Dynamic stiffness matrix for free vibration analysis of flexure hinges based on non-uniform Timoshenko beam

2018 ◽  
Vol 437 ◽  
pp. 40-52 ◽  
Author(s):  
Mingxiang Ling ◽  
Shenglai Chen ◽  
Qisheng Li ◽  
Guangming Tian
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Vibration Analysis ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Dynamic Stiffness Matrix ◽  
Flexure Hinges

COUPLED FREE VIBRATION ANALYSIS OF SHEAR-FLEXIBLE LAMINATED COMPOSITE I-BEAMS

2013 ◽  
Vol 21 (01) ◽  
pp. 1250024
Author(s):  
NAM-IL KIM
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Stiffness Matrix ◽  
Vibration Analysis ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Dynamic Stiffness Matrix ◽  
Analytical Technique

The coupled free vibration analysis of the thin-walled laminated composite I-beams with bisymmetric and monosymmetric cross sections considering shear effects is developed. The laminated composite beam takes into account the transverse shear and the restrained warping induced shear deformation based on the first-order shear deformation beam theory. The analytical technique is used to derive the constitutive equations and the equations of motion of the beam in a systematic manner considering all deformations and their mutual couplings. The explicit expressions for displacement parameters are presented by applying the power series expansions of displacement components to simultaneous ordinary differential equations. Finally, the dynamic stiffness matrix is determined using the force–displacement relationships. In addition, for comparison, a finite beam element with two-nodes and fourteen-degrees-of-freedom is presented to solve the equations of motion. The performance of the dynamic stiffness matrix developed by study is tested through the solutions of numerical examples and the obtained results are compared with results available in literature and the detailed three-dimensional analysis results using the shell elements of ABAQUS. The vibrational behavior and the effect of shear deformation are investigated with respect to the modulus ratios and the fiber angle change.

scholarly journals Out-of-plane free vibration analysis of three-layer sandwich beams using dynamic stiffness matrix

2021 ◽  
Vol 60 (6) ◽  
pp. 4981-4993
Author(s):  
Mohammad Gholami ◽  
Ali Alibazi ◽  
Reza Moradifard ◽  
Samira Deylaghian
Keyword(s):  
Free Vibration ◽  
Stiffness Matrix ◽  
Vibration Analysis ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Sandwich Beams ◽  
Dynamic Stiffness Matrix ◽  
Out Of Plane

Free Vibration of Helicoidal Beams of Arbitrary Shape and Variable Cross Section

2002 ◽  
Vol 124 (3) ◽  
pp. 397-409 ◽  
Author(s):  
Wisam Busool ◽  
Moshe Eisenberger
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Rotational Inertia ◽  
Variable Cross ◽  
Dynamic Stiffness Matrix ◽  
Helical Springs

In this study, the dynamic stiffness method is employed for the free vibration analysis of helical springs. This work gives the exact solutions for the natural frequencies of helical beams having arbitrary shapes, such as conical, hyperboloidal, and barrel. Both the cross-section dimensions and the shape of the beam can vary along the axis of the curved member as polynomial expressions. The problem is described by six differential equations. These are second order equations with variable coefficients, with six unknown displacements, three translations, and three rotations at every point along the member. The proposed solution is based on a new finite-element method for deriving the exact dynamic stiffness matrix for the member, including the effects of the axial and the shear deformations and the rotational inertia effects for any desired precision. The natural frequencies are found as the frequencies that cause the determinant of the dynamic stiffness matrix to become zero. Then the mode shape for every natural frequency is found. Examples are given for beams and helical springs with different shape, which can vary along the axis of the member. It is shown that the present numerical results agree well with previously published numerical and experimental results.

scholarly journals Finite Element Formulation for Stability and Free Vibration Analysis of Timoshenko Beam

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Abbas Moallemi-Oreh ◽  
Mohammad Karkon
Keyword(s):  
Free Vibration ◽  
Shear Strain ◽  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Vibration Analysis ◽  
Mass Matrix ◽  
Free Vibration Analysis ◽  
Element Formulation ◽  
The Stability ◽  
Interpolation Functions

A two-node element is suggested for analyzing the stability and free vibration of Timoshenko beam. Cubic displacement polynomial and quadratic rotational fields are selected for this element. Moreover, it is assumed that shear strain of the element has the constant value. Interpolation functions for displacement field and beam rotation are exactly calculated by employing total beam energy and its stationing to shear strain. By exploiting these interpolation functions, beam elements' stiffness matrix is also examined. Furthermore, geometric stiffness matrix and mass matrix of the proposed element are calculated by writing governing equation on stability and beam free vibration. At last, accuracy and efficiency of proposed element are evaluated through numerical tests. These tests show high accuracy of the element in analyzing beam stability and finding its critical load and free vibration analysis.

Dynamic Stiffness Matrix Method for the Free Vibration Analysis of Rotating Uniform Shear Beams

2009 ◽  
Author(s):  
Dominic R. Jackson ◽  
S. Olutunde Oyadiji
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Power Series Solution ◽  
Dynamic Stiffness Matrix ◽  
Uniform Shear ◽  
Natural Boundary Conditions

The Dynamic Stiffness Method (DSM) is used to analyse the free vibration characteristics of a rotating uniform Shear beam. Starting from the kinetic and strain energy expressions, the Hamilton’s principle is used to obtain the governing differential equations of motion and the natural boundary conditions. The two equations are solved simultaneously and expressed each in terms of displacement and slope only. The Frobenius power series solution is applied to solve the equations and the resulting solutions are also expressed in terms of four independent solutions. Applying the appropriate boundary conditions, the Dynamic Stiffness Matrix is assembled. The natural frequencies of vibration using the DSM are computed by employing the in-built root finding algorithm in Mathematica as well as by implementing the Wittrick-Williams algorithm in a numerical routine in Mathematica. The results obtained using the DSM are presented in tabular and graphical forms and are compared with results obtained using the Timoshenko and the Bernoulli-Euler theories.

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