• Structural Engineering and Mechanics
• /
• v.22 no.6
• /
• pp.701-717
• /
• 2006

In the existing reports regarding free transverse vibrations of the Euler-Bernoulli beams, most of them studied a uniform beam carrying various concentrated elements (such as point masses, rotary inertias, linear springs, rotational springs, spring-mass systems, ${\ldots}$, etc.) or a stepped beam with one to three step changes in cross-sections but without any attachments. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of the multiple-step Euler-Bernoulli beams carrying a number of lumped masses and rotary inertias. First, the coefficient matrices for an intermediate lumped mass (and rotary inertia), left-end support and right-end support of a multiple-step beam are derived. Next, the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions, respectively. The effects of distribution of lumped masses and rotary inertias on the dynamic characteristics of the multiple-step beam are also studied.

• 정보저장시스템학회:학술대회논문집
• /
• 2005.10a
• /
• pp.190-194
• /
• 2005

There is a great demand of micro-actuators for mobile information devices such as SFF optical drives and mobile camera phones. However, conventional magnetic coils of electromagnetic motors are a major obstacle for miniaturization because of their complicated structures and large power consumption. In this paper, a linear ultrasonic motor to actuate focusing lens of mobile devices is proposed. The new actuator uses a ring type bimorph piezoelectric material, and $d_{31}$ mode is adopted for applying linear motion. The interaction between inertia force and friction force makes linear motion by high-frequency saw signal input. The saw signal gives steady forces on the one direction by asymmetric inclination property of the signal itself on time domain. A commercial FEM (ANSYS) was used in this investigation for simulating structural analysis, identification of dynamic property, such as resultant displacement and coupled analysis with piezoelectric material. To evaluate the performance of the new design, a prototype was manufactured and experiments were carried out. Experimental results show the actuator motion of 1.52 mm/s at 10 kHz input signal in 5 V.

• Transactions of the Society of Information Storage Systems
• /
• v.2 no.4
• /
• pp.251-256
• /
• 2006

There is a great demand of micro-actuators for mobile information devices such as SFF optical drives and mobile phone cameras. However, the magnetic coils used in conventional electromagnetic motors are a major obstacle for the miniaturization because of their complicated structures and large power consumption. In this paper, a linear ultrasonic motor to actuate focusing lens of mobile devices is proposed. The new actuator uses a ring type bimorph piezoelectric material, and $d_{31}$ mode is adopted for applying linear motion. The interaction between inertia force and friction force makes linear motion by high-frequency saw signal input. The saw signal gives steady forces on the one direction by asymmetric inclination property of the signal itself on time domain. A commercial FEM(ANSYS) was used in this investigation for simulating structural analysis, identification of dynamic property, such as resultant displacement and coupled analysis with piezoelectric material. To evaluate the performance of the new design, a prototype was manufactured and experiments were carried out. Experimental results show the actuator motion of 5.4 mm/s at 10V saw signal of 41 kHz.

• Proceedings of the KSME Conference
• /
• 2004.04a
• /
• pp.1011-1016
• /
• 2004

All the loads in the real world are dynamic loads and it is well known that structural optimization under dynamic loads is very difficult. Thus the dynamic loads are often transformed to the static loads using dynamic factors. However, due to the difference of load characters, there can be considerable differences between the results from static and dynamic analyses. When the natural frequency of a structure is high, the dynamic analysis result is similar to that of static analysis due to the small inertia effect on the behavior of the structure. However, if the natural frequency is low, the inertia effect should not be ignored. Then, the behavior of the dynamic system is different from that of the static system. The difference of the two cases can be explained from the relationship between the homogeneous and the particular solutions of the differential equation that governs the behavior of the structure. Through various examples, the difference between the dynamic analysis and the static analysis are shown. Also the optimization results considering dynamic loads are compared with static loads.

