• Geomechanics and Engineering
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• v.1 no.2
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• pp.121-142
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• 2009

The paper deals with the applications of spectral finite element method to the dynamic analysis of framed foundations supporting high speed machines. Comparative performance of approximate dynamic stiffness methods formulated using static stiffness and lumped or consistent or average mass matrices with the exact spectral finite element for a three dimensional Euler-Bernoulli beam element is presented. The convergence of response computed using mode superposition method with the appropriate dynamic stiffness method as the number of modes increase is illustrated. Frequency proportional discretisation level required for mode superposition and approximate dynamic stiffness methods is outlined. It is reiterated that the results of exact dynamic stiffness method are invariant with reference to the discretisation level. The Eigen-frequencies of the system are evaluated using William-Wittrick algorithm and Sturm number generation in the $LDL^T$ decomposition of the real part of the dynamic stiffness matrix, as they cannot be explicitly evaluated. Major's method for dynamic analysis of machine supporting structures is modified and the plane frames are replaced with springs of exact dynamic stiffness and dynamically flexible longitudinal frames. Results of the analysis are compared with exact values. The possible simplifications that could be introduced for a typical machine induced excitation on a framed structure are illustrated and the developed program is modified to account for dynamic constraint equations with a master slave degree of freedom (DOF) option.

• Journal of Ocean Engineering and Technology
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• v.1 no.1
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• pp.57-64
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• 1987

Methods of nonlinear stochastic analysis of guyed towers are studied in this paper. Two different kinds of nonlinearities are considered. They are the nonlinear restoring force from the guying system and the nonlinear hydrodynamic force. Analyses are carried out mainly in the frequency domain using linearization techniques. Two methods for the linearization of the nonlinear stiffness are presented, in which the effects of the steady offset and the oscillating component of the structural motion can be adequately analyzed. those two methods are the equivalent linearization method and the average stiffness method. The linearization of the nonlinear drag force is also carried out considering the effect of steady current as well as oscillatory wave motions. Example analyses are performed for guyed tower in 300m water. Transfer functions and the expected maximum values of the deck displacement and the bending moment near the middle of the tower are calculated. Numerical results show that both of the frequency domain methods presented in this paper predict the responses of the sturcture very reasonably compared with those by the time integration method utilzing the random simulations wave particla motions.

• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.601-620
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• 2006

The paper presents an effective stiffness model for deformational analysis of reinforced concrete cracked members in bending throughout the short-term loading up to the near failure. The method generally involves the analytical derivation of an effective moment of inertia based on the smeared crack technique. The method, in a simplified way, enables us to take into account the non linear properties of concrete, the effects of cracking and tension stiffening. A statistical analysis has shown that proposed technique is of adequate accuracy of calculated and experimental deflections data provided for beams with small, average and normal reinforcement ratios.

• Structural Engineering and Mechanics
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• v.83 no.3
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• pp.341-351
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• 2022

During bolted flange assembly, the contact stiffness of some areas of the joint surface may be low due to the elastic interaction. In order to improve the contact stiffness at the lowest position of bolted flange, the correlation model between the initial bolt pre-tightening force and the contact stiffness of bolted flange is established in this paper. According to the stress distribution model of a single bolt, an assumption of uniform local contact stiffness of bolted flange is made. Moreover, the joint surface is divided into the compressive stress region and the elastic interaction region. Based on the fractal contact theory, the relationship model of contact stiffness and contact force of the joint surface is proposed. Considering the elastic interaction coefficient method, the correlation model of the initial bolt pre-tightening force and the contact stiffness of bolted flange is established. This model can be employed to reverse determine the tightening strategy of the bolt group according to working conditions. As a result, this provides a new idea for the digital design of tightening strategy of bolt group for contact stiffness of bolted flange. The tightening strategy of the bolted flange is optimized by using the correlation model of initial bolt pre-tightening force and the contact stiffness of bolted flange. After optimization, the average contact stiffness of the joint surface increased by 5%, and the minimum contact stiffness increased by 6%.

• Smart Structures and Systems
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• v.24 no.3
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• pp.361-377
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• 2019

The stiffness of shape memory alloy (SMA) spring while in actuation is represented by an empirical model that is derived from the logistic differential equation. This model correlates the stiffness to the alloy temperature and the functionality of SMA spring as active variable stiffness actuator (VSA) is analyzed based on factors that are the input conditions (activation current, duty cycle and excitation frequency) and operating conditions (pre-stress and mechanical connection). The model parameters are estimated by adopting the nonlinear least square method, henceforth, the model is validated experimentally. The average correlation factor of 0.95 between the model response and experimental results validates the proposed model. In furtherance, the justification is augmented from the comparison with existing stiffness models (logistic curve model and polynomial model). The important distinction from several observations regarding the comparison of the model prediction with the experimental states that it is more superior, flexible and adaptable than the existing. The nature of stiffness variation in the SMA spring is assessed also from the Dynamic Mechanical Thermal Analysis (DMTA), which as well proves the proposal. This model advances the ability to use SMA integrated mechanism for enhanced variable stiffness actuation. The investigation proves that the stiffness of SMA spring may be altered under controlled conditions.

