Christoph Adam

Flexural vibrations of elastic composite beams with interlayer slip

SummaryThe objective of the present paper is to analyze the dynamic flexural behavior of elastic two-layer beams with interlayer slip. The Bernoulli-Euler hypothesis is assumed to hold for each layer separately, and a linear constitutive equation between the horizontal slip and the interlaminar shear force is considered. The governing sixth-order initial-boundary value problem is solved by separating the dynamic response in a quasistatic and in a complementary dynamic response. The quasistatic portion that may also contain singularities or discontinuities due to sudden load changes is determined in a closed form. The remaining complementary dynamic part is non-singular and can be approximated by a truncated modal series of fast accelerated convergence. The solution of the resulting generalized decoupled single-degree-of-freedom oscillators is given by means of Duhamel,s convolution integral, whereby the velocity and acceleration of the loads are the driving terms. Light damping is considered via modal damping coefficients. The proposed procedure is illustrated for dynamically loaded layered single-span beams with interlayer slip, and the improvement in comparison to the classical modal analysis is demonstrated.

Dynamic analysis of inelastic primary–secondary systems

Abstract Two methods are proposed to compute the response of inelastic composite primary–secondary systems by a decomposition into undamped substructure modes. The first method is based on an iterative syntheses, where interface conditions as well as inelastic deformations of the substructures are treated as additional fictious loadings and their intensities are calculated in an iterative process. Alternatively, only modal coupling of tuned modes is considered, thus, restricting the application to coupled systems with a modal secondary to primary mass ratio much smaller than one. The dynamic behavior of oscillators attached to frames with various inelastic substructure properties is investigated, which are excited by the north–south component of the El Centro earthquake sample. Results derived by the proposed methods are compared to decoupled analyses to estimate their capability with respect to inelastic substructural behavior and non-classical damping.

Piezoelectric vibrations of composite beams with interlayer slip

SummaryActuating piezoelectric effects in two-layer beams with interlayer slip are described in detail, and special attention is given to the identification of the piezoelectric actuation as eigenstrains. It is demonstrated that piezoelectrically induced strains conveniently can be interpreted as eigenstrains acting in a background composite beam without piezoelectric actuators. The analogy between the piezoelectric effect and that of thermal strains is utilized in the present paper, where a layer-wise first-order flexural theory is applied to two-layer beams with various boundary conditions. The layers are assumed to be made of piezoelectric materials. Bernoulli-Euler hypothesis is assumed to hold for each layer separately, and a linear constitutive relation between the horizontal slip and the interlaminar shear force is considered. The governing sixth-order initial-boundary value problem is solved by separating the dynamic response in a quasistatic and in a complementary dynamic portion. The quasistatic solution that may also contain singularities or discontinuities due to sudden load changes is determinded in a closed form. The remaining complementary dynamic part is nonsingular and can be approximated by a truncated modal series of accelerated convergence. The proposed procedure is illustrated for piezoelectrically induced flexural deformations, where the forcing function is the piezoelectric curvature.

Thermally induced vibrations of composite beams with interlayer slip

Thermally excited vibrations of composite viscoelastic two-layer beams with interfacial slip are analyzed. Geometrically linearized conditions are considered, and the Bernoulli-Euler hypothesis is applied to each layer. At the interface a linear viscoelastic slip law is assigned. The resulting sixth-order initial boundary value problem of the deflection is solved in the time domain by separating the dynamic response in a quasistatic and a complementary dynamic portions. The quasistatic solution is determined in closed form, and the remaining complementary dynamic part is approximated by a truncated modal series that exhibits accelerated convergence. Numerical results are obtained for single-span composite beams with interlayer slip by means of a time-stepping procedure based on the linear interpolation of the driving terms within the time intervals.Thermally excited vibrations of composite viscoelastic two-layer beams with interfacial slip are analyzed. Geometrically linearized conditions are considered, and the Bernoulli-Euler hypothesis is applied to each layer. At the interface a linear viscoelastic slip law is assigned. The resulting sixth-order initial boundary value problem of the deflection is solved in the time domain by separating the dynamic response in a quasistatic and a complementary dynamic portions. The quasistatic solution is determined in closed form, and the remaining complementary dynamic part is approximated by a truncated modal series that exhibits accelerated convergence. Numerical results are obtained for single-span composite beams with interlayer slip by means of a time-stepping procedure based on the linear interpolation of the driving terms within the time intervals.

