**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**12

# Search results for: Timoshenko beam theory

##### 12 Forced Vibration of a Planar Curved Beam on Pasternak Foundation

**Authors:**
Akif Kutlu,
Merve Ermis,
Nihal Eratlı,
Mehmet H. Omurtag

**Abstract:**

The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted.

**Keywords:**
Curved beam,
dynamic analysis,
elastic foundation,
finite element method.

##### 11 Free Vibration Analysis of Conical Helicoidal Rods Having Elliptical Cross Sections Positioned in Different Orientation

**Authors:**
Merve Ermis,
Akif Kutlu,
Nihal Eratlı,
Mehmet H. Omurtag

**Abstract:**

**Keywords:**
Conical helix,
elliptical cross section,
finite element,
free vibration.

##### 10 Static and Dynamic Analysis of Hyperboloidal Helix Having Thin Walled Open and Close Sections

**Authors:**
Merve Ermis,
Murat Yılmaz,
Nihal Eratlı,
Mehmet H. Omurtag

**Abstract:**

The static and dynamic analyses of hyperboloidal helix having the closed and the open square box sections are investigated via the mixed finite element formulation based on Timoshenko beam theory. Frenet triad is considered as local coordinate systems for helix geometry. Helix domain is discretized with a two-noded curved element and linear shape functions are used. Each node of the curved element has 12 degrees of freedom, namely, three translations, three rotations, two shear forces, one axial force, two bending moments and one torque. Finite element matrices are derived by using exact nodal values of curvatures and arc length and it is interpolated linearly throughout the element axial length. The torsional moments of inertia for close and open square box sections are obtained by finite element solution of St. Venant torsion formulation. With the proposed method, the torsional rigidity of simply and multiply connected cross-sections can be also calculated in same manner. The influence of the close and the open square box cross-sections on the static and dynamic analyses of hyperboloidal helix is investigated. The benchmark problems are represented for the literature.

**Keywords:**
Hyperboloidal helix,
squared cross section,
thin walled cross section,
torsional rigidity.

##### 9 Out-of-Plane Free Vibrations of Circular Rods

**Authors:**
Faruk Fırat Çalım,
Nurullah Karaca,
Hakan Tacettin Türker

**Abstract:**

**Keywords:**
Circular rod,
Out-of-plane free vibration analysis,
Transfer Matrix Method.

##### 8 Vibration Analysis of Functionally Graded Engesser- Timoshenko Beams Subjected to Axial Load Located on a Continuous Elastic Foundation

**Authors:**
M. Karami Khorramabadi,
A. R. Nezamabadi

**Abstract:**

This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

**Keywords:**
Functionally Graded Beam,
Free Vibration,
Elastic
Foundation,
Engesser-Timoshenko Beam Theory.

##### 7 Mechanical Buckling of Functionally Graded Engesser-Timoshenko Beams Located on a Continuous Elastic Foundation

**Authors:**
M. Karami Khorramabadi,
A. R. Nezamabadi

**Abstract:**

**Keywords:**
Mechanical Buckling,
Functionally graded beam- Engesser-Timoshenko beam theory

##### 6 Dynamic Response of Strain Rate Dependent Glass/Epoxy Composite Beams Using Finite Difference Method

**Authors:**
M. M. Shokrieh,
A. Karamnejad

**Abstract:**

**Keywords:**
Composite beam,
Finite difference method,
Progressive damage modeling,
Strain rate.

##### 5 Mechanical Buckling of Engesser-Timoshenko Beams with a Pair of Piezoelectric Layers

**Authors:**
A. R. Nezamabadi,
M. Karami Khorramabadi

**Abstract:**

**Keywords:**
Mechanical Buckling,
Engesser-Timoshenko
beam theory - Piezoelectric layer.

##### 4 Vibration Suppression of Timoshenko Beams with Embedded Piezoelectrics Using POF

**Authors:**
T. C. Manjunath,
B. Bandyopadhyay

**Abstract:**

**Keywords:**
Smart structure,
Timoshenko beam theory,
Periodic
output feedback control,
Finite Element Method,
State space model,
SISO,
Embedded sensors and actuators,
Vibration control.

##### 3 Modeling and FOS Feedback Based Control of SISO Intelligent Structures with Embedded Shear Sensors and Actuators

**Authors:**
T. C. Manjunath,
B. Bandyopadhyay

**Abstract:**

**Keywords:**
Smart structure,
Timoshenko beam theory,
Fast output sampling feedback control,
Finite Element Method,
State space model,
SISO,
Vibration control,
LMI

##### 2 Multivariable Control of Smart Timoshenko Beam Structures Using POF Technique

**Authors:**
T.C. Manjunath,
B. Bandyopadhyay

**Abstract:**

**Keywords:**
Smart structure,
Timoshenko theory,
Euler-Bernoulli
theory,
Periodic output feedback control,
Finite Element Method,
State space model,
Vibration control,
Multivariable system,
Linear
Matrix Inequality

##### 1 Mathematical Modeling of SISO based Timoshenko Structures – A Case Study

**Authors:**
T.C. Manjunath,
Student Member,
B. Bandyopadhyay

**Abstract:**

This paper features the mathematical modeling of a single input single output based Timoshenko smart beam. Further, this mathematical model is used to design a multirate output feedback based discrete sliding mode controller using Bartoszewicz law to suppress the flexural vibrations. The first 2 dominant vibratory modes is retained. Here, an application of the discrete sliding mode control in smart systems is presented. The algorithm uses a fast output sampling based sliding mode control strategy that would avoid the use of switching in the control input and hence avoids chattering. This method does not need the measurement of the system states for feedback as it makes use of only the output samples for designing the controller. Thus, this methodology is more practical and easy to implement.

**Keywords:**
Smart structure,
Timoshenko beam theory,
Discretesliding mode control,
Bartoszewicz law,
Finite Element Method,
State space model,
Vibration control,
Mathematical model,
SISO.