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.

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.

Dynamic Stiffness Analysis of a Beam Based on Trigonometric Shear Deformation Theory

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Jun Li ◽  
Hongxing Hua ◽  
Rongying Shen
Keyword(s):  
Shear Deformation ◽  
Stiffness Matrix ◽  
Deformation Theory ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Beam Element ◽  
Mode Shapes ◽  
Dynamic Stiffness Matrix ◽  
Stiffness Analysis

The dynamic stiffness matrix of a uniform isotropic beam element based on trigonometric shear deformation theory is developed in this paper. The theoretical expressions for the dynamic stiffness matrix elements are found directly, in an exact sense, by solving the governing differential equations of motion that describe the deformations of the beam element according to the trigonometric shear deformation theory, which include the sinusoidal variation of the axial displacement over the cross section of the beam. The application of the dynamic stiffness matrix to calculate the natural frequencies and normal mode shapes of two rectangular beams is discussed. The numerical results obtained are compared to the available solutions wherever possible and validate the accuracy and efficiency of the present approach.

EXACT VIBRATION FREQUENCIES AND MODES OF BEAMS WITH INTERNAL RELEASES

2002 ◽  
Vol 02 (01) ◽  
pp. 63-75 ◽  
Author(s):  
M. EISENBERGER
Keyword(s):  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Beam Element ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Dynamic Stiffness Matrix ◽  
Continuous Beams ◽  
Stiffness Method ◽  
Dynamic Stiffness Method

The exact vibration frequencies of continuous beams with internal releases are found using the dynamic stiffness method. Two types of releases are considered: hinge and sliding discontinuities. First, the exact dynamic stiffness matrix for a beam element with a release is derived and then used in the assembly of the structure dynamic stiffness matrix. The natural frequencies are found as the values of frequency that make this matrix singular. Then the mode shapes are found exactly. Examples are given for continuous beams with different releases.

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

2021 ◽  
pp. 146442072098817
Author(s):  
Md. Imran Ali ◽  
Mohammad Sikandar Azam
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Stiffness Matrix ◽  
Natural Vibration ◽  
Dynamic Stiffness ◽  
Functionally Graded ◽  
Neutral Surface ◽  
Functionally Graded Plate ◽  
Dynamic Stiffness Matrix ◽  
Graded Material

This paper presents the formulation of dynamic stiffness matrix for the natural vibration analysis of porous power-law functionally graded Levy-type plate. In the process of formulating the dynamic stiffness matrix, Kirchhoff-Love plate theory in tandem with the notion of neutral surface has been taken on board. The developed dynamic stiffness matrix, a transcendental function of frequency, has been solved through the Wittrick–Williams algorithm. Hamilton’s principle is used to obtain the equation of motion and associated natural boundary conditions of porous power-law functionally graded plate. The variation across the thickness of the functionally graded plate’s material properties follows the power-law function. During the fabrication process, the microvoids and pores develop in functionally graded material plates. Three types of porosity distributions are considered in this article: even, uneven, and logarithmic. The eigenvalues computed by the dynamic stiffness matrix using Wittrick–Williams algorithm for isotropic, power-law functionally graded, and porous power-law functionally graded plate are juxtaposed with previously referred results, and good agreement is found. The significance of various parameters of plate vis-à-vis aspect ratio ( L/b), boundary conditions, volume fraction index ( p), porosity parameter ( e), and porosity distribution on the eigenvalues of the porous power-law functionally graded plate is examined. The effect of material density ratio and Young’s modulus ratio on the natural vibration of porous power-law functionally graded plate is also explained in this article. The results also prove that the method provided in the present work is highly accurate and computationally efficient and could be confidently used as a reference for further study of porous functionally graded material plate.

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

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