Antiresonance Assignment in Point and Cross Receptances for Undamped Vibrating Systems

Arch Computat Methods Eng

Tamellin

Trevisani

2021

Self Cite

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.

Section: Assignment Of the Antiresonance Frequenciesmentioning

confidence: 99%

Section: Assignment Of the Antiresonance Frequenciesmentioning

confidence: 99%

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

Arch Computat Methods Eng

Tamellin

Trevisani

2021

Self Cite

“…(29) exploits homotopy optimization and is here briefly described. The proposed technique takes advantage of two methods developed by the Authors of this paper for assigning eigenfrequencies and partial mode shapes [11] or antiresonances [23][24][25][26] in vibrating systems. Homotopy is an optimization technique for nonconvex functions that boosts the convergence to a global minimum by solving a sequence of optimization problems that starts with a convex relaxation of the original problem and then morphs it back to the original non-convex one through a path of solutions.…”

Section: Homotopy Optimizationmentioning

confidence: 99%

Response optimization of underactuated vibration generators through dynamic structural modification and shaping of the excitation forces

Belotti

Int J Adv Manuf Technol

Tamellin

et al. 2020

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Resonant vibration generators, such as vibratory feeders or ultrasonic sonotrodes, are often employed in manufacturing to generate harmonic vibrations with suitable amplitude, spatial shape, and frequency, in order to meet the process requirements. These underactuated systems are usually excited in open loop by few actuators, and therefore, it is not ensured that the desired response is correctly achieved, since the feasible motions should belong to the subset of the allowable motions. To achieve the closest approximation of the desired vibrations, some new solutions are here proposed. The first strategy is the optimal shaping of the harmonic forces exerted by the actuators, by solving an inverse dynamic problem through a coordinate transformation and the projection of the desired response onto the subspace of the allowable motion. By exploiting the formulation of such a subspace, a second approach that involves concurrently both the force shaping and the modification of the inertial and elastic system parameters is proposed. The idea of this approach is to exploit the modification of the elastic and inertial parameters to properly shape the allowable subspace in such a way that it spans the desired response. A solution method is developed, and analytical sensitivity analysis is proposed to choose the design variables. Validation is proposed through a linear vibratory feeder with a long flexible tray, taken from the literature. The results show the effectiveness of the proposed strategies that lead to a very precise approximation of the desired response.

“…A less investigated field is the assignment of antiresonances (see e.g. Belotti et al 2020;Richiedei et al 2019) or antiresonances together with natural frequencies (Richiedei et al 2020). Natural frequencies and damping, i.e.…”

Section: Performance Optimization Through Concurrent Mechanical and Cmentioning

confidence: 99%

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

Belotti

Trevisani

2020

Struct Multidisc Optim

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The paper proposes a multi-domain approach to the optimization of the dynamic response of an underactuated vibrating linear system through eigenstructure assignment, by exploiting the concurrent design of the mechanical properties, the regulator and state observers. The approach relies on handling simultaneously mechanical design and controller synthesis in order to enlarge the set of the achievable performances. The underlying novel idea is that structural properties of controlled mechanical systems should be designed considering the presence of the controller through a concurrent approach: this can considerably improve the optimization possibilities. The method is, first, developed theoretically. Starting from the definition of the set of feasible system responses, defined through the feasible mode shapes, an original formulation of the optimality criterion is proposed to properly shape the allowable subspace through the optimal modification of the design variables. A proper choice of the modifications of the elastic and inertial parameters, indeed, changes the space of the allowable eigenvectors that can be achieved through active control and allows obtaining the desired performances. The problem is then solved through a rank-minimization with constraints on the design variables: a convex optimization problem is formulated through the “semidefinite embedding lemma” and the “trace heuristics”. Finally, experimental validation is provided through the assignment of a mode shape and of the related eigenfrequency to a cantilever beam controlled by a piezoelectric actuator, in order to obtain a region of the beam with negligible oscillations and the other one with large oscillations. The results prove the effectiveness of the proposed approach that outperforms active control and mechanical design when used alone.