R.B. Bhat

NATURAL FREQUENCIES OF RECTANGULAR PLATES USING CHARACTERISTIC ORTHOGONAL POLYNOMIALS IN RAYLEIGH-RITZ METHOD

Natural frequencies of rectangular plates are obtained by employing a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method. The orthogonal polynomials are generated by using a Gram-Schmidt process, after the first member is constructed so as to satisfy all the boundary conditions of the corresponding beam problems accompanying the plate problems. Natural frequencies obtained by using the orthogonal polynomial functions are compared with those obtained by other methods. The method yields superior results for lower modes, particularly when plates have some of the edges free.

Transverse vibrations of a rotating uniform cantilever beam with tip mass as predicted by using beam characteristic orthogonal polynomials in the Rayleigh-Ritz method

Abstract Natural frequencies and mode shapes of a rotating uniform cantilever beam with a tip mass are studied by using beam characteristic orthogonal polynomials in the Rayleigh-Ritz method. The set of orthogonal polynomials which satisfy the geometrical boundary conditions are generated by using the Gram-Schmidt process. The results are compared with those obtained by the Myklestad method, the extended Galerkin method and finite element methods. The variation of natural frequencies with the speed of rotation is plotted for several parameter combinations such as setting angle, tip mass, moment of inertia of tip mass, etc. Mode shapes at different rotational speeds are also plotted. Use of orthogonal polynomials for the deflection shapes enables the computation of higher natural frequencies of any order to be accomplished without facing any numerical difficulties, which is not the case when arbitrary polynomial expressions are used.

Flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables

A set of characteristic orthogonal polynomials in two variables is used as deflection functions to obtain the natural frequencies and mode shapes of polygonal plates by the Rayleigh-Ritz method. The set of orthogonal polynomials is constructed by employing the Gram-Schmidt orthogonalization procedure. The first six natural frequencies are numerically evaluated for triangular plates of different configurations by using these orthogonal functions and the corresponding mode shapes are plotted. Results are compared with those obtained previously by other methods.

Interdigitated comb-like electrodes for continuous separation of malignant cells from blood using dielectrophoresis.

In this paper, a method for continuous flow separation of circulating malignant cells from blood in a microfluidic device using dielectrophoresis is discussed. Separation of MDA231 breast cancer cells after mixing with normal blood cells was achieved with a level of accuracy that enabled precise counting of the malignant cells, separation and eventually, sub‐culturing. MDA231 cells were separated from the blood to a daughter channel using two pairs of interdigitated activated comb‐like electrode structures. All experiments are performed with conductivity adjusted medium samples. The electrode pairs were positioned divergent and convergent with respect to the flow. The AC signals used in the separation are 20 V peak‐to‐peak with frequencies of 10–50 kHz. The separation is based on balance of magnitude of the dielectrophoretic force and hydrodynamic force. The difference in response between circulating malignant cells and normal cells at a certain band of alternating current frequencies was used for rapid separation of cancer cells from blood. The significance of these experimental results is discussed in this paper, with detailed reporting on the suspension medium, preparation of cells, flow condition and the fabrication process of the microfluidic chip. The present technique could potentially be applied to identify incident cancer at a stage and size that is not yet detectable by standard diagnostic techniques (imaging and biochemical testing). Alternatively, it may also be used to detect cancer recurrences.

Numerical experiments on the determination of natural frequencies of transverse vibrations of rectangular plates of non-uniform thickness

Abstract A comparison of natural frequencies of transverse vibration of thin, rectangular plates of non-uniform thickness with different combinations of boundary conditions is presented in this paper, as obtained by using the following methodologies: (1) the Rayleigh-Ritz method with characteristic orthogonal polynomial shape functions; (2) the Rayleigh-Ritz method with a shape function which includes two exponents that are to be determined by minimizing the fundamental frequency coefficient; (3) the optimized Kantorovich method which has been proposed rather recently; (4) the finite element method. The results are presented in tabular form and discussed.

Quantification of cellular penetrative forces using lab-on-a-chip technology and finite element modeling.

