Design method of tuned mass damper by LMI based robust control theory for seismic excitation

This paper presents a new design method based on a robust-control strategy in the form of a linear matrix inequality (LMI) approach for a passive tuned mass damper (TMD), which is one of the common passive-control devices for structural vibration control. To apply the robust control theory, we first present an equivalent expression that describes a passive TMD as an active TMD. Then, some LMI-based condition is derived that not only guarantees robust stability but also allows us to adjust the robust H¥ performance. In particular, this paper considers the transfer function from a seismic-wave input to structural responses. Unlike other methods, this method formulates the problem to be a convex optimization problem that ensures a global optimal solution and considers uncertainties of mass, damping, and stiffness of a structure for designing a TMD. Numerical example uses both a single-degree-of-freedom (SDOF) and 10DOF models, and seismic waves. The simulation results demonstrated that the TMD that is designed by the presented method has good control performance even if the structural model includes uncertainties, which are the modeling errors.

A Circular Eccentric Vibration Absorber with Circumferentially Graded Acoustic Black Hole Features

A previously proposed planar axisymmetric dynamic vibration absorber (DVA), with embedded acoustic black hole (ABH) features, has been shown to suffer from the very selective coupling with the host structure, thus compromising its vibration reduction performance. To tackle the problem, an eccentric ABH-based circular DVA whose thickness profile is tailored according to a circumferential gradient variation is proposed in this paper. This new configuration preserves the ABH profile in the radial direction alongside a continuous variation along the circumferential direction and breaks the axisymmetry of the original DVA design at the same time. While the former permits the ABH features to fully play out in a continuous manner, the later entails a more effective coupling with the host structure. These salient properties have been demonstrated and confirmed both numerically and experimentally by examining a benchmark plate structure. For analyses, a coupling model embracing the host structure and the add-on DVAs is established which allows the calculation of the coupling coefficient, a vital quantity to guide the DVA design. Studies demonstrate the advantages of the proposed DVA over existing designs for the same given mass. The enriched structural coupling and the enhanced modal damping, arising from the eccentric and circumferentially graded ABH design, are shown to be the origin of such improvement. All in all, the physical process underpinning the dynamic absorber principle and waveguide absorber from the host structures is simultaneously consolidated, thus leading to superior broadband structural vibration suppression.

OPTIMAL PIEZOELECTRIC SHUNT DAMPER USING ENHANCED SYNTHETIC INDUCTOR: SIMULATION AND EXPERIMENTAL VALIDATION

Piezoelectric material has the ability to convert mechanical energy to electrical energy and vice versa, making it suitable for use as an actuator and sensor. When used as a controller in sensor mode, the piezoelectric transducer is connected to an external electrical circuit where the converted electrical energy will be dissipated through Joule heat; also known as piezoelectric shunt damper (PSD). In this work, a PSD is used to dampen the first resonance of a cantilever beam by connecting its terminal to an RL shunt circuit configured in series. The optimal resistance and inductance values for maximum energy dissipation are determined by matching the parameters to the first resonant frequency of the cantilever beam, where R = 78.28 k? and L = 2.9 kH are found to be the optimal values. To realize the large inductance value, a synthetic inductor is utilized and here, the design is enhanced by introducing a polarized capacitor to avoid impedance mismatch. The mathematical modelling of a cantilever beam attached with a PSD is derived and simulated where 70% vibration reduction is seen in COMSOL. From experimental study, the vibration reduction obtained when using the piezoelectric shunt circuit with enhanced synthetic inductor is found to be 67.4% at 15.2 Hz. Results from this study can be used to improve PSD design for structural vibration control at targeted resonance with obvious peaks. ABSTRAK: Material piezoelektrik mempunyai keupayaan mengubah tenaga mekanikal kepada tenaga elektrik dan sebaliknya, di mana ia sesuai digunakan sebagai penggerak dan pengesan. Apabila digunakan sebagai alat kawalan dalam mod pengesan, piezoelektrik disambung kepada litar elektrik luaran di mana tenaga elektrik yang ditukarkan akan dibebaskan sebagai haba Joule; turut dikenali sebagai peredam alihan piezoelektrik (PSD). Kajian ini menggunakan PSD sebagai peredam resonan pertama pada palang kantilever dengan menyambungkan terminal kepada litar peredam RL bersiri. Rintangan optimal dan nilai aruhan bagi tenaga maksimum yang dibebaskan terhasil dengan membuat padanan parameter pada frekuensi resonan pertama palang kantilever, di mana R = 78.28 k? dan L = 2.9 kH adalah nilai optimum. Bagi merealisasikan nilai aruhan besar, peraruh buatan telah digunakan dan di sini, rekaan ini ditambah baik dengan memperkenalkan peraruh polaris bagi mengelak ketidakpadanan impedans. Model matematik palang kantilever yang bersambung pada PSD telah diterbit dan disimulasi, di mana 70% getaran berkurang pada COMSOL. Hasil dapatan eksperimen ini menunjukkan pengurangan getaran yang terhasil menggunakan litar peredam piezoelektrik bersama peraruh buatan menghasilkan 67.4% pada 15.2 Hz. Hasil dapatan kajian ini dapat digunakan bagi membaiki rekaan PSD berstruktur kawalan getaran iaitu pada resonan tumpuan di puncak ketara.