Exact dynamic stiffness matrix of a three-dimensional shear beam with doubly asymmetric cross-section

2006 ◽  
Vol 289 (4-5) ◽  
pp. 938-951 ◽  
Author(s):  
B. Rafezy ◽  
W.P. Howson
Keyword(s):  
Cross Section ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Three Dimensional ◽  
Dynamic Stiffness Matrix ◽  
Shear Beam

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.

Simple Modeling and Analysis for Crankshaft Three-Dimensional Vibrations, Part 2: Application to an Operating Engine Crankshaft

1995 ◽  
Vol 117 (1) ◽  
pp. 80-86 ◽  
Author(s):  
T. Morita ◽  
H. Okamura
Keyword(s):  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Inertia Force ◽  
Connecting Rod ◽  
Automobile Engine ◽  
Dynamic Stiffness Matrix ◽  
Modeling And Analysis ◽  
Engine Crankshaft

The modeling and analysis procedures with the dynamic stiffness matrix method described in Part 1 were applied to a crankshaft system, consisting of crankshaft, front pulley, flywheel, piston, and connecting rod, under firing conditions. For firing conditions, (7) one half of the reciprocating masses consisting of the piston, piston pin, and connecting rod small end, and (2) rotating masses of the connecting rod big end mass, were attached to the two ends of the crankpin, taking account of the rigidity of the connecting rod. The excitation forces were calculated from the gas force and the inertia force due to the reciprocating masses. By solving the equations of motion derived in the form of the dynamic stiffness matrix, we calculated the three-dimensional steady-state vibrations of the crankshaft system under firing conditions. A crankshaft system for a four-cylinder in-line automobile engine was used for the analysis. We calculated the influence of the mass and moments of inertia of the front pulley on the behavior of the crankshaft vibrations and the excitation induced at the crankjournal bearings. Calculated values were compared with experimental results.

Simple Modeling and Analysis for Crankshaft Three-Dimensional Vibrations, Part 1: Background and Application to Free Vibrations

1995 ◽  
Vol 117 (1) ◽  
pp. 70-79 ◽  
Author(s):  
H. Okamura ◽  
A. Shinno ◽  
T. Yamanaka ◽  
A. Suzuki ◽  
K. Sogabe
Keyword(s):  
Stiffness Matrix ◽  
Rectangular Cross Section ◽  
Dynamic Stiffness ◽  
Three Dimensional ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Dynamic Stiffness Matrix ◽  
Modeling And Analysis ◽  
Coupling Behavior ◽  
Film Stiffness

To simplify the analysis of the three-dimensional vibrations of automobile engine crankshafts under firing conditions, the crankshaft was idealized by a set of jointed structures consisting of simple round rods and simple beam blocks of rectangular cross-section. The front pulley, timing gear, and the fly-wheel were idealized by a set of masses and moments of inertia. The main journal bearings were idealized by a set of linear springs and dash-pots. For each constituent member, the dynamic stiffness matrix was derived (in closed form) from the transfer matrix. Then the dynamic stiffness matrix for the total crankshaft system was constructed, and the natural frequencies and mode shapes were calculated. The modeling and analysis procedures were applied to the analysis of free vibrations of four kinds of crankshafts: single cylinder, three-cylinder in-line, four-cylinder in-line, and V-six engines. The different coupling behavior of the three-dimensional vibrations in the planar-structure and the solid-structure crankshaft is discussed, and the influence of the bearing oil film stiffness on the crankshaft natural frequency is also analyzed.

scholarly journals Dynamic Stiffness Matrix for a Beam Element with Shear Deformation

1995 ◽  
Vol 2 (2) ◽  
pp. 155-162 ◽  
Author(s):  
Walter D. Pilkey ◽  
Levent Kitiş
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Beam Element ◽  
Stiffness Matrices ◽  
Principal Axes ◽  
Shear Beam ◽  
Shaped Cross Section

A method for calculating the dynamic transfer and stiffness matrices for a straight Timoshenko shear beam is presented. The method is applicable to beams with arbitrarily shaped cross sections and places no restrictions on the orientation of the element coordinate system axes in the plane of the cross section. These new matrices are needed because, for a Timoshenko beam with an arbitrarily shaped cross section, deflections due to shear in the two perpendicular planes are coupled even when the coordinate axes are chosen to be parallel to the principal axes of inertia.

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