Dynamics of elastic-plastic shear frames with secondary structures : shake table and numerical studies

Results from experimental and numerical studies of earthquake-excited small-scale primary–secondary structures are presented. The primary structure considered is a plane three-storey shear frame with a fundamental frequency of 5.5 Hz. The columns of the first floor are built with soft aluminium and they are stressed beyond its linear range of behaviour. After each test the elastic–plastic columns are replaced by a new set of undeformed virgin aluminium bars. The elastic–plastic shear frame is tested with and without an attached secondary structure. The secondary structure is modelled as an elastic SDOF oscillator, and its natural frequency is tuned to the fundamental frequency of the shear frame. Alternatively, the oscillator is mounted on the horizontal beam of the second and third floor. The base excitation of the structural model is characterized by a broad band random process with constant spectral density in a frequency range between 3 and 30 Hz. In the numerical study, the digital recorded acceleration of the base excites the mechanical model of the investigated structures. Numerical outcomes assuming fictitious unlimited elastic material behaviour of the shear frame are set in contrast to results from experiments and computational simulations where the measured non-linear force displacement relation of the elastic–plastic floor is approximated by a piecewise linear curve. The effect of elastic–plastic materials on the dynamic interaction between primary and secondary structure is shown and the difference to unlimited elastic material behaviour is worked out in detail. Copyright

Seismic Performance of Tuned Mass Dampers

In a fundamental parametric study the seismic performance of Tuned Mass Dampers(TMDs) is investigated. Earthquake excited vibration-prone structures are modeled as elastic single-degree-of-freedom oscillators and they are equipped with a single TMD. The TMD performance is assessed by means of response reduction coefficients, which are generated from the ratio of the structural response with and without TMD attached. It is found that TMDs are effective in reducing the dynamic response of seismic excited structures with light structural damping. The results of the presented study are based on a set of 40 recorded ordinary ground motions

Forced flexural vibrations of elastic-plastic composite beams with thick layers

Abstract A theory for predicting the elastic-plastic dynamic response of symmetrically designed thick composite laminates is presented. Piecewise continuous and linear in-plane displacement fields through the layer thickness are assumed. Core and faces are perfectly bonded. By definition of an effective cross-sectional rotation the complex problem reduces to the simpler case of an equivalent homogeneous shear-deformable beam with effective stiffness, effective mass density and with corresponding boundary conditions. Inelastic defects of the material are equivalent to eigenstrains in an identical but elastic background structure of the homogenized beam with effective virgin stiffness. Mathematically, a multiple field approach of the elastic background results. Proper resultants of these eigenstrains are defined. Since the incremental response is linear within a given time step, solution methods of the linear theory of flexural vibrations can be applied both to the given external and the “updated” eigenstrain resultants. Modal expansion is performed on the complementary dynamic part of the solution that contains the inertia effects, whereas the quasistatic portion is determined separately and in closed form. Application for dynamically excited simply supported three-layered beams with different ratios of length to thickness demonstrate the validity, merit and range of applicability of the theory.

Influence of Collapse Definition and Near-Field Effects on Collapse Capacity Spectra

In the present article, the impact of both near fault ground motions and a finite ductility threshold on the collapse capacity is studied. Single-degree-of-freedom systems with non-deteriorating bilinear hysteretic behavior, vulnerable to P-delta effects, are considered. Defining collapse as excessive ductility is investigated, and the difference to collapse associated with instability is elaborated. Medians of individual record dependent collapse capacities are presented as function of the initial structural period for characteristic structural and ground motion parameters. Analytical expressions for influence coefficients, which account for a differing ground motion set, and finite ductility thresholds, respectively, are derived via non-linear regression analysis.

Efficiency of tuned mass dampers with uncertain parameters on the performance of structures under stochastic excitation

Abstract Tuned mass dampers serve the purpose of damping vibrations of structures such as earthquake-induced vibrations. In their design, two types of uncertainty are relevant: the stochastic excitation (e.g. earthquake record) and the inherent uncertainty of internal parameters of the devices themselves. This paper presents a new framework that admits the combination of stochastic processes and interval-type parameter uncertainty, modelled by random sets. The approach is applied to show how the efficiency of tuned mass dampers can be realistically assessed in the presence of uncertainty.

Moderately large flexural vibrations of composite plates with thick layers

Abstract In this paper moderately large amplitude vibrations of a polygonally shaped composite plate with thick layers are analyzed. Three homogeneous and isotropic layers with a common Poisson’s ratio are perfectly bonded and their arbitrary thickness and material properties are symmetrically disposed about the middle plane. Mindlin–Reissner kinematic assumptions are implemented layerwise, and as such model both the global and local response. Geometric nonlinear effects arising from longitudinally constrained supports are taken into account by Berger’s approximation of nonlinear strain–displacement relations. Overall cross-sectional rotations are defined and subsequently a correspondence of this complex problem to the simpler case of a homogenized shear-deformable nonlinear plate with effective stiffness and hard hinged boundary conditions is found. The nonlinear steady-state response of composite plates subjected to a time-harmonic lateral excitation is investigated and the phenomena of nonlinear resonance are studied and evaluated.