Iradj G. Tadjbakhsh

Active flexible rods with embedded SMA fibers

Embedding of shape memory alloy (SMA) fibers in slender flexible bodies results in shape changes of the host medium, whenever shape recovery of the SMA fibers takes place. The shape change of a cylindrical rod with a single off-axis embedded SMA fiber is modeled. The distributed axial compressive force and bending moment due to phase transformation in the SMA fiber is evaluated using an approximate analytical model and the deformed shape of the flexible rod is found by solving the equations of equilibrium of the rod. The stability analysis for the linearized theory is carried out and the critical value of the phase transformation induced strain for buckling is evaluated.

Performance analysis of aseismic base isolation systems for a multi-story building

Abstract A comparative study of the performances of several leading base isolation devices including the Rubber Bearing with and without lead core, the Sliding-Joint, the French System, and the Resilient-Friction isolator with and without upper sliding plate for a multi-story building under seismic ground accelerations is carried out. Several earthquake ground accelerations including El Centro 1940, Pacoima Dam 1971, and Mexico City 1985 earthquakes are considered. The acceleration, the base displacement and the structural deflection response spectra for the structure with different base isolation systems under various conditions are obtained and discussed. Several sensitivity analyses for variations in the parameters of the isolators and/or structure are also carried out. The effectiveness of various base isolators under a variety of conditions are studied and advantages and disadvantages of different systems are discussed. The results show that the acceleration transmitted and the column stresses of the structure can be effectively reduced by using properly designed base isolation systems. The results of the sensitivity analyses show the friction-type isolation systems are less sensitive to the variations in the amplitude and frequency content of the ground excitation in comparison to the Rubber Bearing base isolators. The study also shows that the peak accelerations transmitted by the friction-type isolators are not significantly affected by small variations in friction coefficient. Furthermore, variations in mass ratio and damping of the structure or the isolator do not significantly affect the peak responses.

Multi-story base-isolated buildings under a harmonic ground motion — Part II: Sensitivity analysis

Abstract A series of sensitivity analyses for multi-story base-isolated structures subject to a harmonic ground excitation is carried out. Several base isolation and energy dissipation devices are considered. The effects of variations in properties of structures and base-isolation systems on the peak responses are studied. For a range of natural frequency, friction coefficient, and damping of the isolator, the peak responses are evaluated. The sensitivity of the base-isolated structure to variations in the amplitude and the frequency of ground excitation is also studied. Particular attention is given to the effects of long-period excitations. The study shows that the peak structural responses for base isolators with a frictional element are less sensitive to variations in intensity and frequency of ground excitation when compared with non-frictional systems. Furthermore, the performances of frictional isolators are insensitive to small variations in friction coefficient and its velocity-dependence.

A new approach to microbuckling of fibrous composites

The fibrous composite is represented by an inhomogeneous two-dimensional continuum with spatial variation in the axial Youngs modulus to account for fibers and matrix. The periodicity of the microstructure is taken into account by expanding the axial Youngs modulus in a Fourier series with wavelength the average spacing between fibers. The compressive strength is determined by examining the stability of small perturbations superimposed on a uniform applied compressive strain

Stability and optimum design of arch-type structures

Abstract Based on the Euler-Bernoulli Theory of the nonlinear inextensible plane elasticae, the concept of funicular or momentless design for arches is reviewed and equations determining the buckling load and transitional bending moments are derived. The results obtained for the buckling load of perabolic arches differs considerably from those found in the literature. Finally, the shape and the variable cross-sectional area of a funicular arch of constant stress is determined.

Multi-story base-isolated buildings under a harmonic ground motion — Part I: A comparison of performances of various systems

Abstract The performances of several leading base-isolation devices (Pure-Friction/Sliding-Joint, Rubber Bearing, French System, New Zealand System, and Resilient-Friction) and a newly proposed system (Sliding Resilient-Friction) for a multi-story building subject to a horizontal harmonic ground motion are studied. The governing equations of motion of various systems and the criteria for stick-slip transition are described and a computational algorithm for obtaining their numerical solutions is developed. The responses of the structure with different base-isolation systems under various conditions are analyzed. The peak absolute acceleration, the maximum structural deflection, and the peak base-displacement responses are obtained. The effectiveness of various base isolators are studied and advantages and disadvantages of different systems are discussed. The results show that the base-isolation devices effectively reduce the column stresses and the acceleration transmitted to the superstructure.

