PARAMETER OPTIMIZATION OF TUNED MASS DAMPER FOR

MUlTIPLE DEGREE-OF-FREEDOM VIBRATION SYSTEMS

Nguyen Van Khang1

, Trieu Quoc Loc

2

, Nguyen Anh Tuan2

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 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].   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.

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. The method has a theoretical basis that is related to (1)

the solution of a set of nonlinear equations using Newton’s method,  and (2) the derivation of

simultaneous nonlinear equations using Kuhn–Tücker 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

hk(x) = 0, k = 1, 2, . . . , p.                             (1)

The Lagrange function, L(x, λ), for this problem is:

where λk  is the Lagrange multiplier for the equality constraint

k

h . The Kuhn–Tucker  necessary

conditions can be stated as