• Steel and Composite Structures
• /
• 제39권5호
• /
• pp.615-630
• /
• 2021

The main purpose of the present work was to study the dynamic instability of a three-layered, thick composite sandwich beam with the functionally graded (FG) flexible core subjected to an axial compressive follower force. Flutter instability of a sandwich cantilever beam was analyzed using the high-order theory of sandwich beams, for the first time. The governing equations in general for sandwich beams with an FG core were extracted and could be used for all types of sandwich beams with any types of face sheets and cores. A polynomial function is considered for the vertical distribution of the displacement field in the core layer along the thickness, based on the results of the first Frosting's higher order model. The governing partial differential equations and the equations of boundary conditions of the dynamic system are derived using Hamilton's principle. By applying the boundary conditions and numerical solution methods of squares quadrature, the beam flutter phenomenon is studied. In addition, the effects of different geometrical and material parameters on the flutter threshold were investigated. The results showed that the responses of the dynamic instability of the system were influenced by the follower force, the coefficients of FGs and the geometrical parameters like the core thickness. Comparison of the present results with the published results in the literature for the special case confirmed the accuracy of the proposed theory. The results showed that the follower force of the flutter phenomenon threshold for long beams tends to the corresponding results in the Timoshenko beam.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2005년도 춘계학술대회논문집
• /
• pp.424-429
• /
• 2005

In this paper, the response characteristics of one to one resonance on the rectangular cantilever beam in which basic harmonic excitations are applied by nonlinear coupled differential integral equations are studied. This equations have 3-dimensional non-linearity of nonlinear inertia and nonlinear curvature. Galerkin and multi scale methods are used for theoretical approach to one to one internal resonance. Nonlinear response characteristics of 1st, 2nd, 3rd modes are measured from the experiment for basic harmonic excitation. From the experimental result, geometrical terms of nonlinearity display light spring effect and these terms play an important role in the response characteristics of low frequency modes. Dynamic behaviors in the out of plane are also studied.

• 한국소음진동공학회논문집
• /
• 제15권7호
• /
• pp.851-858
• /
• 2005

The response characteristics of one to one resonance on the quadrangle cantilever beam in which basic harmonic excitations are applied by nonlinear coupled differential-integral equations are studied. This equations have 3-dimensional non-linearity of nonlinear inertia and nonlinear curvature. Galerkin and multi scale methods are used for theoretical approach to one-to-one internal resonance. Nonlinear response characteristics of 1st, 2nd, 3rd modes are measured from the experiment for basic harmonic excitation. From the experimental result, geometrical terms of non-linearity display light spring effect and these terms play an important role in the response characteristics of low frequency modes. Nonlinear nitration in the out of plane are also studied.

• 대한기계학회논문집
• /
• 제19권1호
• /
• pp.263-270
• /
• 1995

The use of the shape memory alloy, Nitinol wire, is investigated as an actuator for enhancing the damping in structural vibration systems. The first-order mathematical model of the Nitinol wire is obtained from the experimental data for an actuator. Finite element method is utilized for the strain gage sensor model, which is installed at the root of cantilever beam. A simple system, cantilever beam, is built as a flexible structural system to implement a control law with the Nitinol wire actuator. The system model including sensor and actuator is derived, which agrees with the experimental results. The actuator dynamics is augmented with the system so as to design PI controller and the one of robust controllers, LQG/LTR controller, and the control laws are implemented experimentally. The experimental study shows the feasibility of utilizing the Nitinol wire as an actuator for the purpose of vibration control.

• 대한전기학회논문지:시스템및제어부문D
• /
• 제52권7호
• /
• pp.401-409
• /
• 2003

This paper describes the design and the performance analysis of an $H_2$ controller for noncollocated active vibrating systems. An experiment for the active vibration control of a flexible structure is performed. The experimental model used is a cantilever beam controlled by an active damping system consisting of a laser sensor and an electromagnetic actuator. The $H_2$ controller design is based on the reduced order model and the designed system is capable of attenuating vibration without causing spillover instability. The design procedure to prevent spillover instability is described via the sensitivity analysis. The performances of the controller are verified by experimental results.

