Simultaneous assignment of resonances and antiresonances in vibrating systems through inverse dynamic structural modification

Active control of linear vibrating systems for antiresonance assignment with regional pole placement

Vibration absorption is a core research area in the design and control of structures and machines, and exploiting antiresonances is an effective approach for systems under harmonic excitation. This paper proposes a comparative study and a review of the main passive techniques to antiresonance assignment proposed in the recent literature, by discussing them through some numerical examples too. The techniques discussed include the well-known Tuned Mass Damper, which has been widely developed in the literature. However, as the title reveals, great attention is paid to the methods inherited from the field of dynamic structural modification that assign antiresonances without modifying the number of degrees of freedom, by exploiting a proper modification of the system inertial and stiffness parameters. Due to higher mathematical complexity, these approaches have been less investigated in the literature although they are an effective and less invasive approach to antiresonance assignment, especially for machines. To puzzle out the complicated subject matter of antiresonances, their background and their key features are also discussed by reviewing the main theoretical results and their relationship with the assignment techniques. The paper is also enriched with several numerical examples to compare different methods and investigate the features of antiresonances. The concluding remarks of the paper bring together some open issues in this field of research and outlines some possible research directions.

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Beyond the Tuned Mass Damper: a Comparative Study of Passive Approaches to Vibration Absorption Through Antiresonance Assignment

Vibration absorption is a core research topic in structural dynamics and the mechanics of machines, and antiresonance assignment is an effective solution to such a problem in the presence of harmonic excitation forces Due to recent developments in the theory of feedback control systems, the use of active control approaches to antiresonance assignment has been recently gaining more attention in the literature Therefore, several methods exploiting state feedback or output feedback have been proposed in recent years These techniques that just rely on servo-controlled actuators are becoming an interesting alternative to active approaches that emulate the well-known Tuned Mass Damper in an active (or semi-active) framework This paper reviews and compares the most important approaches, with a greater focus on the methods exploiting the concept of control theory without adding new degrees of freedom in the system The theoretical results, with the underlying theory, are discussed to highlight the key features of each assignment techniques Several numerical examples where different techniques are applied and compared, also providing some analysis usually neglected in the literature, enrich the paper and demonstrate the key concepts

Active Approaches to Vibration Absorption through Antiresonance Assignment: A Comparative Study

This paper proposes a novel method for pole placement in linear vibrating systems through state feedback and rank-one control. Rather than assigning all the poles to the desired locations of the complex plane, the proposed method exactly assigns just the dominant poles, while the remaining ones are free to assume arbitrary positions within a pre-specified region in the complex plane. Therefore, the method can be referred to as “regional pole placement”. A two-stage approach is proposed to accomplish both the tasks. In the first stage, the subset of dominant poles is assigned to exact locations by exploiting the receptance method, formulated for either symmetric or asymmetric systems. Then, in the second stage, a first-order model formulated with a reduced state, together with the theory of Linear Matrix Inequalities, are exploited to cluster the subset of the unassigned poles into some stable regions of the complex plane while keeping unchanged the poles assigned in the first stage. The additional degrees of freedom in the choice of the gains, i.e., the non-uniqueness of the solution, is exploited through a semidefinite programming problem to reduce the control gains. The method is validated by means of four meaningful and challenging test-cases, also borrowed from the literature. The results are also compared with those of classic partial pole placement, to show the benefits and the effectiveness of the proposed approach.

https://www.mdpi.com/2076-3417/10/16/5494/pdf

Pole Assignment for Active Vibration Control of Linear Vibrating Systems through Linear Matrix Inequalities

\n This paper proposes an inverse structural modification method for the assignment of antiresonances in undamped vibrating systems by modifying the inertial and elastic properties of the existing degrees of freedom of the original system. Hence, no additional degrees of freedom are added to the system. The problem is formulated as an eigenstructure assignment approach since such a novel formulation is suitable for complex systems, such as those modeled through finite elements. Indeed, these systems are difficult to handle with the methods already proposed in the literature. Additionally, the proposed approach is suitable for both point and cross receptances. Assignment is cast as a constrained non-convex non-linear minimization problem and the proposed solving strategy is based on the homotopy optimization approach. The method effectiveness is shown through three meaningful test cases.

Iacopo Tamellin

Papers

Simultaneous assignment of resonances and antiresonances in vibrating systems through inverse dynamic structural modification

Active control of linear vibrating systems for antiresonance assignment with regional pole placement

Beyond the Tuned Mass Damper: a Comparative Study of Passive Approaches to Vibration Absorption Through Antiresonance Assignment

Active Approaches to Vibration Absorption through Antiresonance Assignment: A Comparative Study

Antiresonance Assignment in Point and Cross Receptances for Undamped Vibrating Systems