Calculation of natural frequencies of beam structures including concentrated mass effects by the dynamic stiffness matrix method

2001 ◽  
Vol 34 (2) ◽  
pp. 71-75
Author(s):  
R. Aït-Djaoud ◽  
I. Djeran-Maigre ◽  
R. Cabrillac
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Concentrated Mass ◽  
Beam Structures ◽  
Dynamic Stiffness Matrix ◽  
Mass Effects

Vibration Modeling of Machine Tool Spindles: A Calibrated Dynamic Stiffness Matrix Method

2013 ◽  
Vol 651 ◽  
pp. 710-716 ◽  
Author(s):  
Omar Gaber ◽  
Seyed M. Hashemi
Keyword(s):  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Dynamic Stiffness Matrix ◽  
Spring Element ◽  
Linear Spring ◽  
Beam Bending ◽  
The Stability ◽  
Spinning Speed ◽  
Vibration Modeling

The effects of spindles vibrational behavior on the stability lobes and the Chatter behavior of machine tools have been established. The service life has been observed to reducethe system natural frequencies. An analytical model of a multi-segment spinning spindle, based on the Dynamic Stiffness Matrix (DSM) formulation, exact within the limits of the Euler-Bernoulli beam bending theory, is developed. The system exhibits coupled Bending-Bending (B-B) vibration and its natural frequencies are found to decrease with increasing spinning speed. The bearings were included in the model usingboth rigid, simply supported, frictionless pins and flexible linear spring elements. The linear spring element stiffness is then calibrated so that the fundamental frequency of the system matches the nominal value.

scholarly journals Vibration analysis of cable-driven parallel robots based on the dynamic stiffness matrix method

2017 ◽  
Vol 394 ◽  
pp. 527-544 ◽  
Author(s):  
Han Yuan ◽  
Eric Courteille ◽  
Marc Gouttefarde ◽  
Pierre-Elie Hervé
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Dynamic Stiffness ◽  
Parallel Robots ◽  
Dynamic Stiffness Matrix

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.

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.

Natural Frequencies of Rotating Bladed Disks Using Clamped-Free Blade Modes

1983 ◽  
Vol 105 (4) ◽  
pp. 416-424
Author(s):  
S. J. Wildheim
Keyword(s):  
Periodic Structure ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Calculation Procedure ◽  
Dynamic Stiffness Matrix ◽  
Bladed Disk ◽  
Count Method ◽  
Dynamic Substructuring ◽  
Bladed Disk Assembly

The problem of calculating the natural frequencies of a practical rotating bladed disk assembly is solved by use of a new dynamic substructuring method employing the free modes of the disk and the clamped-free modes of the blade. The bladed disk may have lacing-wires at any radius. The lacing-wire, or any other general elastic connection element, is assumed to extend around the whole circumference. Hence, the assembly fulfills the requirements for a circumferentially periodic structure. Centrifugal effects are included. The free modes of the disk are used to describe the dynamics of the disk by a 4 × 4 receptance matrix. The row of blades is described by a dynamic stiffness matrix of order 4 + 10l, where l is the number of lacing-wires. The dynamic stiffness matrix of the blading is formed directly from the modes of one single clamped-free blade without any lacing-wire. The lacing-wires are treated as elastic and massless. The zeroes of the resulting transcendental frequency determinant of order 4 + 10l are solved by the sign-count method. The calculation procedure has proved to be very efficient. Further, it enjoys the precious property of being automatic and infallible in the sense that there is no risk of missing any frequency whatever the spacing of natural frequencies. Experimentally found frequencies are compared to calculated ones.

Sign in / Sign up

Export Citation Format

Share Document