Tip-growing cells have the unique property of invading living tissues and abiotic growth matrices. To do so, they exert significant penetrative forces. In plant and fungal cells, these forces are generated by the hydrostatic turgor pressure. Using the TipChip, a microfluidic lab-on-a-chip device developed for tip-growing cells, we tested the ability to exert penetrative forces generated in pollen tubes, the fastest-growing plant cells. The tubes were guided to grow through microscopic gaps made of elastic polydimethylsiloxane material. Based on the deformation of the gaps, the force exerted by the elongating tubes to permit passage was determined using finite element methods. The data revealed that increasing mechanical impedance was met by the pollen tubes through modulation of the cell wall compliance and, thus, a change in the force acting on the obstacle. Tubes that successfully passed a narrow gap frequently burst, raising questions about the sperm discharge mechanism in the flowering plants.

Optimized Control of Semiactive Suspension Systems Using H

In this paper, an optimized modified skyhook control for the semiactive Macpherson suspension system, equipped with a magnetorheological (MR) damper, is investigated. Using H∞ robust control theory and a 2-D dynamic model, including the kinematics of the suspension system, a robust output feedback controller is developed. The combination of a linear matrix inequality (LMI) solver and genetic algorithm (GA) is adopted to optimize the control gains. Further a 3-D kinematic model is introduced to evaluate the kinematic performance of the controlled suspension system. An inverse dynamic model of the MR damper is obtained based on the experimental results for tuning the input current signal. The effectiveness of the control system is discussed and validated through the simulations and experiment.

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Vibration analysis of arbitrary shaped structures has been of interest to structural designers for several decades. Dynamic behavior of these structures is strongly dependent on boundary conditions, geometrical shapes, material properties, different theories, and various complicating effects. Closed-form solutions are possible only for a limited set of simple boundary conditions and geometries. For analysis of arbitrary shaped structures, several numerical methods, such as finite element method, finite difference method, boundary element method, and so on, are usually applied. Although such discretization methods provide a general framework for general structures, they invariably result in problems with a large number of degrees of freedom. This deficiency is overcome by using the Rayleigh-Ritz method. Recently, a tremendous amount of work has been done by using the newly developed method of boundary characteristic orthogonal polynomials, first proposed in 1985, with the Rayleigh-Ritz method. This method provides better accuracy of results, is more efficient and simple, and is easier for computer implementation. This paper gives a survey of the research that has been done for the analysis of vibration of various structures with different effects using this method. More than a hundred papers have been reported and discussed that use this method over the past 12 years.

Robust Control Theory and Current Signal Estimation

Abstract Automatic balancing of flexible vertical rotors using a ball guided to move freely in a circular groove housed in the rotor disk is studied. The dynamic interaction between the balancing ball and the rotor is investigated using an undamped three-degrees-of-freedom system model in a rotating reference frame. The centrifugal force on the balancing-ball moves it to a relative rest position in the groove and thereby modifies the effective rotor unbalance. The stability of balancing ball position during the rotor whirling motion is analyzed and the conditions under which the unbalanced rotor vibration can be neutralized by the automatic balancer are identified. The stability results are presented graphically to facilitate an effective automatic balancer design. The results show that the automatic balancer can neutralize the unbalance whirling motion of the rotor, when operated at speeds higher than its critical speed.

Recent Research on Vibration of Structures Using Boundary Characteristic Orthogonal Polynomials in the Rayleigh-Ritz Method

Abstract A five-degrees-of-freedom (DOF) bio-mechanical model of the hand-arm system is developed to study the vibration transmissibility characteristics of the human hand-arm. The model parameters are identified from the characteristics of vibration transmitted to the hand, forearm and upper arm, measured in the 10–200 Hz frequency range under a constant 25.0 N grip force. A concept of an energy flow divider is proposed to reduce the flow of vibration energy into the hand. The coupled hand-arm-divider is modeled as a six-DOF dynamical system and the response characteristics are evaluated for handle excitations caused by a palm-grip orbital sander. The response characteristics of the coupled hand-arm-divider model are compared to those of the hand-arm model to demonstrate the potential performance benefits of the proposed energy flow divider. The hand-transmitted vibration is further assessed using the overall weighted acceleration response, and it is concluded that the proposed energy flow divider can reduce the magnitude of hand-transmitted vibration considerably.