• 대한전기학회논문지:전기물성ㆍ응용부문C
• /
• 제52권7호
• /
• pp.401-401
• /
• 2003

This paper describes the design and the performance analysis of an Ha controller for noncollocated active vibrating systems. An experiment for the active vibration control of a flexible structure is performed. The experimental model used is a cantilever beam controlled by an active damping system consisting of a laser sensor and an electromagnetic actuator. The $H_2$ controller design is based on the reduced order model and the designed system is capable of attenuating vibration without causing spillover instability, The design procedure to prevent spillover instability is described via the sensitivity analysis. The performances of the controller are verified by experimental results.

• 한국정밀공학회지
• /
• 제13권11호
• /
• pp.132-142
• /
• 1996

This paper presents a technique to model and control a manipulator which has a flexible link and moves in a vertical plane. The flexible link is modeled as an Euler-Bernoulli Beam. Elastic deformation of the flexible link is represented using the assumed modes method. A comparison function which satisfies all geometric and natural boundary conditions of a cantilever beam with an end mass is used as an assumed mode shape. Lagrange's equation is utilized for the development of a discretized model. This paper presents a simple technique to improve the correctness of the developed model. The final model including the shortening effect due to elastic deformation correlates very well with experimental results. The free body motion simulation shows that two assumed modes for the representation of the elastic deformation is proper in terms of the model size and correctness. A control algorithm is developed using PID control technique. The proportional, integral and derivative control gains are determined based on dominant pole placement method with a rigid one-link manipulator. A position control simulation shows that the control algorithm can be used to control the position and residual oscillation of the flexible one-link manipulator effectively.

• 대한기계학회논문집A
• /
• 제23권11호
• /
• pp.1940-1951
• /
• 1999

In this paper, the equations of motion of a Bernoulli-Euler cantilever beam fixed on a moving cart and carrying a lumped mass concentrated at an arbitrary position along the beam is derived. The motion of the beam-mass-cart system is analyzed through unconstrained modal analysis, and a unified characteristic equation for calculating the natural frequencies of the system is obtained. The changes of natural frequencies and the corresponding mode shapes with respect to the changes in mass ratios of the system and to the concentrated position of the lumped mass are investigated with the frequency equation, which can be generally applied to this kind of systems. The exact and assumed-mode solutions including the dynamics of the base cart are obtained, and the open-loop responses of the system by arbitrarily designed forcing function are given by numerical simulations. The results match well with physical phenomena even at the extreme cases where the concentrated mass is attached to the bottom and to the top of the beam.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2007년도 추계학술대회논문집
• /
• pp.356-359
• /
• 2007

In this paper, the stability of a rotating cantilever pipe conveying fluid with a crack is investigated by the numerical method. That is, the influences of the rotating angular velocity, mass ratio and crack severity on the critical flow velocity for flutter instability of system are studied. The equations of motion of rotating pipe are derived using the Euler beam theory and the Lagrange's equation. The crack section of pipe is represented by a local flexibility matrix connecting two undamaged pipe segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. Generally, the critical flow velocity for flutter is proportional to the angular velocity and the depth of crack. Also, the critical flow velocity and stability maps of the rotating pipe system as a function of mass ratio for the changing each parameter are obtained.

• 소음진동
• /
• 제11권2호
• /
• pp.292-300
• /
• 2001

This research is concerned with the validation of the modeling technique and controller design for slewing beam structures. When cantilever beam rotates about axes perpendicular to the undeformed beam's longitudinal axis, it experiences inertial loading. Hence, the beam vibrates from the initial stage of slewing. In this paper, the analytical model for a single slewing flexible beam with surface bonded piezoelectric sensor and actuator is developed using the Hamilton's principle with discretization by the assumed mode method. Comparisons with the theoretical model are made based upon the frequency responses and time responses. A new factor called the coupling coefficient is introduced to incorporate the discrepancies between the theoretical and experimental results. The slewing is achieved by applying the PID control, which is found to be less sensitive to vibrations. The vibrations are controlled by PPF controller, which is found to be effective in suppressing residual vibrations after slewing. The vibrations occurred during slewing is difficult to control because the piezoceramic actuator is not powerful enough to overcome inertial loadings.