Assessment of the fundamental natural frequency of bridge decks

2019 ◽  
Vol 20 (7) ◽  
pp. 933-948
Author(s):  
Farnoush Karimi ◽  
Reza Akbari ◽  
Shahrokh Maalek
Keyword(s):  
Natural Frequency ◽  
Bridge Decks ◽  
Fundamental Natural Frequency

Component Rearrangement on Printed Wiring Boards to Maximize the Fundamental Natural Frequency

1993 ◽  
Vol 115 (3) ◽  
pp. 312-321 ◽  
Author(s):  
Tien-Sheng Chang ◽  
E. B. Magrab
Keyword(s):  
Simulated Annealing ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Printed Wiring Board ◽  
Computationally Efficient ◽  
Additional Increase ◽  
Simulated Annealing Method ◽  
Fundamental Natural Frequency ◽  
Rearrangement Algorithm ◽  
Annealing Method

A methodology to attain the highest fundamental natural frequency of a printed wiring board by rearranging its components has been developed. A general two-dimensional rearrangement algorithm is developed by which the rearrangement of the component-lead-board (CLB) assemblies is performed automatically for any combination of equal size, unequal size, movable and immovable CLBs. This algorithm is also capable of incorporating two design restrictions: fixed (immovable) components and prohibited (non-swappable) areas. A highly computationally efficient objective function for the evaluation of the automatic rearrangement process is introduced, which is a linear function of the size of the individual CLBs that have been selected for each interchange. The simulated annealing method is adapted to solve the combinatorial rearrangement of the CLBs. Using 61 combinations of boundary conditions, equal and unequal sized CLBs, movable and immovable CLBs, various CLB groupings and sets of material properties, it is found that, when compared to the exact solution obtained by an exhaustive search method, the simulated annealing method obtained the highest fundamental natural frequency within 1 percent for 87 percent of the cases considered, within 0.5 percent for 72 percent of the cases and the true maximum in 43 percent of them. To further increase the fundamental natural frequency the introduction of a single interior point support is analyzed. Depending on the boundary conditions an additional increase in the maximum fundamental natural frequency of 44 to 198 percent can be obtained.

An integrated numerical–experimental study on the optimum utilization of carbon nanotubes in laminated composites

2016 ◽  
Vol 19 (2) ◽  
pp. 231-258 ◽  
Author(s):  
Mahmood Heshmati ◽  
Bandar Astinchap ◽  
Masoud Heshmati ◽  
Mohammad Hosein Yas ◽  
Yasser Amini
Keyword(s):  
Carbon Nanotubes ◽  
Natural Frequency ◽  
Experimental Studies ◽  
Distribution Patterns ◽  
Weight Percent ◽  
Composite Beams ◽  
Linear Distribution ◽  
Fundamental Natural Frequency ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this paper, a set of numerical and experimental studies are performed to improve mechanical and vibrational properties of carbon nanotubes-reinforced composites. First, at a design concept level, linear distribution patterns of multi-walled carbon nanotubes through the thickness of a typical beam is adopted to investigate its fundamental natural frequency for a given weight percent of multi-walled carbon nanotubes. Both Timoshenko and Euler-Bernoulli beam theories are used in the derivation of the governing equations. The finite element method is employed to obtain a numerical approximation of the motion equation. Next, based on the introduced distribution patterns, laminated multi-walled carbon nanotubes-reinforced polystyrene-amine composite beams are fabricated. Static and experimental modal tests are performed to measure the effective stiffness and fundamental natural frequencies of the fabricated composite beams. Also, in order to generate realistic model to investigate the material properties of fabricated composite beams, the actual tensile specimens of multi-walled carbon nanotubes/polystyrene-amine composites are successfully fabricated and the tensile behaviors of both pure matrix and composites are investigated. To better interfacial bonding between carbon nanotubes and polymer, a chemical treatment is performed on carbon nanotubes. It is seen that the addition of a few wt. % of multi-walled carbon nanotubes make considerable increase in the Young's modulus and the tensile strength of the composite. It is observed from the free vibration tests that the uniform distribution of multi-walled carbon nanotubes results in an increase of 9.5% in the fundamental natural frequency of the polymer cantilever beam, whereas using the symmetric multi-walled carbon nanotube distribution increased its fundamental natural frequency by 17.32%.

Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

1996 ◽  
Vol 118 (2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Abrate
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Composite Structures ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Fundamental Natural Frequency ◽  
Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

Free and Forced Longitudinal Vibrations of a Cantilevered Bar With a Crack

1992 ◽  
Vol 114 (2) ◽  
pp. 171-177 ◽  
Author(s):  
K. R. Collins ◽  
R. H. Plaut ◽  
J. Wauer
Keyword(s):  
Steady State ◽  
Natural Frequency ◽  
Transverse Crack ◽  
Breathing Crack ◽  
Longitudinal Vibrations ◽  
Harmonic Force ◽  
Frequency Spectra ◽  
Crack Location ◽  
Fundamental Natural Frequency ◽  
Steady State Amplitude

Longitudinal vibrations of a cantilevered bar with a transverse crack are investigated. For undamped, unforced vibrations, frequency spectra are computed and the effects of the crack location and compliance on the fundamental natural frequency are determined. For vibrations caused by a distributed, longitudinal, harmonic force, the steady-state amplitude of motion of the free end is plotted as a function of the forcing frequency, crack location, and crack compliance, and frequency spectra are also obtained. Results for a breathing crack are compared to those for a crack which remains open and those for an uncracked bar.

Tapered Beam Fundamental Natural Frequency Based on Rayleigh Quotient

2013 ◽  
Vol 330 ◽  
pp. 526-530 ◽  
Author(s):  
Farid Chalah ◽  
Salah Eddine Djellab ◽  
Kamel Falek ◽  
Lila Chalah-Rezgui ◽  
Abderrahim Bali
Keyword(s):  
Natural Frequency ◽  
Order Differential Equation ◽  
Rayleigh Quotient ◽  
Beam Element ◽  
Functional Design ◽  
Linear Mass ◽  
Fixed Boundary ◽  
Tapered Beam ◽  
Fundamental Natural Frequency ◽  
Constant Coefficients

Different continuous variations in the inertia are considered in achieving cantilever tapered beams to match functional design and resistance requirements. In this investigation, the expressions of linear and cubic variations in the inertia are associated to a linear mass distribution. An exact solution of the fourth order differential equation, with none constant coefficients governing the studied tapered beam element equilibrium, is obtained for each case. These displacements functions are normalized and introduced in the well known Rayleigh quotient formula for calculating the fundamental natural frequency. The accuracy of the approach over the use of the above approximation has been validated by beam references results, produced quite interesting results in numerical comparisons. Also, two curves corresponding to fixed-free and free-fixed boundary conditions, for a graphical evaluation of the natural frequency are given. They consider various degrees of taper corresponding to the two inertia variations.

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