Fundamental Mode Response Research Articles

Modelling and nonlinear dynamics of dielectric elastomer sandwich cantilever-plate actuators

Inspired from the bimorph actuators for flapping and propelling swimming vehicles, a soft actuator made of two dielectric elastomer layers and a hyperelastic material core is presented. This actuator is also termed as a sandwich cantilever rectangular plate, which is stimulated by alternating voltages with a phase difference. Based on the classical plate theory and the variational method, the governing equation describing the nonlinear vibration of the sandwich cantilever plate is formulated. Employing the harmonic balance method and the arc-length continuation method, periodic solutions are obtained, then the convergence analyses of the numbers of discrete modes and harmonics are conducted. In order to illustrate the frequency features more clearly, a modified mode numbering scheme is developed. The numerical results manifest that, the combined DC-AC voltage excitation and the AC voltage excitation can excite abundant nonlinear behaviors of the soft actuator, including the local peak and the isolated bubble aroused by the nonlinear coupling. Additionally, the fundamental mode response keeps dominating the dynamic behaviors of the cantilever-plate actuator. The nonlinear dynamics broaden the resonant domain significantly, which can be potentially applied to the design and manufacture of high-performance soft actuators through the vibration enhancement strategy.

Pseudo-double impulse for simulating critical response of elastic-plastic MDOF model under near-fault earthquake ground motion

A pseudo-double impulse (PDI) is proposed as an extension of the ordinary double impulse (DI) as a substitute of a one-cycle sine wave. PDI is treated as a set of impulsive lateral forces while the ordinary DI was introduced as an impulsive ground acceleration. The deformation and acceleration responses of multi-degree-of-freedom (MDOF) models under DI largely exceed those under the corresponding one-cycle sine wave as a main part of a near-fault ground motion. This is because DI has multiple frequency components and the higher-mode responses are excited. While the influence coefficient vector of the ordinary DI consists of 1 at every component, the influence coefficient vector of PDI is set to be proportional to the undamped fundamental natural mode. Therefore, the fundamental-mode response is mainly excited and the higher-mode responses are hardly excited by PDI. The displacement responses, the velocity responses and the input energy under DI and those under PDI are derived here for both elastic proportionally and non-proportionally damped MDOF models. The critical timing under PDI is also derived. The critical timing can be obtained by the time-history response analysis without repetition. It is demonstrated through the time-history response analysis that the distributions of interstory drifts and floor accelerations under the critical PDI correspond well to those under the critical one-cycle sine wave. Moreover, it is shown that, as far as the input level is large, the critical input period of PDI and that of the one-cycle sine wave correspond well. Since this procedure is not limited to elastic models, the proposed procedure helps to efficiently estimate the critical responses under the one-cycle sine wave for elastic-plastic MDOF models. Finally, the responses under recorded near-fault ground motions are compared with those under PDI. It is shown that the correspondence of the response under PDI and that under the recorded ground motions is fairly good although recorded ground motions are not always critical inputs for elastic-plastic MDOF models.

Improvement of Dynamic Response of Structures on Sandy Soil by Means of Viscous Dampers

Superstructure models used in optimal damper problem are usually connected rigidly to ground, and ground effects are not taken into account. This study reveals the effect of relative density of sandy soils on the damper problems. The optimal distribution of viscous dampers and the effect of relative density of sandy soils on the dynamic response of structure for an n-storey shear-building model are examined. The governing equation of soil–structure model is established and the equations in the frequency domain are derived using Fourier transformation. Steepest direction search algorithm is used as an optimization method. The four different objective functions, which are the top displacement, top absolute acceleration, base shear and base moment behaviour of the structure defined in the frequency domain, are minimized. The fundamental mode response of structural model is taken into account, and the time history analyses are conducted by using El Centro (NS) earthquake acceleration record. The effect of relative density of sandy soils on the responses of structure with optimal design and the effect of the variation of total damper capacity used in the optimization stage are investigated. It is observed that the variation of the objective functions, total damping capacity and ground conditions can change the optimal design. The low displacement in damped systems has occurred in comparison with no damper. The structural response in the rigid case is less than those in the different relative density of sandy soils. The added dampers placed according to the different objectives have improved the structural response and also reduced the harmful effects caused by poor ground conditions.

