Journal ArticleDOI
Apparently first closed-form solution for vibrating: inhomogeneous beams
Isaac Elishakoff,S. Candan +1 more
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TLDR
In this article, the fundamental natural frequency of non-uniform beams with non-homogeneous material density and elastic modulus along their axis has been studied under various boundary conditions.About:
This article is published in International Journal of Solids and Structures.The article was published on 2001-05-01. It has received 81 citations till now. The article focuses on the topics: Elastic modulus & Elasticity (physics).read more
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Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory
Bekir Akgöz,Ömer Civalek +1 more
TL;DR: In this article, the vibration response of non-homogenous and non-uniform microbeams is investigated in conjunction with Bernoulli-Euler beam and modified couple stress theory, where boundary conditions of the microbeam are considered as fixed at one end and free at the other end.
Journal ArticleDOI
A new approach for free vibration of axially functionally graded beams with non-uniform cross-section
Yong Huang,Xian-Fang Li +1 more
TL;DR: In this article, a simple approach is presented to solve natural frequencies of free vibration of axially functionally graded beams with non-uniform cross-section for various end supports including simply supported, clamped, and free ends.
Journal ArticleDOI
Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions
TL;DR: In this article, the free vibration and stability analysis of axially functionally graded tapered Timoshenko beams is studied through a finite element approach, where exact shape functions for uniform homogeneous Timoshenko beam elements are used to formulate the proposed element.
Journal ArticleDOI
Free vibration and stability of tapered Euler–Bernoulli beams made of axially functionally graded materials
TL;DR: In this paper, the free vibration and stability of axially functionally graded tapered Euler-Bernoulli beams were studied through solving the governing differential equations of motion. But, the convergence rate of the conventional differential transform method (DTM) does not necessarily converge to satisfactory results, and a new approach based on DTM called differential transform element method (DTEM) is introduced which considerably improves the convergence of the method.
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Free vibration of axially functionally graded Timoshenko beams with non-uniform cross-section
TL;DR: In this paper, a new approach for investigating the vibration behaviors of axially functionally graded Timoshenko beams with non-uniform cross-section is presented. And the derived characteristic equation is a polynomial equation, where the lower and higher-order natural frequencies can be determined simultaneously from the multi-root.
References
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Journal ArticleDOI
Inverse Problems in Vibration
TL;DR: In this article, a review of the literature on inverse problems relating to the reconstruction or estimation of the physical properties of mechanical systems from a knowledge of (some of) their spectral and/or modal data is presented.
Book
Inverse Problems in Vibration
TL;DR: In this paper, a review of the literature on inverse problems relating to the reconstruction or estimation of the physical properties of mechanical systems from a knowledge of (some of) their spectral and/or modal data is presented.
Journal ArticleDOI
Vibration of non-uniform rods and beams
TL;DR: In this article, it was shown that for some non-uniform rods and beams the equation of motion can be transformed into the equation for a uniform rod or beam, and when the ends are completely fixed, the eigenvalues of the nonuniform continuum are the same as those of uniform rods or beams.
Journal ArticleDOI
The eigenvalue problem for structural systems with statistical properties.
TL;DR: In this paper, the treatment of matrix eigenvalue problems with statistical properties is presented in a general form including correlation between matrix elements and linear equations are formulated for the statistics of the eigenvectors as well as eigenvalues.
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A new approach for free vibration of axially functionally graded beams with non-uniform cross-section
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