A one-dimensional (1D) analytic example for dynamic displacement tracking in linear viscoelastic solids is presented. Displacement tracking is achieved by actuation stresses that are produced by eigenstrains. Our 1D example deals with a viscoelastic half-space under the action of a suddenly applied tensile surface traction. The surface traction induces a uni-axial shock wave that travels into the half-space. Our tracking goal is to add to the applied surface traction a transient spatial distribution of actuation stresses such that the total displacement of the viscoelastic half-space coincides with the shock wave produced by the surface traction in a purely elastic half-space. We particularly consider a half-space made of a viscoelastic Maxwell-type material. Analytic solutions to this tracking problem are derived by means of the symbolic computer code MAPLE. The 1D solution presented below exemplifies a formal 3D solution derived earlier by the present authors for linear viscoelastic solids that are described by Boltzmann hereditary laws. In the latter formal solution, no reference was made to shock waves. Our present solution demonstrates its validity also in the presence of singular wave fronts. Moreover, in our example, we show that, as was also indicated in our earlier work, the actuation stress can be split into two parts, one of them producing no stresses, and the other no displacements in two properly enlarged problems.

It is highly important to determine eigenvalues before and after certain extreme events that may cause damage accumulation, such as earthquake, blasts and mining or seismic tests on research models. Unique experiment design and shake table testing was performed to investigate seismic performance of a 3D RC building model with infill walls and advanced protection with polyurethane-based joints and fiber polymer reinforced light and emergency jackets. For the purpose of wider experimental activities, three methods for determination of the dynamic characteristics were used during multiple successive shake table tests following a dynamic pushover approach, and they are presented in detail. They are: inertance function through impact hammer tests, standard Fourier transformation of measured acceleration time history and digital image correlation. The expected differences in the results are related to the type and intensity of excitation used, the involvement of materials with different mechanical and physical properties, and with the different rate and extent of damage accumulation, as well as to local or global measurements. Y et, all methods lead to reliable results when a consistent methodology is being used, that takes into account locality or globality of measurements, leaving a choice for the most suitable one, depending on the site conditions. The inertance function method presented manifested its high efficiency in analysis of dynamic properties of large-scale structures and in monitoring of their changes caused by the damage and repair process. It offers quite a wide range of useful information, does not require very expensive equipment and its transportation cost is negligible. This method seems to be a proper diagnostic tool for simple experimental modal analysis of real structures and their structural elements, where detection of changes in the structural condition and in dynamic properties is required, also as a non-destructive testing and monitoring method. Digital image correlation proved to be a promising non-contact tool, strongly supporting the conventional instrumentation of shake table testing, while the Fourier transformation was used as a benchmark method yielding the most reliable results.

The paper presents its contribution to tracking control design of mechanical systems in underactuated mode conditions, i.e. when the number of actuators is less than the number of possible control inputs. Fully actuated mechanical systems are quite well-researched and controller designs are well-developed for them as well. However, due to costs, weight, design, and performance regimes or due to an actuator failure, the underactuated control mode is required in applications. With the aid of the computational procedure for constrained dynamics (CoPCoD), the constrained dynamics, i.e. the reference motion dynamics, and tracking control in an underactuated mode are designed for an example of a three-link planar manipulator model with rigid and flexible links. A dynamic optimization problem is formulated in the paper to obtain optimal time courses of manipulator joint coordinates in underactuated mode conditions in order to apply them to a manipulator driving links controller.

This paper presents the experimental results of a new proof mass actuator for the implementation of velocity feedback control loops to reduce the flexural vibration of a thin plate structure. Classical proof mass actuators are formed by coil–magnet linear motors. These actuators can generate constant force at frequencies above the fundamental resonance frequency of the spring–magnet system, which can be used to efficiently implement point velocity feedback control loops. However, the dynamics of the spring–magnet system limit the stability and control performance of the loops when the actuators are exposed to shocks. The proof mass actuator investigated in this paper includes an additional flywheel element that improves the stability of the velocity feedback loop both by increasing the feedback gain margin and by reducing the fundamental resonance frequency of the actuator. This paper is focused on the stability and control performance of decentralized velocity feedback control loops.