Wind-driven nonlinear oscillations of cables

The objective of this paper is the study of the dynamics of damped cable systems, which are suspended in space, and their resonance characteristics. Of interest is the study of the nonlinear behavior of large amplitude forced vibrations in three dimensions. As a first-order nonlinear problem the forced oscillations of a system having three-degrees-of-freedom with quadratic nonlinearities is developed in order to consider the resonance characteristics of the cable and the possibility of dynamic instability. The cables are acted upon by their own weight in the perpendicular direction and a steady horizontal wind. The vibrations take place about the static position of the cables as determined by the nonlinear equilibrium equations. Preliminary to the nonlinear analysis the linear mode shapes and frequencies are determined. These mode shapes are used as coordinate functions to form weak solutions of the nonlinear autonomous partial differential equations.In order to investigate the behavior of the cable motion in detail, the linear and the nonlinear analyses are discussed separately. The first part of this paper deals with the solution to the self adjoint boundary-value problem for small-amplitude vibrations and the determination of mode shapes and natural frequencies. The second problem dealt with in this paper is the determination of the phenomena produced by the primary resonance of the system. The method of multiple time scales is used to develop solutions for the resulting multi-dimensional dynamical system with quadratic nonlinearity.Numerical results for the steady state response amplitude, and their variation with external excitation and external detuning for various values of internal detuning parameters are obtained. Saturation and jump phenomena are also observed. The jump phenomenon occurs when there are multi-valued solutions and there exists a variation of kinetic energy among solutions.

Variational Theory of Motion of Curved, Twisted and Extensible Elastic Rods

Abstract The variational theory of 3-D motions of curved twisted and extensible elastic rods is obtained based entirely on the kinematical variables of position and rotations. The constitutive relations that define the resistive couples and the axial force as gradients of the strain energy function are established. A candidate for the strain energy function, derived on the basis of classical assumptions, is presented.

Responses of base-isolated shear beam structures to random excitations

Abstract Responses of base-isolated shear beam type structures subject to random ground excitations are studied. Several base isolation systems, including the laminated rubber bearing, the resilient-friction base isolator with and without sliding upper plate, and the EDF system, are considered. Stationary and nonstationary stochastic models for earthquake ground accelerations are considered and the method of time-dependent equivalent linearization in conjunction with moments of the Fokker-Planck equation are used for response analysis. Mean-square statistics of the base raft displacement and the absolute acceleration at the roof of the base-isolated structure are evaluated. A series of parametric studies are also carried out. Comparisons of the results with those for the fixed-base structure show that base isolation systems are, in general, highly effective in reducing mean-square responses of the superstructure. The advantages and disadvantages of various base isolation systems are also discussed.

Design of flexible rods with embedded SMA actuators

The shape change of a stress free cylindrical flexible rod with embedded SMA actuators is modeled in this paper for rods with single or multiple SMA actuators placed parallel to the long axis of the rod for the first heating of the SMA actuators. The deformed shape of the rod is found by solving the nonlinear equations of equilibrium of the rod. For multiple actuators the resultant forces and moments are considered. A design analysis is performed for the active rod with a single SMA actuator. Key design variables are: EROD, the thermal bond strength of the rod to the SMA actuator, and the rod dimensions. Key design parameters are: maximum rod/actuator interfacial shear stress, rod strain, rod slenderness ratio, and rod deflection. An analysis is then performed which investigates the influence of the design variables on each of the design parameters. Optimal values are obtained which yield desired design parameter values. Experimental prototypes are fabricated, tested, and the deformed shape is compared to the theoretical prediction.