The iterative solution of flexural vibration problems based on the Myklestad method

1962 ◽  
Vol 4 (3) ◽  
pp. 241-251 ◽  
Author(s):  
S. Mahalingam
Keyword(s):  
Flexural Vibration ◽  
Iterative Solution ◽  
Vibration Problems

Numerical Solution of Some Three-State Random Vibration Problems

1995 ◽  
Author(s):  
S. F. Wojtkiewicz ◽  
L. A. Bergman ◽  
B. F. Spencer
Keyword(s):  
Finite Element ◽  
Random Vibration ◽  
Gaussian White Noise ◽  
Three Dimensional ◽  
Planck Equation ◽  
Iterative Solution ◽  
Response Characteristics ◽  
Solution Strategies ◽  
Gaussian White Noise Process ◽  
Vibration Problems

Abstract This paper reports some of the recent efforts by the authors to examine the random vibration of mechanical systems of large dimension. A finite element solution method for the stationary three-dimensional Fokker-Planck equation, employing sparse storage and iterative solution strategies, is outlined and then applied to several representative systems. The first of these is a linear oscillator subjected to a first order linearly filtered Gaussian white noise process. This problem is used to verify and assess the accuracy of the method. After verification, two Duffing systems are analyzed, one exhibiting unimodal and the other bimodal response characteristics. Finally, some comparisons of the finite element results with those from Monte Carlo simulation are made for the two nonlinear systems.

Receptance Methods in the Iterative Solution of Torsional Vibration Problems

1966 ◽  
Vol 70 (670) ◽  
pp. 953-955 ◽  
Author(s):  
S. Mahalingam
Keyword(s):  
Natural Frequency ◽  
Torsional Vibration ◽  
Iterative Solution ◽  
Transfer Matrices ◽  
Lumped Parameter ◽  
Vibration Problems ◽  
True Frequency

The Holzer method is widely used in the solution of the modes and frequencies of lumped parameter torsional systems. Basically the method consists of assuming an approximate value of the required frequency and, starting from one end of the system, determining the amplitudes of vibration station by station. Since the assumed frequency is an approximate one there will be a residual (torque or displacement) at the last station. The true frequency to be determined is that for which the residual is zero. Among the special advantages of the method are that any natural frequency may be obtained directly without a knowledge of the lower modes and, with the use of transfer matrices, the method may be readily adapted for the solution of complex vibration problems using a computer.

The Wave Method for Solving Flexural Vibration Problems

1954 ◽  
Vol 21 (1) ◽  
pp. 75-80
Author(s):  
R. P. N. Jones
Keyword(s):  
Normal Mode ◽  
Flexural Vibration ◽  
Initial Response ◽  
Time Base ◽  
Subsequent Response ◽  
Mode Solution ◽  
Vibration Problems ◽  
Wave Methods ◽  
Theoretical Results ◽  
Good Agreement

Abstract In this paper the use of normal mode and wave methods in problems of dynamic loading on beams is discussed, and the methods are applied to simple problems of uniform beams under a suddenly applied load. For these problems, mathematically exact results have been obtained, enabling a comparison to be made between the two types of solution. Experimental results for these problems also have been obtained, using an apparatus which releases the beam from a deflected position, and displays a record of the resultant response on an oscillograph screen, using a time base synchronized with the release of the beam. Good agreement is obtained between the experimental and theoretical results, and it is shown that the wave solution is useful for determining the initial response of the beam, while the subsequent response can be better obtained from the normal-mode solution.

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