Approximate Analysis for Shear Force Amplification Effect in Ordinary RC Shear Walls

An approximate analysis method is proposed to predict the dynamic amplification of shear forces in ordinary reinforced concrete shear walls as a preliminary study. First, a seismic design for three groups of ordinary reinforced concrete shear walls higher than 60 m was created on the basis of nonlinear dynamic analysis. Causes for the dynamic amplification effect of shear forces were investigated through a detailed evaluation of the nonlinear dynamic analysis result. A new modal combination rule was proposed on the basis of that observation, in which fundamental mode response and combined higher mode response were summed directly. The fundamental mode response was approximated by nonlinear static analysis result, while higher mode response was computed using response spectrum analysis for equivalent linear structural models with the effective stiffness based on the nonlinear dynamic analysis result. The proposed approximate analysis generally predicted vertical distribution of story shear and shear forces of individual walls from the nonlinear dynamic analysis with comparable accuracy.

New Nonlinear Modal Decomposition Method for Seismic Analysis of Tall RC Core Wall Buildings

Significant research has been conducted in the past to develop simplified seismic evaluation procedures for tall buildings. However, most of these procedures are based on the use of fundamental mode response while ignoring the responses from higher modes. Moreover, such seismic evaluation procedures are unable to accurately predict individual-member responses. Evaluation of individual-member responses is an important part of damage and loss prediction estimation due to seismic hazard. In this research work, a new nonlinear modal decomposition approach is proposed for seismic evaluation of tall RC core wall buildings that can take into account the higher mode effects. This procedure is an extension of the classical Uncoupled Modal Response History Analysis procedure. A 44-story reinforced concrete core wall building is selected to verify the accuracy of the proposed procedure. A comparison between the outcomes of the proposed procedure and the nonlinear response history analysis procedure shows that this procedure is reasonably accurate in predicting important global and member responses.

Effect of frequency dependence of large mass ratio viscoelastic tuned mass damper on seismic performance of structures

Abstracts This paper investigates the effect of the frequency dependence of the large mass ratio viscoelastic tuned mass damper (VTMD) on the seismic performance of structures. Compared with conventional TMDs, the frequency dependence of the complex stiffness of VTMD affects its control performance but is always neglected in the seismic analysis of structures. A linear function is introduced to describe the frequency dependence of the real stiffness of the VTMD. An indicator is defined to quantitatively characterize the frequency dependence level of the real stiffness. The effects of the frequency dependence on the control effectiveness and robustness are illustrated by a two degree of freedom (DOF) system under the Gaussian white noise excitation. At last, a numerical simulation of a five-story frame structure under real earthquakes and filtered white noises is presented to illustrate the mitigation effect of the large mass ratio VTMD under different ground conditions. The results show that the frequency dependence level of the VTMD depends on both the type of viscoelastic materials and controlled modal frequency. In the fundamental mode response mitigation, the frequency dependence of the real stiffness improves the control effectiveness and robustness of the VTMD, while in the non-fundamental mode response mitigation, the control effect of the VTMD is weaker to that of the conventional TMD because of the damping characteristic of the complex stiffness element.

Broadband terahertz perfect light absorber based on the modes of fundamental response and surface lattice resonance

Traditional broadband metamaterial absorbers are typically based on the combining effects of several fundamental mode responses resulted from different dimensions of metallic elements. We report here that simple single-sized cross-shaped resonator (placed on an insulator dielectric slab and an opaque metallic mirror) having the modes of fundamental response and surface lattice resonance can be used to achieve the broadband absorption performance. A continuous bandwidth of 1.97 THz with absorptivity bigger than 50% is realized at central frequency of 2.72 THz. The device relative absorption bandwidth (RAB) can be up to 72.43%, which is superior to traditional broadband absorption devices with multiple different-sized resonators (i.e., the complex structure designs). The device RAB can be further broadened by varying the frequencies of the fundamental mode response or surface lattice resonance using different geometrical parameters. In addition, the device performance can be tuned from broadband absorption to dual-band absorption with the decrease of the dielectric slat thickness.

