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The theory of mechanical-vibration energy harvesting from the environment has been studied by researchers in the recent decade. In the present research, the vibration of the viscoelastic cantilever beam was analyzed with two piezoelectric layers including series and parallel connections. The beam was exposed under moving and rotating base excitation and aeroelastic force. The beam viscoelastic material was described using the generalized Kelvin-Voigt mechanical model. The aero-elastic force based on piston theory is considered while the base excitation is selected harmonic and randomly. The stress field coupling among the beam and piezoelectric as well as Gauss equation were utilized to extract the vibration and electrical equations respectively. The vibratory equation was converted into a set of ordinary differential equations using the Galerkin approach. The obtained equations with electrical equation were solved by the Runge-Kutta method numerically. Then, by studying the response of the governing equations, the effect of system parameters on the vibrational behavior of the beam and the output voltage was investigated. The results showed that the system and response frequencies are not affected via circuit connection types (series or parallel). The natural vibratory frequency is increased with enhancing the beam stiffness. The structural damping has a significant effect on the output voltage value. Also, the output voltage is increased by enhancing the environmental pressure. [ABSTRACT FROM AUTHOR]

In this article, the flexural sensitivity and flexural resonant frequency of the atomic force microscope made of functionally graded materials is investigated by modified couple stress theory (MCST). In MCST, the size effect of the system is taking into account by means of the material length scale parameter. Microbeam is made of a mixture of metal and ceramic with properties varying through the thickness following a simple power law of n. In this work, due to the kinematic energy and potential energy of microbeam, the governing equations of motion and corresponding boundary conditions are derived on the basis of Hamilton principle by considering Euler-Bernoulli beam theory. Based on the results, it is clear that when the contact stiffness increases, the flexural sensitivity of the system decreases, and flexural resonant frequency increases. Moreover, when the microbeam thickness comes approximately close to material length scale parameter, the difference between MCST and classical continuum mechanic becomes significant. Furthermore, in low contact stiffness, increasing the power n reduces the flexural sensitivity of microbeam, while in high contact stiffness, increasing the power n increases the flexural sensitivity of the system. Results also show that at each value of contact stiffness, as ceramic volume fraction increases the flexural resonant frequency will be increased, too. [ABSTRACT FROM AUTHOR]

In this paper based on the Euler-Bernoulli beam model, the primary resonance a curved single carbon nanotube subjected to axial thermal force in the case of low temperature and high temperature and resting on a viscoelastic foundation is analytically investigated. The nonlinear partial differential governing equation is reduced to nonlinear ordinary differential governing equation by using of a single-mode Galerkin approximation along with the sinusoidal curvature for clamped-clamped single walled carbon nanotube under harmonic external force. The method of multiple scales is applied to determine the analytical primary resonance frequency response. Considering the curved geometry and the mid-plane stretching, a quadratic and cubic terms are presented in the governing equation. The effects of temperature change in high temperature and low temperature conditions, viscoelastic coefficients of medium, amplitude of sinusoidal curvature and excitation amplitude are investigated to study the property frequency response and development or elimination of forward and backward jumping phenomenon in primary resonance frequency response. The results show that these parameters have a significant effect on the frequency response of a curved single walled carbon nanaotubes under transvers harmonic force. [ABSTRACT FROM AUTHOR]

In this paper, a sandwich beam of a SMP material which have a corrugated core is studied. The corrugated core is from a polymeric material. Structures with corrugated profiles show higher stiffnessto-mass ratio in the transverse to corrugation direction compared to flat structures. As a result, the beam with corrugation along the transverse direction is stiffer than the one with corrugation along the beam length. The flexural behavior of the composite corrugated beam is studied employing a developed constitutive model for SMP and the Euler-Bernoulli beam theory. The constitutive model utilized is in integral form and is discretized employing finite difference scheme. To verify the results of the EulerBernoulli beam theory and finite difference method, finite element models of different corrugated sections have been simulated in a 3D finite element program. The results demonstrate that the developed model for the composite beam presented in this study predicts the behavior of the beam successfully. The sandwich beam with different corrugated cores (triangular, sinusoidal and trapezoidal shapes) are compared with each other. Also, results show that the shape fixity is decreased a little, like any other reinforcing method. This decrease in shape fixity results in increase of load capacity in composite beams. The stress-free strain recovery and constrained stress-recovery cycles are both studied. [ABSTRACT FROM AUTHOR]

Fractional calculus is a branch of mathematics which in recent decades has been of great interest to scientists in various disciplines, including engineering. One of the applications of this branch in engineering is in modeling the viscoelastic materials using fractional differentiation. In this article, by inserting fractional calculus as viscoelastic material compatibility equations in nonlocal beam theory, a viscoelastic Euler-Bernoulli nano-beam with different boundary conditions at two ends has been modeled. Material properties of a carbon nanotube are considered and two methods, pure numerical and numerical-analytical have been used for solving obtained equations in time domain. The main method is completely numerical and operator matrices used it to discrete equations in time and spatial domain. The second method is introduced for validation of the previous method's answers. In this method, equation of system is reduced to an ordinary differential equation using Galerkin and the obtained equation is solved using a numerical direct integrator method. Finally, in a case study, the effects of fractional order, viscoelasticity coefficient and nonlocal theory coefficient on the time response of the viscoelastic Euler-Bernoulli nanobeam with different boundary conditions have been studied. [ABSTRACT FROM AUTHOR]

In this article, an improved 3D finite element (FE) model of low velocity transverse impact on armchair and zigzag single-walled carbon nanotubes (SWNTs) has been developed. Numerical examples for estimating the Young's modulus of nanotubes are presented based on explicit and implicit analysis to illustrate the accuracy of this simulation technique. Based on explicit finite element model, maximum dynamic deflections of single-walled carbon nanotubes with different boundary conditions, geometries, as well as chiralities are obtained and then compared with theory investigation. Impact of mass on simply supported and clamped nanobeams is investigated by using nonlocal Euler-Bernoulli and Timoshenko beam theory. The simulation results demonstrated good agreement with analytical results based on Euler-Bernoulli and Timoshenko nonlocal theory. When aspect ratio is increased, maximum dynamic deflection at the center of the beam is increased for both the simply supported and the clamped-clamped nanobeams. The inclusion of the nonlocal effect increases the magnitudes of dynamic deflections. The dynamic deflections predicted by the classical theory are always smaller than those predicted by the nonlocal theory due to the nonlocal effects. [ABSTRACT FROM AUTHOR]

A vibration absorber is used to reduce vibration of an Euler-Bernoulli beam with elastic supports subjected to a moving oscillator. Dynamic response of the beam under moving harmonic exciter with different moving velocities and different parameters are obtained. The critical velocity of the moving oscillator is determined and absorber parameters are optimized by numerical algorithm and effect of mass and damping on the absorber performance is investigated. When absorber is applied to the beam, effect of crack occurrence on its performance is investigated. Crack is assumed to be open and is modeled by sectional flexibility increase. Two different cases considered for crack severity. In each case, optimal absorber for intact beam is applied and dynamic response of the midpoint of the beam with different velocities of moving exciter is obtained. Results show although crack can increase dynamic deflection of the beam with absorber, dynamic deflection of cracked beam without considering absorber is higher than dynamic deflection of cracked beam with absorber used. It is found that the vibration absorber designed for intact beam keeps its performance in dynamic deflection reduction after crack occurrence and changing in structural dynamic. [ABSTRACT FROM AUTHOR]