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Abstract. Vibratory Finishing is a commonly used process for deburring and polishing. The process effectiveness is difficult to quantify due to a nexus of variables relating to workpiece, media, compound and machine. In this paper, effect of orientation of rectangular Al6061 workpieces is considered with respect to the motion of ceramic media using water as lubricant. It is found that parallel orientation of workpiece to media motion and higher lubrication level lead to higher degree of sliding, thereby leading to smoother finish. Experiments with different ceramic media showed smoother finish with the geometry more susceptible to rounding. The aforesaid findings can be employed in applications requiring superpolished surfaces.

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The study of approximation properties of the periodic functions in Lp (p ≥ 1)-spaces, in general and in Lipschitz classes Lip α, Lip (α, p), Lip (ξ(t), p) and weighted Lipschitz class W(Lp, ω(t), β), in particular, through trigonometric Fourier series, although is an old problem and known as Fourier approximation in the existing literature, has been of a growing interests over the last four decades due to its application in filters and signals [E. Z. Psarakis and G. V. Moustakides, An L2-based method for the design of 1-D zero phase FIR digital filters, IEEE Trans. Circuits Systems I Fundam. Theory Appl., 44(7) (1997) 551–601]. The most common methods used for the determination of the degree of approximation of periodic functions are based on the minimization of the Lp-norm of f(x) - Tn(x), where Tn(x) is a trigonometric polynomial of degree n and called approximant of the function f. In this paper, we discuss the approximation properties of the periodic functions in the Lipschitz classes Lip α and W(Lp , ω(t), β), p ≥ 1 by a trigonometric polynomial generated by the product matrix means of the Fourier series associated with the function. The degree of approximation obtained in our theorems of this paper is free from p and sharper than earlier results.

Introduction Acoustic-Gravity Waves From EarthquakesIonospheric disturbances following seismic events arising due to surface-atmosphere coupling have been studied previously (Calais & Minster, 1995;K. Davies & Baker, 1965). Earthquakes result in vertical and horizontal ground displacement. Normal and reverse thrust fault earthquakes result in mostly vertical while strike-slip faults result in mostly horizontal displacement. These ground movements can induce acoustic-gravity waves in the atmosphere (Rolland, Lognonné, & Munekane, 2011;Rolland, Occhipinti, et al., 2010). Waves originating from the source region first propagate obliquely upward and then spread horizontally as acoustic-gravity waves (Mikumo & Watada, 2010).There are four different pathways for atmospheric wave generation due to earthquakes (Mikumo & Watada, 2010;Occhipinti, 2016;ReVelle, 2008). The first is low-frequency (less than Brunt-Väisälä frequency) gravity waves generated at the source and propagating upward to long distances (Afraimovich, Perevalova, et al., 2001). The second one is higher-frequency infrasonic or acoustic waves (higher than acoustic cutoff frequency) also generated at the source (Bolt, 1964). These infrasonic waves can get reflected or diffracted due to topography (Young & Greene, 1982) or sound velocity variations (Drob, Picone, & Garcés, 2003) during propagation. The third case is also infrasonic waves but generated due to coupling of atmosphere with seismic Rayleigh waves along the ground surface (Donn & Posmentier, 1964). Coupling of the atmosphere with Rayleigh surface waves is found to be most effective at frequency ∼3.7 mHz. Ionospheric disturbances corresponding to Rayleigh waves travel at ∼3-4.5 km/s, much higher than direct acoustic waves from the source (∼1 km/s at 400 km altitude) (Ducic et al., 2003;Heki & Ping, 2005). Thus, two kinds of acoustic infrasonic waves are generated by earthquakes (Le Pichon et al., 2002). Some simulations (Artru et al., 2005) suggest that trapping of acoustic waves with periods between 4 and 6 min can occur in lower atmosphere. The fourth case is generation of gravity waves by ocean tsunami waves that are themselves generated from large earthquakes. These waves occur due to coupling of the atmosphere with ocean surface displacement and are detected in the ionosphere a few hours after the earthquake (Artru et al., 2005;Occhipinti, Lognonné, et al., 2006) as opposed to ∼10 min for waves due to seismic Rayleigh origin.