• Smart Structures and Systems
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• v.3 no.3
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• pp.245-261
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• 2007

Nonlinear time-domain system identification (SI) algorithm is proposed to assess damage in a shear building by synchronously estimating time-varying stiffness and damping parameters using measured acceleration data. Mass properties have been assumed as the a priori known information. Viscous damping was utilized for the current research. To chase possible nonlinear dynamic behavior under severe vibration, an incremental governing equation of vibrational motion has been utilized. Stiffness and damping parameters are estimated at each time step by minimizing the response error between measured and computed acceleration increments at the measured degrees-of-freedom. To solve a nonlinear constrained optimization problem for optimal structural parameters, sensitivities of acceleration increment were formulated with respect to stiffness and damping parameters, respectively. Incremental state vectors of vibrational motion were computed numerically by Newmark-${\beta}$ method. No model is pre-defined in the proposed algorithm for recovering the nonlinear response. A time-window scheme together with Monte Carlo iterations was utilized to estimate parameters with noise polluted sparse measured acceleration. A moving average scheme was applied to estimate the time-varying trend of structural parameters in all the examples. To examine the proposed SI algorithm, simulation studies were carried out intensively with sample shear buildings under earthquake excitations. In addition, the algorithm was applied to assess damage with laboratory test data obtained from free vibration on a three-story shear building model.

• Journal of Power System Engineering
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• v.4 no.1
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• pp.60-67
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• 2000

As the speed of rotating machines increases and also their weight decreases, the coupling between lateral and torsional vibrations must be considered. In the past, rotordynamics and geardynamics have tended to treat the lateral and torsional vibrations of the system elements as separate and decoupled mechanisms. In the paper, the coupled lateral-torsional free and forced vibration of rotors trained by gears is analyzed using finite element method. Also the complicated variation of the meshing stiffness as a function of contact point along the line of action is estimated correctly. The gear mesh model is assumed to be linear with constant average mesh stiffness.

• Journal of Magnetics
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• v.20 no.4
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• pp.387-393
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• 2015

Torque ripple is necessarily generated in interior permanent magnet synchronous motors (IPMSMs) due to the non-sinusoidal distribution of flux density in the air gap and the magnetic reluctance by stator slots. This paper deals with an asymmetric rotor shape to reduce torque ripple which can make sinusoidal flux density distribution in the air gap. Meanwhile the average torque is relatively increased by the asymmetric rotor. Response surface method (RSM) is applied to find the optimum position of the permanent magnets for the IMPSM with improved torque performance. Consequently, an asymmetric structure is the result of RSM and the structure has disadvantage of a mechanical stiffness. Finally, the performance of suggested shape is verified by finite element analysis and structural analysis is conducted for the mechanical stiffness.

• International Journal of Precision Engineering and Manufacturing
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• v.9 no.1
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• pp.47-50
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• 2008

This paper presents a new water-lubricated hybrid sliding bearing for a high speed and high accuracy main shaft system, along with the numerical method used for its design. The porous material for the restrictor and the restriction parameter were chosen based on the special requirements of the water-lubricated bearing. Subsequent numerical calculations give the load capacity, stiffness, and friction power of different forms of water-lubricated bearings. The pressure distribution of the water film in a 6-cavity bearing is shown, based on the results of the numerical calculations. A comparison of oil-lubricated and water-lubricated bearings shows that the latter benefits more from improved processing precision and efficiency. An analysis of the stiffness and friction power results shows that 6-cavity bearings are the preferred type, due their greater stiffness and lower friction power. The average elevated temperature was calculated and found to be satisfactory. The relevant parameters of the porous restrictor were determined by calculating the restriction rate. All these results indicate that this design for a water-lubricated bearing meets specifications for high speed and high accuracy.

• Structural Monitoring and Maintenance
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• v.6 no.3
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• pp.237-254
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• 2019

This paper presents an improved time series based damage detection approach with experimental verifications for detection, localization, and quantification of damage in shear-type structures under varying mass effects using output-only vibration data. The proposed method can be very effective for automated monitoring of buildings to develop proactive maintenance strategies. In this method, Auto-Regressive Moving Average models with eXogenous inputs (ARMAX) are built to represent the dynamic relationship of different sensor clusters. The damage features are extracted based on the relative difference of the ARMAX model coefficients to identify the existence, location and severity of damage of stiffness and mass separately. The results from a laboratory-scale shear type structure show that different damage scenarios are revealed successfully using the approach. At the end of this paper, the methodology limitations are also discussed, especially when simultaneous occurrence of mass and stiffness damage at multiple locations.