PARAMETER OPTIMIZATION OF TUNED MASS DAMPER FOR MUlTIPLE DEGREE-OF-FREEDOM VIBRATION SYSTEMS Nguyen Van Khang 1 , Trieu Quoc Loc 2 , Nguyen Anh Tuan 2 1 Hanoi University of Science and Technology 2 National Institute of Labour Protection Abstract. There are variety of problems in mechanical, structural and aerospace engineering that can be formulated as Nonlinear Programming. The quality of the developed solution significantly affect the performance of such systems.
In this paper, the problem of parameters optimization of tuned mass damper for multiple degree of freedom vibration systems using sequential quadratic programming method is investigated. The objective is to minimize the extreme vibration amplitude of vibration models. It is shown that the constrained formulation, that includes lower and upper bounds on the updating parameters in the form of inequality constraints, is important for obtaining a correct updated model.
I. INTRODUCTION Optimal design of multibody systems is characterized by a specific kind of optimization problem. Generally, an optimization problem is formulated to determine the design variable values that will minimize an objective function subject to constraints.
Additionally, for many engineering applications, multibody analysis routine are used to calculate the kinematic and dynamic behavior of the mechanical design. As a result, most objective function ... more. less.
and constraint values follow from the numerical analysis. Use of the tuned mass damper (TMD) as an independent means of vibration control is especially important, particularly as it is almost the only or the main means of vibration protection[1- 6].<br><br> A tuned mass damper, also known as an active mass damper (AMD) or harmonic absorber, is a device mounted in structures to reduce the amplitude of mechanical vibrations. Their application can prevent discomfort, damage, or outright structural failure. They are frequently used in power transmission, automobiles, machine and buildings.<br><br> This paper, we consider the problem of parameter optimization of tuned mass damper for multiple degree of freedom vibration systems using sequential quadratic programming method [7-12]. II. REVIEW OF SEQUENTIAL QUADRATIC PROGRAMMING METHOD The sequential quadratic programming, or called SQP, is an efficient and powerful algorithm to solve the nonlinear programming problems.<br><br> The method has a theoretical basis that is related to (1) the solution of a set of nonlinear equations using Newton 9s method, and (2) the derivation of simultaneous nonlinear equations using Kuhn 3Tücker conditions to the Lagrangian of the constrained optimization problem. In this section we review some basic concepts of the sequential quadratic programming (SQP) method [7-10] for understanding the parameter optimization of the TMD installed in vibration systems. Consider a nonlinear optimization problem with equality constraints: Find x which minimizes f ( x ) subject to h k ( x ) = 0, k = 1, 2, .<br><br> . . , p.<br><br> (1) The Lagrange function, L( x , » ), for this problem is: 1 ( , ) ( ) ( ) ( ) ( ) p T k k k L f h f \x4 x » x x x » h x (2) where » k is the Lagrange multiplier for the equality constraint k h . The Kuhn 3Tucker necessary conditions can be stated as 1 ( ) or ( ) ( ) p T x k k k L f h f \x2 \x3 \x2 \x2 \x2 \x4 0 x 0 x » h x 0 (3) L \x2 \x3 0 h k ( x ) = 0, k = 1, 2, . .<br><br> . , p or ( ) h x 0 (4)