Plane waves in linear elastic materials with voids

Abstract

The behavior of plane harmonic waves in a linear elastic material with voids is analyzed. There are two dilational waves in this theory, one is predominantly the dilational wave of classical linear elasticity and the other is predominantly a wave carrying a change in the void volume fraction. Both waves are found to attenuate in their direction of propagation, to be dispersive and dissipative. At large frequencies the predominantly elastic wave propagates with the classical elastic dilational wave speed, but at low frequencies it propagates at a speed less than the classical speed. It makes a smooth but relatively distinct transition between these wave speeds in a relatively narrow range of frequency, the same range of frequency in which the specific loss has a relatively sharp peak. Dispersion curves and graphs of specific loss are given for four particular, but hypothetical, materials, corresponding to four cases of the solution.

A nonlinear model of thermoelastic beams with voids, with applications

“…In Table 1 we give the effects of the node distribution on the DQ solution of the dimensionless deflection and void moment at the middle point of the beam for four different materials. The parameters are chosen as follows (see [Puri and Cowin 1985;Kumar and Rani 2005]): β 1 = 0.1, a 1 = 0.33, a 2 = 0.027, a 3 = 5, a 4 = 6, a 11 = 4.56 × 10 6 , θ 0 = 10,p = 0.0001.…”

“…The Runge-Kutta method of fourth order is used to solve the nonlinear dynamical system (25)-(27) numerically, to obtain time-history curves of the corresponding variables at the middle point of the beam. In computation, setting N = 15, the parameters are given as follows (see [Puri and Cowin 1985;Kumar and Rani 2005] For comparison, the time-history curves of the deflection for four beams (EB, TEB, EVB, TEVB) are presented in Figure 10a, and those of the thermal moment for TEB and TEVB are shown in Figure 10b. It can be observed that the presence of voids enlarges beam deflection, while the thermal effect is the opposite: maybe the external work is partially transformed to thermal energy and dissipated.…”

“…Iesan [1986] developed a linear theory of thermoelastic materials with voids. Puri and Cowin [1985] studied the behavior of plane waves in linear elastic materials with voids. Chirit ,ȃ and Scalia [2001] considered the spatial and temporal behaviors in linear thermoelasticity of materials with voids.…”

Gravitational effect on surface waves in a homogeneous fibre-reinforced anisotropic general viscoelastic media of higher and fractional order with voids

“…Nunziato and Cowin (1979) and Cowin and Nunziato (1983) discussed the theory in elastic media with voids. Puri and Cowin (1985) studied the effects of voids on plane waves in linear elastic media and it is evident that pure shear waves remain unaffected by the presence of pores. Theory of thermoelastic material with voids is investigated by Lesan (1986).…”

Fundamental Solution in Micropolar Viscothermoelastic Solids with Void

“…Cowin and Nunziato (1983) established the linear theory of elasticity with voids, while Nunziato and Cowin (1979) derived the non-linear theory of elastic materials with voids. Puri and Cowin (1985) studied the behavior of plane harmonic waves in linear elastic materials with voids. Chandrasekharaiah (1987a;b) investigated the effect of voids on Rayleigh-Lamb waves in a homogeneous elastic plate with voids.…”