Vibration of Beam with Elastically Restrained Ends and Rotational Spring-Lumped Rotary Inertia System at Mid-Span

Hozhabrossadati, Seyed Mojtaba; Sani, Ali Mohamadi; Mofid, Massood

doi:10.1142/s0219455414500400

Cited by 7 publications

(5 citation statements)

References 18 publications

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“…(1-a)-(1-d) can be rewritten as: in which u 1 , u 2 , v 1 and v 2 are mode shape functions of beams. Equations (2-a)-(2-d) have the following solutions [8]:…”

Section: Problem Formulationmentioning

confidence: 99%

Analyzing free vibration of a double-beam joined by a three-degree-of-freedom system

Rezaiee‐Pajand

Sani

Hozhabrossadati

2019

J Braz. Soc. Mech. Sci. Eng.

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A double-beam system is a suitable device for vibration control of structures, and studying its behavior is very important. The mechanical system under study includes two beams, which are interconnected by a three-degree-of-freedom system. This structure has a rigid disk and a suspended mass. The main contribution of this paper involves the inclusion of a threedegree-of-freedom system in vibration analysis of double-beams, which has not been considered yet. Moreover, in order to generalize the model, nine translational and rotational springs are identified within the main model. Besides, two solution methods are employed to obtain the problem solution. A closed-form solution is found by solving the governing eigenvalue problem analytically. Furthermore, due to the complexity of the problem and for the sake of verification, a finite element solution is presented. Comparing the findings by both methods gives an indication of the accuracy of the proposed solutions. A sensitivity analysis on the system parameters is also conducted.

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“…(1-a)-(1-d) can be rewritten as: in which u 1 , u 2 , v 1 and v 2 are mode shape functions of beams. Equations (2-a)-(2-d) have the following solutions [8]:…”

Section: Problem Formulationmentioning

confidence: 99%

Analyzing free vibration of a double-beam joined by a three-degree-of-freedom system

Rezaiee‐Pajand

Sani

Hozhabrossadati

2019

J Braz. Soc. Mech. Sci. Eng.

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“…Concerning that it is a widespread phenomenon to add elastic constraints to beams, a large number of scholars have studied natural characteristics of this type of beams from different insights, such as the number of translational springs of different constant stiffness supporting an Euler-Bernoulli beam [1] , adopting the limited stiffness of a simple support of Euler-Bernoulli beam to increase the natural frequencies [11], dynamic response of an Euler-Bernoulli beam resting on an elastic foundation [12,13]. For some special cases, such as hinge connection in the middle of the beam with elastic restraints [14], moving elastic support on the beam [15], a rotating hub-beam with elastic boundary restraints [7], equivalent dynamic models were individually studied according to their specific features.…”

Section: Introductionmentioning

confidence: 99%

Natural characteristics for transverse vibration of Euler Bernoulli beams with variable end constraints

Song

Dong

Yan

et al. 2022

J. Phys.: Conf. Ser.

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The transverse vibration of Euler Bernoulli beam with mass of ends and springs is studied. The exact frequency equation is derived and natural frequencies and the corresponding mode shapes are calculated. With the linearly increasing mass of ends, natural frequencies and the rate of frequency change of the beam system initially decrease sharply and then level out, which demonstrates that the beam system is transforming from the free beam to the pinned beam. When the springs are added at two tips, the natural characteristics of the beam are affected by mass of ends and spring stiffness. If the added mass has much lower magnitude than that of the beam, the stiffness of springs exerts major impact on the increase of natural frequencies. While the added mass of ends is increased to the same magnitude of the beam, the natural characteristics of the beam are determined by both the mass of ends and spring stiffness. As the growing magnitude of added mass, mass of ends performs a dominant role in decreasing the natural frequencies. Therefore, spring stiffness and mass of ends should be first considered to establish different dynamic models accurately.

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“…Furthermore, an Euler–Bernoulli beam carrying a lumped rotary inertial-rotational spring was investigated by Hozhabrossadati et al. 33 Also, much of research works have been done in the field of vibration analysis of structures. 20,22,23,34–44…”

Section: Introductionmentioning

confidence: 99%

Influence of system parameters on buckling and frequency analysis of a spinning cantilever cylindrical 3D shell coupled with piezoelectric actuator

Shokrgozar

Safarpour

Habibi

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this research, buckling and vibrational characteristics of a spinning cylindrical moderately thick shell covered with piezoelectric actuator carrying spring-mass systems are performed. This structure rotates about axial direction and the formulations include the Coriolis and centrifugal effects. In addition, various cases of thermal (uniform, linear, and nonlinear) distributions are studied. The modeled cylindrical moderately thick shell covered with piezoelectric actuator, its equations of motion, and boundary conditions are derived by the Hamilton's principle and based on a moderately cylindrical thick shell theory. For the first time in the present study, attached mass-spring systems has been considered in the rotating cylindrical moderately thick shells covered with piezoelectric actuator. The accuracy of the presented model is verified with previous studies. The novelty of the current study is consideration of the applied voltage, rotation, various temperature distributions, and mass-spring systems implemented on proposed model using moderately cylindrical thick shell theory. Generalized differential quadrature method is examined to discretize the model and to approximate the governing equations. In this study, the simply supported conditions have been applied to edges [Formula: see text] and cantilever (clamped–free) boundary conditions has been studied in x = 0, L, respectively. Finally, the effects of the applied voltage, angular velocity, temperature changes, and spring-mass systems on the critical voltage, critical angular speed, critical temperature, and natural frequency of the structure are investigated.

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Vibration of Beam with Elastically Restrained Ends and Rotational Spring-Lumped Rotary Inertia System at Mid-Span

Cited by 7 publications

References 18 publications

Analyzing free vibration of a double-beam joined by a three-degree-of-freedom system

Analyzing free vibration of a double-beam joined by a three-degree-of-freedom system

Natural characteristics for transverse vibration of Euler Bernoulli beams with variable end constraints

Influence of system parameters on buckling and frequency analysis of a spinning cantilever cylindrical 3D shell coupled with piezoelectric actuator

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