Dynamic and Sensitivity Analysis General Non-Conservative Asymmetric Mechanical Systems

Abstract

In this paper the concept of generalized form of proportional damping is proposed. Classical modal analysis of non-conservative continua is extended to multi DOF linear dynamic systems with asymmetric matrices. Mode orthogonality relationships have been generalized to non-conservative systems. Several discretization methods of continua are presented. Finally, an expression for derivatives of eigenvalues and eigenvectors of non-conservative system is presented. Examples are provided to illustrate the proposed methods.

Eigenvalue sensitivity analysis based on the transfer matrix method

“…k , It can be shown that this procedure works in principle, however, it has several drawbacks: (i) it requires specially normalized eigenvectors and reordering of equations according to Equation ( 6 , ≙ a complete system of equations (8) has to be set up and solved; (iii) since the system transfer matrix U results from a multiplication of several element transfer matrices, the product rule will produce multiple product terms in the derivatives U ω , and U k , where identical matrix products are used several times. Thus, the procedure is computationally inefficient and not recommendable for complex models of technically relevant systems.…”

“…Also specific approaches are published, for example, by Fox and Kapoor 6 or Choi and Kim 7 for the generalized eigenproblem resulting from the ansatz for undamped mechanical systems described by equations of motion . Further, damped mechanical vibration systems have been studied, for example, by Zmindak 8 …”

“…Further, damped mechanical vibration systems have been studied, for example, by Zmindak. 8 A major feature of all these classical sensitivity studies is that the involved matrices A or M K , are independent of the eigenvalue, whereas the coefficient matrix in Equation ( 2) is a highly nonlinear function of ω. Therefore, classical approaches cannot be applied to the transfer matrix method, neither for finding the eigenfrequencies ω ω p = ( ) nor for computing their sensitivities ω p ∂ /∂ k .…”

Sensitive Analysis on Selection of Piston Material Using MADM Techniques

“…Sensitivity analysis is a methodology used to validate the stability of implemented MADM methods.it is also used to validate many mechanical applications in both static and dynamic analysis [30] this is the most important predominant factor to be determine, for applying these techniques practically. The main reason that lead to this analysis is the Variations in weighing criteria which effect the attribute rankings.…”

The Finite Element Analysis of High Precision Positioning System

“…The behaviour of mechanisms under loading was checked by the finite element method using linear elasticity theory. The numerical simulation was realized on high precision positioning system [6][7][8], the model of which is given in Fig. 1.…”