinning tapered Timoshenko beams using modal reduction (original) (raw)
Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams
Shock and Vibration, 2005
Timoshenko beams have been widely used in structural and mechanical systems. Under dynamic loading, the analytical solution of a Timoshenko beam is often difficult to obtain due to the complexity involved in the equation of motion. In this paper, a modal perturbation method is introduced to approximately determine the dynamic characteristics of a Timoshenko beam. In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. Therefore, the solution process can be simplified significantly for the Timoshenko beam with arbitrary boundaries. Several examples are given to illustrate the application of the proposed method. Numerical results have shown that the modal perturbation method is effective in determining the modal characteristics of Timoshenko beams with high accuracy. The effects of shear distortion and moment of inertia on the natural frequencies of Timoshenko beams are...
Modal Analysis of the Dynamic Response of Timoshenko Beam under Moving Mass
Scientia Iranica
In this study, the dynamic response of a Timoshenko beam under moving mass is investigated. To this end, vectorial form orthogonality property of the Timoshenko beam free vibration modes is applied to the EEM (Eigenfunction Expansion Method). The implication of the vectorial form series and an appropriate inner product of mode shapes in combination are focused for a beam with arbitrary boundary conditions. Consequently, signi cant simpli cations and e cacy in the utilization of the EEM in eliminating the spatial domain is achieved. In order to comprise validation, the present study is compared with the DET (Discrete Element Technique) and the RKPM (Reproducing Kernel Particle Method).
Modal Analysis of Small Frames using High Order Timoshenko Beams
World Academy of Science, Engineering and Technology, International Journal of Mechanical and Mechatronics Engineering, 2015
In this paper, we consider the modal analysis of small frames. Firstly, we construct the 3D model using H8 elements and find the natural frequencies of the frame focusing our attention on the modes in the XY plane. Secondly, we construct the 2D model (plane stress model) using Q4 elements. We concluded that the results of both models are very close to each other’s. Then we formulate the stiffness matrix and the mass matrix of the 3-noded Timoshenko beam that is well suited for thick and short beams like in our case. Finally, we model the corners where the horizontal and vertical bar meet with a special matrix. The results of our new model (3-noded Timoshenko beam for the horizontal and vertical bars and a special element for the corners based on the Q4 elements) are very satisfying when performing the modal analysis.
Journal of the Korea Society for Industrial and Applied Mathematics, 2016
In this study, the dynamic behaviour of a rotating Timoshenko beam when under the actions of a variable magnitude load moving at non-uniform speed is carried out. The effect of cross-sectional dimension and damping on the flexural motions of the elastic beam was neglected. The coupled second order partial differential equations incorporating the effects of rotary and gyroscopic moment describing the motions of the beam was scrutinized in order to obtain the expression for the dynamic deflection and rotation of the vibrating system using an elegant technique called Galerkin's Method. Analyses of the solutions obtained were carried out and various results were displayed in plotted curve. It was found that the response amplitude of the simply supported beam increases with an increase in the value of the foundation reaction modulus. Effects of other vital structural parameters were also established.
Dynamic response of Timoshenko beam under moving mass
Scientia Iranica, 2012
In this study, the dynamic response of a Timoshenko beam under moving mass is investigated. To this end, vectorial form orthogonality property of the Timoshenko beam free vibration modes is applied to the EEM (Eigenfunction Expansion Method). The implication of the vectorial form series and an appropriate inner product of mode shapes in combination are focused for a beam with arbitrary boundary conditions. Consequently, signi cant simpli cations and e cacy in the utilization of the EEM in eliminating the spatial domain is achieved. In order to comprise validation, the present study is compared with the DET (Discrete Element Technique) and the RKPM (Reproducing Kernel Particle Method).
Experimental Modal Analysis of Rectangular and Circular Beams
Analytical and experimental methods are used to determine the natural frequencies and mode shapes of Aluminum 6061-T651 beams with rectangular and circular cross-sections. A unique test stand is developed to provide the rectangular beam with different boundary conditions including clamped-free, clampedclamped, clamped-pinned, and pinned-pinned. The first 10 bending natural frequencies and mode shapes for each set of boundary conditions are measured. The effect of the bolt torque on the measured natural frequencies is examined. A new technique is used to mount an accelerometer on the circular beam to measure its torsional modes; its first 20 natural frequencies and first 10 mode shapes are measured. The measured natural frequencies and mode shapes of both beams are compared with their theoretical predictions. The Timoshenko beam theory is shown to provide better predictions of the higher bending natural frequencies of the circular beam than the Bernoulli-Euler beam theory. The material properties of the circular beam, including the elastic modulus, shear modulus, and Poisson's ratio, are determined accurately. The use of the rectangular and circular beam test stands as a teaching tool for undergraduate and graduate students is discussed. The laboratory demonstration using the test stands was well received by students in the undergraduate vibrations class.
On damping effects in Timoshenko beams
In this paper, the dynamic response of a Timoshenko beam with distributed internal viscous damping (DIVD) is analyzed with the aim to ascertain their relative effects on the whole range of beam slenderness. With respect to some previous and quite recent works, some further and fundamental generalizations are therefore introduced. First, the decoupling of shear and bending damping mechanisms , with or without the presence of the external classical viscous contribution. This splitting allows the outlining of the relevant influences on the dynamic response associated to any singular damping mechanism and the evaluation of the modal critical damping. As a second contemporary step, an explicit dependency is set upon the shear slenderness of the beam model, allowing to study the dependence of each single damping mechanism upon the relevant kinematic model, spanning from truly Bernoulli's behavior to mainly Shear controlled responses. According to the selected damping model, the dynamic behavior automatically selects the characteristics of kinematical response (relative levels of shear and bending contributions) depending of the minimization of the total internal energy (i.e. elastic energy and dissipation). In the folds of this study, the problem of optimal piece-wise constant distribution of DIVD is finally also addressed, firstly showing that is possible to find non-trivial and interesting solutions.
IJERT-Modal Analysis of Beam Type Structures
International Journal of Engineering Research and Technology (IJERT), 2015
https://www.ijert.org/modal-analysis-of-beam-type-structures https://www.ijert.org/research/modal-analysis-of-beam-type-structures-IJERTV4IS040847.pdf The purpose of this project is to study Modal behaviour of Beam type structures. Beams under study include Cantilever, Simply Supported and Fixed beam. Mode shapes and natural frequencies of these three types of beams are obtained using Theoretical analysis, Simulation in ANSYS and Experiment using FFT analyser. Finally natural frequencies obtained from Simulation and Experiment are compared with Theoretical values of natural frequency. The mode shapes obtained from simulation and experiment are matching closely with analytical ones. Natural frequencies obtained by simulation are within 6% deviation when compared to theoretical results whereas for experimental natural frequencies the maximum deviation from theoretical values is 19.31%.