Dynamic behavior of a building structure tested with base and mid-story isolation systems

The discrepancies of dynamic behavior in base-isolated and mid-story isolated buildings are investigated experimentally in this study. In a mid-story isolated building, the isolation system is incorporated into the mid-story rather than the base of the building. The shaking table test results disclose that with the same design of the isolated superstructure and isolation system, a mid-story isolated building has smaller fundamental modal quantities than a base-isolated building. Besides, the seismic response at the superstructure is mainly attributed to the fundamental mode response, while the higher mode responses contribute significantly to the seismic responses at the substructure below the isolation system. Therefore, the modal response spectrum analysis appropriately considering the contribution of higher modes, rather than the equivalent lateral force procedure only considering the fundamental mode, is suggested for the preliminary design of mid-story isolated buildings prior to performing nonlinear responses history analyses.

Fundamental Design Issues for Supplemental Damping Applications

In considering supplemental damping for a project, immediate questions that the structural engineer must address are: 1) Is the building suitable for supplemental damping; 2) How much damping should be provided; and 3) How should the dampers be distributed in the building? These are issues that need to be resolved irrespective of the type of damper used. The evaluation in this paper shows that supplemental damping is ideally suited for flexible frame buildings, or buildings detailed to accommodate interstory drift ratios of about 0.01 without significant damage. Providing 10% to 20% supplemental damping reduces response significantly for most structures. Providing more damping is difficult to justify from a cost-benefit perspective. Providing less supplemental damping can reduce earthquake response for structures having only small amounts of inherent damping; e.g., 1% to 2%. For most buildings having predominant fundamental mode response, the distribution of dampers in a structure is determined mostly from designing to carry the damper lateral forces. Frame member stresses, plan stiffness regularity, and elevation stiffness regularity are critical design considerations for establishing damper distributions in buildings.

Earthquake Response Spectrum Analysis of Intake‐Outlet Towers

A simplified analysis procedure is developed to determine the maximum earthquake forces in intake‐outlet towers directly from the design earthquake spectrum without the need for a response history analysis. All the significant effects of tower‐water interaction and tower‐foundation‐soil, interaction are included in the analysis. It is demonstrated that the hydrodynamic effects can be approximated by added mass functions for outside and inside water. An equivalent SDF system is developed to consider approximately the effects of tower‐foundation‐soil interaction in the fundamental mode response of towers.

Simplified Earthquake Analysis of Concrete Gravity Dams: Combined Hydrodynamic and Foundation Interaction Effects

A companion paper presented simplified procedures for earthquake analysis of the fundamental mode response of concrete gravity dams including the separate effects of dam‐foundation rock interaction and dam‐water interaction with reservoir bottom absorption. These procedures are extended to develop a simplified analytical procedure for evaluation of the response of concrete gravity dams to earthquake ground motion including the simultaneous effects of dam‐water interaction, reservoir bottom absorption, and dam‐foundation rock interaction. Expressions for the parameters of an equivalent SDF system that models the fundamental mode response of dams are derived, a procedure to implement the analytical procedure is outlined, and an extension to consider the response contributions of the higher vibration modes of the dam is briefly mentioned.

境界層内圧力変動による板の振動解析

The response cross-correlation of the simply supported elastic panel is derived through the normal mode approach assuming the analytic formula for the space-time cross-correlation of pressure fluctuations and non-interference between the vibration modes. The author has proposed new quantites "Dynamic Effect Function (DEF)" and "Orientation Sensitivity Factor (OSF)" as the measures to estimate dependency of vibration modes on pressure fluctuation convecting velocity, response magnification due to difference of flow direction respectively. Numerical examples state that DEF of the fundamental mode (DEF11)takes the maximum among the vibration modes, and it is almost ten times larger than other modes, moreover OSF11 is nearly equal to unity for various rectangular plates, which means response of fundamental mode is very insensitive to panel orientation.