• Structural Engineering and Mechanics
• /
• v.72 no.2
• /
• pp.229-244
• /
• 2019

Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

• Structural Engineering and Mechanics
• /
• v.77 no.5
• /
• pp.627-635
• /
• 2021

The speed of rail vehicles become higher and higher over two decades, and China has unveiled a prototype high-speed train in October 2020 that has been able to reach 400 km/h. At such high speeds, wheel-rail force items that had previously been ignored in common computational model should be reevaluated and reconsidered. Aiming at this problem, a new model for investigating the vehicle-bridge interaction at high moving speed is proposed. Comparing with the common model, the new model was more accurate and applicable, because it additionally considers the second-order pseudo-inertia forces effect and its modeling equilibrium position was based on the initial deformed curve of bridge, which could include the influences of temperature, pre-camber, shrinkage and creep deformation, and pier uneven settlement, etc. Taking 5 km/h as the speed interval, the dynamic responses of the classical vehicle-bridge system in the speed range of 5 km/h to 400 km/h are studied. The results show that ignoring the second-order pseudo-inertia force will underestimate the dynamic response of vehicle-bridge system and make the high-speed railway bridge structure design unsafe.

• Structural Engineering and Mechanics
• /
• v.86 no.6
• /
• pp.751-764
• /
• 2023

In practical engineering such as aerial refueling pipes, the boundary of the fluid-conveying pipe is difficult to be completely immovable. Pipes under movable and immovable boundaries are controlled by different dominant nonlinear factors, where the boundary mobility will affect the nonlinear dynamic characteristics, which should be focused on for adopting different strategies for vibration suppression and control. The nonlinear dynamic instability characteristics of functionally graded fluid-conveying pipes lying on a viscoelastic foundation under movable and immovable boundary conditions are systematically studied for the first time. Nonlinear factors involving nonlinear inertia and nonlinear curvature for pipes with a movable boundary as well as tensile hardening and nonlinear curvature for pipes with an immovable boundary are comprehensively considered during the derivation of the governing equations of the principal parametric resonance. The stability boundary and amplitude-frequency bifurcation diagrams are obtained by employing the two-step perturbation- incremental harmonic balance method (TSP-IHBM). Results show that the movability of the boundary of the pipe has a great influence on the vibration amplitude, bifurcation topology, and the physical meanings of the stability boundary due to different dominant nonlinear factors. This research has guidance significance for nonlinear dynamic design of fluid-conveying pipe with avoiding in the instability regions.

• Structural Engineering and Mechanics
• /
• v.53 no.3
• /
• pp.537-573
• /
• 2015

Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.15 no.1
• /
• pp.189-195
• /
• 2002

This paper deals with the free vibration of horizontally curved beams with transition currie. Based on the dynamic equilibrium equations of a curved beam element subjected to the stress resultants and inertia forces, the governing differential equations are derived for the out-of-plane vibration of curved beam with variable curvature. These equations are applied to the beam having transition curve in which the clothiod curve is chosen in this study. The differential equations are solved by the numerical methods lot calculating the natural frequencies and mode shapes. For verifying theories developed herein, the frequency parameters obtained from this studs and ADINA are compared with each other. As the numerical results, the various parametric studies effecting on natural frequencies are investigated and those results are presented in tables and figures.

• Computers and Concrete
• /
• v.14 no.1
• /
• pp.73-90
• /
• 2014

The traditional destructive tests in damage detection require high cost, long consuming time, repairing of damaged members, etc. In addition to these, powerful equipments with advanced technology have motivated development of global vibration based damage detection methods. These methods base on observation of the changes in the structural dynamic properties and updating finite element models. The existence, location, severity and effect on the structural behavior of the damages can be identified by using these methods. The main idea in these methods is to minimize the differences between analytical and experimental natural frequencies. In this study, an application of damage detection using model updating method was presented on a one storey reinforced concrete (RC) building model. The model was designed to be 1/2 scale of a real building. The measurements on the model were performed by using ten uni-axial seismic accelerometers which were placed to the floor level. The presented damage identification procedure mainly consists of five steps: initial finite element modeling, testing of the undamaged model, finite element model calibration, testing of the damaged model, and damage detection with model updating. The elasticity modulus was selected as variable parameter for model calibration, while the inertia moment of section was selected for model updating. The first three modes were taken into consideration. The possible damaged members were estimated by considering the change ratio in the inertia moment. It was concluded that the finite element model calibration was required for structures to later evaluations such as damage, fatigue, etc. The presented model updating based procedure was very effective and useful for RC structures in the damage identification.